Bayesian Statistics with PyMC.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "1de1318f",
   "metadata": {},
   "source": [
    "# Automated Inference with PyMC\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "a715c2b5",
   "metadata": {},
   "source": [
    "## Fit a posterior\n",
    "\n",
    "\n",
    "\n",
    "* We will use PyMC to fit the model below to the data set provided.\n",
    "* Check that the sampler is working correctly.\n",
    "* Plot and interpret the posterior distribution.\n",
    "\n",
    "**Given Model:**\n",
    "\n",
    "$$p \\sim \\text{Beta}(\\alpha=2,\\beta=2)$$\n",
    "\n",
    "$$x_i \\sim \\text{Negative-Binomial}(r=3,p) \\quad i=1,\\ldots,20$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "d13b6727",
   "metadata": {},
   "outputs": [],
   "source": [
    "# Import Libraries\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "import scipy.stats as sts\n",
    "import matplotlib.pyplot as plt\n",
    "import arviz as az\n",
    "import random\n",
    "from IPython.display import Image"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "12daa09a",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Upgrading PyMC to version 5. This takes about 50 seconds...\n",
      "We're running PyMC v5.10.3 today.\n"
     ]
    }
   ],
   "source": [
    "# Import PyMC \n",
    "print('Upgrading PyMC to version 5. This takes about 50 seconds...')\n",
    "!pip install --ignore-installed llvmlite > /dev/null 2> /dev/null\n",
    "!pip install --upgrade \"pymc>=5,<6\" numexpr matplotlib numba > /dev/null 2> /dev/null\n",
    "\n",
    "import pymc as pm\n",
    "print(f\"We're running PyMC v{pm.__version__} today.\")\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "6b7a81df",
   "metadata": {},
   "outputs": [],
   "source": [
    "data = [9, 15, 4, 7, 7, 1, 3, 5, 8, 7, 9, 8, 4, 3, 0, 4, 6, 9, 2, 4]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "783611d8",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<IPython.core.display.Image object>"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Create a model matches the way we expect data to be generated in the real world.\n",
    "data = [9, 15, 4, 7, 7, 1, 3, 5, 8, 7, 9, 8, 4, 3, 0, 4, 6, 9, 2, 4]\n",
    "with pm.Model() as model:\n",
    "    p = pm.Beta('p', alpha=2, beta=2)\n",
    "    pm.NegativeBinomial(\n",
    "        'x', n=data, p=p, observed=data)\n",
    "Image(pm.model_to_graphviz(model).render(format='png'))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "a428f37e",
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Auto-assigning NUTS sampler...\n",
      "Initializing NUTS using jitter+adapt_diag...\n",
      "Multiprocess sampling (4 chains in 4 jobs)\n",
      "NUTS: [p]\n"
     ]
    },
    {
     "data": {
      "text/html": [
       "\n",
       "<style>\n",
       "    /* Turns off some styling */\n",
       "    progress {\n",
       "        /* gets rid of default border in Firefox and Opera. */\n",
       "        border: none;\n",
       "        /* Needs to be in here for Safari polyfill so background images work as expected. */\n",
       "        background-size: auto;\n",
       "    }\n",
       "    progress:not([value]), progress:not([value])::-webkit-progress-bar {\n",
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       "\n",
       ".xr-attrs dt,\n",
       ".xr-attrs dd {\n",
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       "\n",
       ".xr-attrs dt {\n",
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       "\n",
       ".xr-attrs dt:hover span {\n",
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       "\n",
       ".xr-attrs dd {\n",
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       ".xr-icon-database,\n",
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       "</style><pre class='xr-text-repr-fallback'>&lt;xarray.Dataset&gt;\n",
       "Dimensions:  (chain: 4, draw: 2000)\n",
       "Coordinates:\n",
       "  * chain    (chain) int64 0 1 2 3\n",
       "  * draw     (draw) int64 0 1 2 3 4 5 6 7 ... 1993 1994 1995 1996 1997 1998 1999\n",
       "Data variables:\n",
       "    p        (chain, draw) float64 0.3749 0.3572 0.3304 ... 0.3762 0.3849 0.3468\n",
       "Attributes:\n",
       "    created_at:                 2024-01-30T22:16:53.116825\n",
       "    arviz_version:              0.17.0\n",
       "    inference_library:          pymc\n",
       "    inference_library_version:  5.10.3\n",
       "    sampling_time:              88.75693082809448\n",
       "    tuning_steps:               1000</pre><div class='xr-wrap' style='display:none'><div class='xr-header'><div class='xr-obj-type'>xarray.Dataset</div></div><ul class='xr-sections'><li class='xr-section-item'><input id='section-24e377f0-63dc-48c4-9067-9443891509b5' class='xr-section-summary-in' type='checkbox' disabled ><label for='section-24e377f0-63dc-48c4-9067-9443891509b5' class='xr-section-summary'  title='Expand/collapse section'>Dimensions:</label><div class='xr-section-inline-details'><ul class='xr-dim-list'><li><span class='xr-has-index'>chain</span>: 4</li><li><span class='xr-has-index'>draw</span>: 2000</li></ul></div><div class='xr-section-details'></div></li><li class='xr-section-item'><input id='section-64a33e2c-1451-46fc-8253-3ef5bf06f8ea' class='xr-section-summary-in' type='checkbox'  checked><label for='section-64a33e2c-1451-46fc-8253-3ef5bf06f8ea' class='xr-section-summary' >Coordinates: <span>(2)</span></label><div class='xr-section-inline-details'></div><div class='xr-section-details'><ul class='xr-var-list'><li class='xr-var-item'><div class='xr-var-name'><span class='xr-has-index'>chain</span></div><div class='xr-var-dims'>(chain)</div><div class='xr-var-dtype'>int64</div><div class='xr-var-preview xr-preview'>0 1 2 3</div><input id='attrs-be25f7b0-0687-4598-b2f3-ecb97e09e809' class='xr-var-attrs-in' type='checkbox' disabled><label for='attrs-be25f7b0-0687-4598-b2f3-ecb97e09e809' title='Show/Hide attributes'><svg class='icon xr-icon-file-text2'><use xlink:href='#icon-file-text2'></use></svg></label><input id='data-61a1af34-b690-4ee4-b20e-a32e2e2588de' class='xr-var-data-in' type='checkbox'><label for='data-61a1af34-b690-4ee4-b20e-a32e2e2588de' title='Show/Hide data repr'><svg class='icon xr-icon-database'><use xlink:href='#icon-database'></use></svg></label><div class='xr-var-attrs'><dl class='xr-attrs'></dl></div><div class='xr-var-data'><pre>array([0, 1, 2, 3])</pre></div></li><li class='xr-var-item'><div class='xr-var-name'><span class='xr-has-index'>draw</span></div><div class='xr-var-dims'>(draw)</div><div class='xr-var-dtype'>int64</div><div class='xr-var-preview xr-preview'>0 1 2 3 4 ... 1996 1997 1998 1999</div><input id='attrs-411814f2-440d-4d6f-9123-727146f0819c' class='xr-var-attrs-in' type='checkbox' disabled><label for='attrs-411814f2-440d-4d6f-9123-727146f0819c' title='Show/Hide attributes'><svg class='icon xr-icon-file-text2'><use xlink:href='#icon-file-text2'></use></svg></label><input id='data-2809eadb-e416-49e4-980b-74cc89d65e2e' class='xr-var-data-in' type='checkbox'><label for='data-2809eadb-e416-49e4-980b-74cc89d65e2e' title='Show/Hide data repr'><svg class='icon xr-icon-database'><use xlink:href='#icon-database'></use></svg></label><div class='xr-var-attrs'><dl class='xr-attrs'></dl></div><div class='xr-var-data'><pre>array([   0,    1,    2, ..., 1997, 1998, 1999])</pre></div></li></ul></div></li><li class='xr-section-item'><input id='section-28c60e3a-519d-4a70-a64b-9bf0bbbd46a2' class='xr-section-summary-in' type='checkbox'  checked><label for='section-28c60e3a-519d-4a70-a64b-9bf0bbbd46a2' class='xr-section-summary' >Data variables: <span>(1)</span></label><div class='xr-section-inline-details'></div><div class='xr-section-details'><ul class='xr-var-list'><li class='xr-var-item'><div class='xr-var-name'><span>p</span></div><div class='xr-var-dims'>(chain, draw)</div><div class='xr-var-dtype'>float64</div><div class='xr-var-preview xr-preview'>0.3749 0.3572 ... 0.3849 0.3468</div><input id='attrs-cd8cc213-4b03-4413-b674-a82983afd934' class='xr-var-attrs-in' type='checkbox' disabled><label for='attrs-cd8cc213-4b03-4413-b674-a82983afd934' title='Show/Hide attributes'><svg class='icon xr-icon-file-text2'><use xlink:href='#icon-file-text2'></use></svg></label><input id='data-f8bfe356-d588-49c7-93a1-fb00794cd029' class='xr-var-data-in' type='checkbox'><label for='data-f8bfe356-d588-49c7-93a1-fb00794cd029' title='Show/Hide data repr'><svg class='icon xr-icon-database'><use xlink:href='#icon-database'></use></svg></label><div class='xr-var-attrs'><dl class='xr-attrs'></dl></div><div class='xr-var-data'><pre>array([[0.37486421, 0.35715878, 0.33041443, ..., 0.30930141, 0.35965615,\n",
       "        0.33709512],\n",
       "       [0.36534704, 0.3847507 , 0.3814223 , ..., 0.31841916, 0.33688262,\n",
       "        0.31876392],\n",
       "       [0.3289434 , 0.36796185, 0.36887751, ..., 0.33054285, 0.369049  ,\n",
       "        0.47069892],\n",
       "       [0.33472317, 0.35115783, 0.35874627, ..., 0.37617499, 0.38493028,\n",
       "        0.34683153]])</pre></div></li></ul></div></li><li class='xr-section-item'><input id='section-28722927-eac6-45ec-afe0-481e14f8c99a' class='xr-section-summary-in' type='checkbox'  ><label for='section-28722927-eac6-45ec-afe0-481e14f8c99a' class='xr-section-summary' >Indexes: <span>(2)</span></label><div class='xr-section-inline-details'></div><div class='xr-section-details'><ul class='xr-var-list'><li class='xr-var-item'><div class='xr-index-name'><div>chain</div></div><div class='xr-index-preview'>PandasIndex</div><div></div><input id='index-9819cc77-d8c7-4a66-968d-0f0fe3802f24' class='xr-index-data-in' type='checkbox'/><label for='index-9819cc77-d8c7-4a66-968d-0f0fe3802f24' title='Show/Hide index repr'><svg class='icon xr-icon-database'><use xlink:href='#icon-database'></use></svg></label><div class='xr-index-data'><pre>PandasIndex(Int64Index([0, 1, 2, 3], dtype=&#x27;int64&#x27;, name=&#x27;chain&#x27;))</pre></div></li><li class='xr-var-item'><div class='xr-index-name'><div>draw</div></div><div class='xr-index-preview'>PandasIndex</div><div></div><input id='index-b3cc51d3-59b4-4faf-b454-f0d7bf7f0423' class='xr-index-data-in' type='checkbox'/><label for='index-b3cc51d3-59b4-4faf-b454-f0d7bf7f0423' title='Show/Hide index repr'><svg class='icon xr-icon-database'><use xlink:href='#icon-database'></use></svg></label><div class='xr-index-data'><pre>PandasIndex(Int64Index([   0,    1,    2,    3,    4,    5,    6,    7,    8,    9,\n",
       "            ...\n",
       "            1990, 1991, 1992, 1993, 1994, 1995, 1996, 1997, 1998, 1999],\n",
       "           dtype=&#x27;int64&#x27;, name=&#x27;draw&#x27;, length=2000))</pre></div></li></ul></div></li><li class='xr-section-item'><input id='section-f1dfef04-e5fc-4245-9904-132b4193aa49' class='xr-section-summary-in' type='checkbox'  checked><label for='section-f1dfef04-e5fc-4245-9904-132b4193aa49' class='xr-section-summary' >Attributes: <span>(6)</span></label><div class='xr-section-inline-details'></div><div class='xr-section-details'><dl class='xr-attrs'><dt><span>created_at :</span></dt><dd>2024-01-30T22:16:53.116825</dd><dt><span>arviz_version :</span></dt><dd>0.17.0</dd><dt><span>inference_library :</span></dt><dd>pymc</dd><dt><span>inference_library_version :</span></dt><dd>5.10.3</dd><dt><span>sampling_time :</span></dt><dd>88.75693082809448</dd><dt><span>tuning_steps :</span></dt><dd>1000</dd></dl></div></li></ul></div></div><br></div>\n",
       "                      </ul>\n",
       "                  </div>\n",
       "            </li>\n",
       "            \n",
       "            <li class = \"xr-section-item\">\n",
       "                  <input id=\"idata_sample_stats4917fa76-08c5-4f4f-a2bd-8b5caf98fcd1\" class=\"xr-section-summary-in\" type=\"checkbox\">\n",
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       "                  <div class=\"xr-section-inline-details\"></div>\n",
       "                  <div class=\"xr-section-details\">\n",
       "                      <ul id=\"xr-dataset-coord-list\" class=\"xr-var-list\">\n",
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       "\n",
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       "  margin-bottom: 4px;\n",
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       "}\n",
       "\n",
       ".xr-header > div,\n",
       ".xr-header > ul {\n",
       "  display: inline;\n",
       "  margin-top: 0;\n",
       "  margin-bottom: 0;\n",
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       "\n",
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       "  margin-left: 2px;\n",
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       "\n",
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       "\n",
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       "\n",
       ".xr-section-summary > span {\n",
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       "\n",
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       "\n",
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       "  font-size: 11px;\n",
       "  width: 15px;\n",
       "  text-align: center;\n",
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       "\n",
       ".xr-section-summary-in:disabled + label:before {\n",
       "  color: var(--xr-disabled-color);\n",
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       "\n",
       ".xr-section-summary-in:checked + label:before {\n",
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       "}\n",
       "\n",
       ".xr-section-summary-in:checked + label > span {\n",
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       "\n",
       ".xr-section-summary,\n",
       ".xr-section-inline-details {\n",
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       "  padding-bottom: 4px;\n",
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       "\n",
       ".xr-section-inline-details {\n",
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       "\n",
       ".xr-section-details {\n",
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       "\n",
       ".xr-section-summary-in:checked ~ .xr-section-details {\n",
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       "\n",
       ".xr-array-wrap {\n",
       "  grid-column: 1 / -1;\n",
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       "  grid-template-columns: 20px auto;\n",
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       "\n",
       ".xr-array-wrap > label {\n",
       "  grid-column: 1;\n",
       "  vertical-align: top;\n",
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       "\n",
       ".xr-preview {\n",
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       "\n",
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       "  grid-column: 2;\n",
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       "\n",
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       "\n",
       ".xr-array-in:checked ~ .xr-array-data,\n",
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       "\n",
       ".xr-dim-list {\n",
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       "\n",
       ".xr-dim-list li {\n",
       "  display: inline-block;\n",
       "  padding: 0;\n",
       "  margin: 0;\n",
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       "\n",
       ".xr-dim-list:before {\n",
       "  content: '(';\n",
       "}\n",
       "\n",
       ".xr-dim-list:after {\n",
       "  content: ')';\n",
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       "\n",
       ".xr-dim-list li:not(:last-child):after {\n",
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       "\n",
       ".xr-has-index {\n",
       "  font-weight: bold;\n",
       "}\n",
       "\n",
       ".xr-var-list,\n",
       ".xr-var-item {\n",
       "  display: contents;\n",
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       "\n",
       ".xr-var-item > div,\n",
       ".xr-var-item label,\n",
       ".xr-var-item > .xr-var-name span {\n",
       "  background-color: var(--xr-background-color-row-even);\n",
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       "\n",
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       "\n",
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       "\n",
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       "\n",
       ".xr-attrs dt,\n",
       ".xr-attrs dd {\n",
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       "\n",
       ".xr-attrs dt {\n",
       "  font-weight: normal;\n",
       "  grid-column: 1;\n",
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       "\n",
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       "\n",
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       "\n",
       ".xr-icon-database,\n",
       ".xr-icon-file-text2,\n",
       ".xr-no-icon {\n",
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       "  stroke-width: 0;\n",
       "  stroke: currentColor;\n",
       "  fill: currentColor;\n",
       "}\n",
       "</style><pre class='xr-text-repr-fallback'>&lt;xarray.Dataset&gt;\n",
       "Dimensions:                (chain: 4, draw: 2000)\n",
       "Coordinates:\n",
       "  * chain                  (chain) int64 0 1 2 3\n",
       "  * draw                   (draw) int64 0 1 2 3 4 5 ... 1995 1996 1997 1998 1999\n",
       "Data variables: (12/17)\n",
       "    smallest_eigval        (chain, draw) float64 nan nan nan nan ... nan nan nan\n",
       "    perf_counter_diff      (chain, draw) float64 0.001402 0.0007148 ... 0.001297\n",
       "    energy                 (chain, draw) float64 54.01 53.89 ... 54.52 53.98\n",
       "    perf_counter_start     (chain, draw) float64 2.512e+04 ... 2.513e+04\n",
       "    tree_depth             (chain, draw) int64 2 1 2 1 2 2 1 2 ... 2 2 2 1 2 2 2\n",
       "    n_steps                (chain, draw) float64 3.0 1.0 3.0 1.0 ... 3.0 3.0 3.0\n",
       "    ...                     ...\n",
       "    energy_error           (chain, draw) float64 0.1465 -0.1279 ... -0.2781\n",
       "    max_energy_error       (chain, draw) float64 0.1465 -0.1279 ... -0.2781\n",
       "    diverging              (chain, draw) bool False False False ... False False\n",
       "    acceptance_rate        (chain, draw) float64 0.9101 1.0 ... 0.8814 1.0\n",
       "    process_time_diff      (chain, draw) float64 0.001402 0.000715 ... 0.001297\n",
       "    step_size_bar          (chain, draw) float64 1.303 1.303 ... 1.224 1.224\n",
       "Attributes:\n",
       "    created_at:                 2024-01-30T22:16:53.189155\n",
       "    arviz_version:              0.17.0\n",
       "    inference_library:          pymc\n",
       "    inference_library_version:  5.10.3\n",
       "    sampling_time:              88.75693082809448\n",
       "    tuning_steps:               1000</pre><div class='xr-wrap' style='display:none'><div class='xr-header'><div class='xr-obj-type'>xarray.Dataset</div></div><ul class='xr-sections'><li class='xr-section-item'><input id='section-f8c62176-684c-4b65-94b1-29565b7c3fb0' class='xr-section-summary-in' type='checkbox' disabled ><label for='section-f8c62176-684c-4b65-94b1-29565b7c3fb0' class='xr-section-summary'  title='Expand/collapse section'>Dimensions:</label><div class='xr-section-inline-details'><ul class='xr-dim-list'><li><span class='xr-has-index'>chain</span>: 4</li><li><span class='xr-has-index'>draw</span>: 2000</li></ul></div><div class='xr-section-details'></div></li><li class='xr-section-item'><input id='section-135d8297-7d28-425f-a892-0d78f9a912f4' class='xr-section-summary-in' type='checkbox'  checked><label for='section-135d8297-7d28-425f-a892-0d78f9a912f4' class='xr-section-summary' >Coordinates: <span>(2)</span></label><div class='xr-section-inline-details'></div><div class='xr-section-details'><ul class='xr-var-list'><li class='xr-var-item'><div class='xr-var-name'><span class='xr-has-index'>chain</span></div><div class='xr-var-dims'>(chain)</div><div class='xr-var-dtype'>int64</div><div class='xr-var-preview xr-preview'>0 1 2 3</div><input id='attrs-52d74424-aeb2-487f-9cbb-b80afd2fd88b' class='xr-var-attrs-in' type='checkbox' disabled><label for='attrs-52d74424-aeb2-487f-9cbb-b80afd2fd88b' title='Show/Hide attributes'><svg class='icon xr-icon-file-text2'><use xlink:href='#icon-file-text2'></use></svg></label><input id='data-16e77886-6c7a-472b-9583-5cac1686f23e' class='xr-var-data-in' type='checkbox'><label for='data-16e77886-6c7a-472b-9583-5cac1686f23e' title='Show/Hide data repr'><svg class='icon xr-icon-database'><use xlink:href='#icon-database'></use></svg></label><div class='xr-var-attrs'><dl class='xr-attrs'></dl></div><div class='xr-var-data'><pre>array([0, 1, 2, 3])</pre></div></li><li class='xr-var-item'><div class='xr-var-name'><span class='xr-has-index'>draw</span></div><div class='xr-var-dims'>(draw)</div><div class='xr-var-dtype'>int64</div><div class='xr-var-preview xr-preview'>0 1 2 3 4 ... 1996 1997 1998 1999</div><input id='attrs-bfa5a83b-0831-412c-a3ea-fb9831488330' class='xr-var-attrs-in' type='checkbox' disabled><label for='attrs-bfa5a83b-0831-412c-a3ea-fb9831488330' title='Show/Hide attributes'><svg class='icon xr-icon-file-text2'><use xlink:href='#icon-file-text2'></use></svg></label><input id='data-c54730ef-7c25-43c1-bd83-15f79703f44d' class='xr-var-data-in' type='checkbox'><label for='data-c54730ef-7c25-43c1-bd83-15f79703f44d' title='Show/Hide data repr'><svg class='icon xr-icon-database'><use xlink:href='#icon-database'></use></svg></label><div class='xr-var-attrs'><dl class='xr-attrs'></dl></div><div class='xr-var-data'><pre>array([   0,    1,    2, ..., 1997, 1998, 1999])</pre></div></li></ul></div></li><li class='xr-section-item'><input id='section-8a5c0c31-3bba-4c35-a90d-4435643e8997' class='xr-section-summary-in' type='checkbox'  ><label for='section-8a5c0c31-3bba-4c35-a90d-4435643e8997' class='xr-section-summary' >Data variables: <span>(17)</span></label><div class='xr-section-inline-details'></div><div class='xr-section-details'><ul class='xr-var-list'><li class='xr-var-item'><div class='xr-var-name'><span>smallest_eigval</span></div><div class='xr-var-dims'>(chain, draw)</div><div class='xr-var-dtype'>float64</div><div class='xr-var-preview xr-preview'>nan nan nan nan ... nan nan nan nan</div><input id='attrs-35469618-b03b-40a7-a4cd-9317ee0ea303' class='xr-var-attrs-in' type='checkbox' disabled><label for='attrs-35469618-b03b-40a7-a4cd-9317ee0ea303' title='Show/Hide attributes'><svg class='icon xr-icon-file-text2'><use xlink:href='#icon-file-text2'></use></svg></label><input id='data-d1fae9a3-42fc-4b8a-8467-a9406b48bd05' class='xr-var-data-in' type='checkbox'><label for='data-d1fae9a3-42fc-4b8a-8467-a9406b48bd05' title='Show/Hide data repr'><svg class='icon xr-icon-database'><use xlink:href='#icon-database'></use></svg></label><div class='xr-var-attrs'><dl class='xr-attrs'></dl></div><div class='xr-var-data'><pre>array([[nan, nan, nan, ..., nan, nan, nan],\n",
       "       [nan, nan, nan, ..., nan, nan, nan],\n",
       "       [nan, nan, nan, ..., nan, nan, nan],\n",
       "       [nan, nan, nan, ..., nan, nan, nan]])</pre></div></li><li class='xr-var-item'><div class='xr-var-name'><span>perf_counter_diff</span></div><div class='xr-var-dims'>(chain, draw)</div><div class='xr-var-dtype'>float64</div><div class='xr-var-preview xr-preview'>0.001402 0.0007148 ... 0.001297</div><input id='attrs-f7da097f-01a6-4051-be0c-0c8c8ce09656' class='xr-var-attrs-in' type='checkbox' disabled><label for='attrs-f7da097f-01a6-4051-be0c-0c8c8ce09656' title='Show/Hide attributes'><svg class='icon xr-icon-file-text2'><use xlink:href='#icon-file-text2'></use></svg></label><input id='data-d8b1114b-b953-4c1a-a5d9-b2ff9f8d36c9' class='xr-var-data-in' type='checkbox'><label for='data-d8b1114b-b953-4c1a-a5d9-b2ff9f8d36c9' title='Show/Hide data repr'><svg class='icon xr-icon-database'><use xlink:href='#icon-database'></use></svg></label><div class='xr-var-attrs'><dl class='xr-attrs'></dl></div><div class='xr-var-data'><pre>array([[0.00140165, 0.00071476, 0.00137504, ..., 0.00072725, 0.00139727,\n",
       "        0.00137088],\n",
       "       [0.00144306, 0.0007108 , 0.00071174, ..., 0.00223449, 0.00075657,\n",
       "        0.00192488],\n",
       "       [0.00118484, 0.00201365, 0.00094736, ..., 0.00070682, 0.00133582,\n",
       "        0.00067959],\n",
       "       [0.00130696, 0.00252963, 0.00126011, ..., 0.00136765, 0.00133505,\n",
       "        0.00129674]])</pre></div></li><li class='xr-var-item'><div class='xr-var-name'><span>energy</span></div><div class='xr-var-dims'>(chain, draw)</div><div class='xr-var-dtype'>float64</div><div class='xr-var-preview xr-preview'>54.01 53.89 53.98 ... 54.52 53.98</div><input id='attrs-50a5bf85-fce9-4416-b922-4a6cf8240725' class='xr-var-attrs-in' type='checkbox' disabled><label for='attrs-50a5bf85-fce9-4416-b922-4a6cf8240725' title='Show/Hide attributes'><svg class='icon xr-icon-file-text2'><use xlink:href='#icon-file-text2'></use></svg></label><input id='data-83e613cf-67e0-42c1-a588-95b8fd2f7f78' class='xr-var-data-in' type='checkbox'><label for='data-83e613cf-67e0-42c1-a588-95b8fd2f7f78' title='Show/Hide data repr'><svg class='icon xr-icon-database'><use xlink:href='#icon-database'></use></svg></label><div class='xr-var-attrs'><dl class='xr-attrs'></dl></div><div class='xr-var-data'><pre>array([[54.0068989 , 53.89460637, 53.97980298, ..., 54.29703405,\n",
       "        55.62813188, 54.28199176],\n",
       "       [53.84452358, 54.31743483, 54.43618287, ..., 54.04484184,\n",
       "        53.89043576, 54.04572071],\n",
       "       [54.10325217, 54.01873988, 53.97125227, ..., 53.90693761,\n",
       "        55.01326877, 59.43925336],\n",
       "       [53.76930213, 54.17127531, 53.75448158, ..., 54.03598518,\n",
       "        54.52272951, 53.9823898 ]])</pre></div></li><li class='xr-var-item'><div class='xr-var-name'><span>perf_counter_start</span></div><div class='xr-var-dims'>(chain, draw)</div><div class='xr-var-dtype'>float64</div><div class='xr-var-preview xr-preview'>2.512e+04 2.512e+04 ... 2.513e+04</div><input id='attrs-562fc365-7e23-43a4-ab33-0cf97dc80019' class='xr-var-attrs-in' type='checkbox' disabled><label for='attrs-562fc365-7e23-43a4-ab33-0cf97dc80019' title='Show/Hide attributes'><svg class='icon xr-icon-file-text2'><use xlink:href='#icon-file-text2'></use></svg></label><input id='data-f2f0d411-48e8-48ee-a2cf-08c22fcfaf2e' class='xr-var-data-in' type='checkbox'><label for='data-f2f0d411-48e8-48ee-a2cf-08c22fcfaf2e' title='Show/Hide data repr'><svg class='icon xr-icon-database'><use xlink:href='#icon-database'></use></svg></label><div class='xr-var-attrs'><dl class='xr-attrs'></dl></div><div class='xr-var-data'><pre>array([[25123.46524574, 25123.46701756, 25123.46808646, ...,\n",
       "        25127.51587733, 25127.51697345, 25127.51873134],\n",
       "       [25123.41586655, 25123.41768173, 25123.41874586, ...,\n",
       "        25127.45625775, 25127.45891191, 25127.46002451],\n",
       "       [25123.46689358, 25123.46856482, 25123.47096378, ...,\n",
       "        25127.75237175, 25127.75341929, 25127.75509948],\n",
       "       [25123.918481  , 25123.92194194, 25123.92514788, ...,\n",
       "        25128.3862723 , 25128.38798645, 25128.3896883 ]])</pre></div></li><li class='xr-var-item'><div class='xr-var-name'><span>tree_depth</span></div><div class='xr-var-dims'>(chain, draw)</div><div class='xr-var-dtype'>int64</div><div class='xr-var-preview xr-preview'>2 1 2 1 2 2 1 2 ... 1 2 2 2 1 2 2 2</div><input id='attrs-cb95464e-de3b-4b8f-aaa0-aab8d202981a' class='xr-var-attrs-in' type='checkbox' disabled><label for='attrs-cb95464e-de3b-4b8f-aaa0-aab8d202981a' title='Show/Hide attributes'><svg class='icon xr-icon-file-text2'><use xlink:href='#icon-file-text2'></use></svg></label><input id='data-7b9edc01-3f1f-45bd-b290-294b1cf9c963' class='xr-var-data-in' type='checkbox'><label for='data-7b9edc01-3f1f-45bd-b290-294b1cf9c963' title='Show/Hide data repr'><svg class='icon xr-icon-database'><use xlink:href='#icon-database'></use></svg></label><div class='xr-var-attrs'><dl class='xr-attrs'></dl></div><div class='xr-var-data'><pre>array([[2, 1, 2, ..., 1, 2, 2],\n",
       "       [2, 1, 1, ..., 2, 1, 2],\n",
       "       [1, 2, 1, ..., 1, 2, 1],\n",
       "       [1, 2, 1, ..., 2, 2, 2]])</pre></div></li><li class='xr-var-item'><div class='xr-var-name'><span>n_steps</span></div><div class='xr-var-dims'>(chain, draw)</div><div class='xr-var-dtype'>float64</div><div class='xr-var-preview xr-preview'>3.0 1.0 3.0 1.0 ... 1.0 3.0 3.0 3.0</div><input id='attrs-9a97f062-eb75-45f1-adf9-86c008adf00c' class='xr-var-attrs-in' type='checkbox' disabled><label for='attrs-9a97f062-eb75-45f1-adf9-86c008adf00c' title='Show/Hide attributes'><svg class='icon xr-icon-file-text2'><use xlink:href='#icon-file-text2'></use></svg></label><input id='data-67faebd1-587e-4a11-bbba-cc2ec791c245' class='xr-var-data-in' type='checkbox'><label for='data-67faebd1-587e-4a11-bbba-cc2ec791c245' title='Show/Hide data repr'><svg class='icon xr-icon-database'><use xlink:href='#icon-database'></use></svg></label><div class='xr-var-attrs'><dl class='xr-attrs'></dl></div><div class='xr-var-data'><pre>array([[3., 1., 3., ..., 1., 3., 3.],\n",
       "       [3., 1., 1., ..., 3., 1., 3.],\n",
       "       [1., 3., 1., ..., 1., 3., 1.],\n",
       "       [1., 3., 1., ..., 3., 3., 3.]])</pre></div></li><li class='xr-var-item'><div class='xr-var-name'><span>index_in_trajectory</span></div><div class='xr-var-dims'>(chain, draw)</div><div class='xr-var-dtype'>int64</div><div class='xr-var-preview xr-preview'>-1 1 2 1 0 2 -1 ... 1 2 0 -2 -3 1</div><input id='attrs-0c85664e-c683-4f6b-8c90-136bcca73b89' class='xr-var-attrs-in' type='checkbox' disabled><label for='attrs-0c85664e-c683-4f6b-8c90-136bcca73b89' title='Show/Hide attributes'><svg class='icon xr-icon-file-text2'><use xlink:href='#icon-file-text2'></use></svg></label><input id='data-e24283ef-bafe-4ed2-8a37-1a68b3529aa9' class='xr-var-data-in' type='checkbox'><label for='data-e24283ef-bafe-4ed2-8a37-1a68b3529aa9' title='Show/Hide data repr'><svg class='icon xr-icon-database'><use xlink:href='#icon-database'></use></svg></label><div class='xr-var-attrs'><dl class='xr-attrs'></dl></div><div class='xr-var-data'><pre>array([[-1,  1,  2, ...,  1, -2,  2],\n",
       "       [-1, -1,  1, ...,  1,  1,  3],\n",
       "       [-1,  2,  1, ..., -1,  2, -1],\n",
       "       [-1,  2,  1, ..., -2, -3,  1]])</pre></div></li><li class='xr-var-item'><div class='xr-var-name'><span>lp</span></div><div class='xr-var-dims'>(chain, draw)</div><div class='xr-var-dtype'>float64</div><div class='xr-var-preview xr-preview'>-54.0 -53.74 ... -54.26 -53.69</div><input id='attrs-d39e380c-468f-4b93-9c44-658f3b50d99d' class='xr-var-attrs-in' type='checkbox' disabled><label for='attrs-d39e380c-468f-4b93-9c44-658f3b50d99d' title='Show/Hide attributes'><svg class='icon xr-icon-file-text2'><use xlink:href='#icon-file-text2'></use></svg></label><input id='data-1084b06b-8288-4f1d-9e3f-3c1d2f130163' class='xr-var-data-in' type='checkbox'><label for='data-1084b06b-8288-4f1d-9e3f-3c1d2f130163' title='Show/Hide data repr'><svg class='icon xr-icon-database'><use xlink:href='#icon-database'></use></svg></label><div class='xr-var-attrs'><dl class='xr-attrs'></dl></div><div class='xr-var-data'><pre>array([[-54.00411045, -53.73620432, -53.79277184, ..., -54.25450909,\n",
       "        -53.75960663, -53.72490375],\n",
       "       [-53.83070777, -54.25527944, -54.16271681, ..., -54.00803534,\n",
       "        -53.72650059, -54.00013917],\n",
       "       [-53.8126584 , -53.87159374, -53.88712614, ..., -53.791121  ,\n",
       "        -53.89010506, -59.35965498],\n",
       "       [-53.74481288, -53.69963993, -53.75052667, ..., -54.03327681,\n",
       "        -54.260503  , -53.69069624]])</pre></div></li><li class='xr-var-item'><div class='xr-var-name'><span>largest_eigval</span></div><div class='xr-var-dims'>(chain, draw)</div><div class='xr-var-dtype'>float64</div><div class='xr-var-preview xr-preview'>nan nan nan nan ... nan nan nan nan</div><input id='attrs-b60d6a26-4ad1-42c3-ab4b-64575dfce49e' class='xr-var-attrs-in' type='checkbox' disabled><label for='attrs-b60d6a26-4ad1-42c3-ab4b-64575dfce49e' title='Show/Hide attributes'><svg class='icon xr-icon-file-text2'><use xlink:href='#icon-file-text2'></use></svg></label><input id='data-59d07868-baff-4a39-b425-9d9687d493b6' class='xr-var-data-in' type='checkbox'><label for='data-59d07868-baff-4a39-b425-9d9687d493b6' title='Show/Hide data repr'><svg class='icon xr-icon-database'><use xlink:href='#icon-database'></use></svg></label><div class='xr-var-attrs'><dl class='xr-attrs'></dl></div><div class='xr-var-data'><pre>array([[nan, nan, nan, ..., nan, nan, nan],\n",
       "       [nan, nan, nan, ..., nan, nan, nan],\n",
       "       [nan, nan, nan, ..., nan, nan, nan],\n",
       "       [nan, nan, nan, ..., nan, nan, nan]])</pre></div></li><li class='xr-var-item'><div class='xr-var-name'><span>reached_max_treedepth</span></div><div class='xr-var-dims'>(chain, draw)</div><div class='xr-var-dtype'>bool</div><div class='xr-var-preview xr-preview'>False False False ... False False</div><input id='attrs-ed508f7f-f41c-4a58-8e1a-f8e229cef0e0' class='xr-var-attrs-in' type='checkbox' disabled><label for='attrs-ed508f7f-f41c-4a58-8e1a-f8e229cef0e0' title='Show/Hide attributes'><svg class='icon xr-icon-file-text2'><use xlink:href='#icon-file-text2'></use></svg></label><input id='data-68a56c2a-2b44-427f-87e4-6ca141f566e9' class='xr-var-data-in' type='checkbox'><label for='data-68a56c2a-2b44-427f-87e4-6ca141f566e9' title='Show/Hide data repr'><svg class='icon xr-icon-database'><use xlink:href='#icon-database'></use></svg></label><div class='xr-var-attrs'><dl class='xr-attrs'></dl></div><div class='xr-var-data'><pre>array([[False, False, False, ..., False, False, False],\n",
       "       [False, False, False, ..., False, False, False],\n",
       "       [False, False, False, ..., False, False, False],\n",
       "       [False, False, False, ..., False, False, False]])</pre></div></li><li class='xr-var-item'><div class='xr-var-name'><span>step_size</span></div><div class='xr-var-dims'>(chain, draw)</div><div class='xr-var-dtype'>float64</div><div class='xr-var-preview xr-preview'>1.841 1.841 1.841 ... 1.261 1.261</div><input id='attrs-08ca03f9-cb12-42ee-b372-614024519a08' class='xr-var-attrs-in' type='checkbox' disabled><label for='attrs-08ca03f9-cb12-42ee-b372-614024519a08' title='Show/Hide attributes'><svg class='icon xr-icon-file-text2'><use xlink:href='#icon-file-text2'></use></svg></label><input id='data-cfebfe5f-1f7d-4f05-bf7b-c3f2d1523e40' class='xr-var-data-in' type='checkbox'><label for='data-cfebfe5f-1f7d-4f05-bf7b-c3f2d1523e40' title='Show/Hide data repr'><svg class='icon xr-icon-database'><use xlink:href='#icon-database'></use></svg></label><div class='xr-var-attrs'><dl class='xr-attrs'></dl></div><div class='xr-var-data'><pre>array([[1.84120542, 1.84120542, 1.84120542, ..., 1.84120542, 1.84120542,\n",
       "        1.84120542],\n",
       "       [1.91724964, 1.91724964, 1.91724964, ..., 1.91724964, 1.91724964,\n",
       "        1.91724964],\n",
       "       [1.57408293, 1.57408293, 1.57408293, ..., 1.57408293, 1.57408293,\n",
       "        1.57408293],\n",
       "       [1.26059643, 1.26059643, 1.26059643, ..., 1.26059643, 1.26059643,\n",
       "        1.26059643]])</pre></div></li><li class='xr-var-item'><div class='xr-var-name'><span>energy_error</span></div><div class='xr-var-dims'>(chain, draw)</div><div class='xr-var-dtype'>float64</div><div class='xr-var-preview xr-preview'>0.1465 -0.1279 ... 0.113 -0.2781</div><input id='attrs-8ff0a26d-35fc-49fd-85aa-1502d064bdca' class='xr-var-attrs-in' type='checkbox' disabled><label for='attrs-8ff0a26d-35fc-49fd-85aa-1502d064bdca' title='Show/Hide attributes'><svg class='icon xr-icon-file-text2'><use xlink:href='#icon-file-text2'></use></svg></label><input id='data-585cd666-b749-46b3-9f7d-03ead3bf938e' class='xr-var-data-in' type='checkbox'><label for='data-585cd666-b749-46b3-9f7d-03ead3bf938e' title='Show/Hide data repr'><svg class='icon xr-icon-database'><use xlink:href='#icon-database'></use></svg></label><div class='xr-var-attrs'><dl class='xr-attrs'></dl></div><div class='xr-var-data'><pre>array([[ 1.46547194e-01, -1.27867711e-01,  3.19373698e-02, ...,\n",
       "         1.97920754e-01, -3.27594511e-01, -3.52069235e-03],\n",
       "       [ 5.10622480e-02,  2.05239688e-01, -4.51787959e-02, ...,\n",
       "         1.00678400e-01, -1.28432492e-01,  1.25734277e-01],\n",
       "       [-1.98431301e-01,  2.14503574e-02,  7.32342135e-03, ...,\n",
       "        -6.12056489e-02,  2.75772272e-03,  2.66720299e+00],\n",
       "       [ 1.18706780e-03, -3.08784352e-02,  2.46930218e-02, ...,\n",
       "         5.67079134e-03,  1.13029064e-01, -2.78119010e-01]])</pre></div></li><li class='xr-var-item'><div class='xr-var-name'><span>max_energy_error</span></div><div class='xr-var-dims'>(chain, draw)</div><div class='xr-var-dtype'>float64</div><div class='xr-var-preview xr-preview'>0.1465 -0.1279 ... 0.1816 -0.2781</div><input id='attrs-2ed476af-3a40-49dc-8593-e738c695ffc9' class='xr-var-attrs-in' type='checkbox' disabled><label for='attrs-2ed476af-3a40-49dc-8593-e738c695ffc9' title='Show/Hide attributes'><svg class='icon xr-icon-file-text2'><use xlink:href='#icon-file-text2'></use></svg></label><input id='data-43fbd0aa-71bb-471e-b7a5-8019230bcf7b' class='xr-var-data-in' type='checkbox'><label for='data-43fbd0aa-71bb-471e-b7a5-8019230bcf7b' title='Show/Hide data repr'><svg class='icon xr-icon-database'><use xlink:href='#icon-database'></use></svg></label><div class='xr-var-attrs'><dl class='xr-attrs'></dl></div><div class='xr-var-data'><pre>array([[ 1.46547194e-01, -1.27867711e-01,  1.54405905e-01, ...,\n",
       "         1.97920754e-01,  1.14401947e+00,  4.65622762e-01],\n",
       "       [ 5.10622480e-02,  2.05239688e-01, -4.51787959e-02, ...,\n",
       "         1.00678400e-01, -1.28432492e-01,  1.46223339e-01],\n",
       "       [-1.98431301e-01,  8.01930998e-02,  7.32342135e-03, ...,\n",
       "        -6.12056489e-02,  9.73831008e-01,  2.66720299e+00],\n",
       "       [ 1.18706780e-03,  3.94317828e-01,  2.46930218e-02, ...,\n",
       "        -1.60676508e-01,  1.81582633e-01, -2.78119010e-01]])</pre></div></li><li class='xr-var-item'><div class='xr-var-name'><span>diverging</span></div><div class='xr-var-dims'>(chain, draw)</div><div class='xr-var-dtype'>bool</div><div class='xr-var-preview xr-preview'>False False False ... False False</div><input id='attrs-519e4476-1861-4507-82c1-75e71df6fc47' class='xr-var-attrs-in' type='checkbox' disabled><label for='attrs-519e4476-1861-4507-82c1-75e71df6fc47' title='Show/Hide attributes'><svg class='icon xr-icon-file-text2'><use xlink:href='#icon-file-text2'></use></svg></label><input id='data-cce9aa3b-4a03-4894-8a2d-faff37c4a859' class='xr-var-data-in' type='checkbox'><label for='data-cce9aa3b-4a03-4894-8a2d-faff37c4a859' title='Show/Hide data repr'><svg class='icon xr-icon-database'><use xlink:href='#icon-database'></use></svg></label><div class='xr-var-attrs'><dl class='xr-attrs'></dl></div><div class='xr-var-data'><pre>array([[False, False, False, ..., False, False, False],\n",
       "       [False, False, False, ..., False, False, False],\n",
       "       [False, False, False, ..., False, False, False],\n",
       "       [False, False, False, ..., False, False, False]])</pre></div></li><li class='xr-var-item'><div class='xr-var-name'><span>acceptance_rate</span></div><div class='xr-var-dims'>(chain, draw)</div><div class='xr-var-dtype'>float64</div><div class='xr-var-preview xr-preview'>0.9101 1.0 0.9005 ... 0.8814 1.0</div><input id='attrs-b54f423d-0a4f-46cc-80e1-5061e201bc4a' class='xr-var-attrs-in' type='checkbox' disabled><label for='attrs-b54f423d-0a4f-46cc-80e1-5061e201bc4a' title='Show/Hide attributes'><svg class='icon xr-icon-file-text2'><use xlink:href='#icon-file-text2'></use></svg></label><input id='data-0ce7b6cb-7120-4a27-bfd7-822d8db00b83' class='xr-var-data-in' type='checkbox'><label for='data-0ce7b6cb-7120-4a27-bfd7-822d8db00b83' title='Show/Hide data repr'><svg class='icon xr-icon-database'><use xlink:href='#icon-database'></use></svg></label><div class='xr-var-attrs'><dl class='xr-attrs'></dl></div><div class='xr-var-data'><pre>array([[0.91012693, 1.        , 0.90053208, ..., 0.82043487, 0.55014174,\n",
       "        0.76530075],\n",
       "       [0.96949641, 0.81445208, 1.        , ..., 0.94218131, 1.        ,\n",
       "        0.91285236],\n",
       "       [1.        , 0.95034467, 0.99270333, ..., 1.        , 0.60791962,\n",
       "        0.0694462 ],\n",
       "       [0.99881364, 0.78570629, 0.97560936, ..., 0.99811509, 0.88138147,\n",
       "        1.        ]])</pre></div></li><li class='xr-var-item'><div class='xr-var-name'><span>process_time_diff</span></div><div class='xr-var-dims'>(chain, draw)</div><div class='xr-var-dtype'>float64</div><div class='xr-var-preview xr-preview'>0.001402 0.000715 ... 0.001297</div><input id='attrs-23d650e3-94c7-4b52-b735-f7ce3d04cc3a' class='xr-var-attrs-in' type='checkbox' disabled><label for='attrs-23d650e3-94c7-4b52-b735-f7ce3d04cc3a' title='Show/Hide attributes'><svg class='icon xr-icon-file-text2'><use xlink:href='#icon-file-text2'></use></svg></label><input id='data-e6c6249a-bbf9-4257-9fcd-e8c3663e8c75' class='xr-var-data-in' type='checkbox'><label for='data-e6c6249a-bbf9-4257-9fcd-e8c3663e8c75' title='Show/Hide data repr'><svg class='icon xr-icon-database'><use xlink:href='#icon-database'></use></svg></label><div class='xr-var-attrs'><dl class='xr-attrs'></dl></div><div class='xr-var-data'><pre>array([[0.001402, 0.000715, 0.001375, ..., 0.000728, 0.001399, 0.001372],\n",
       "       [0.001443, 0.000711, 0.000713, ..., 0.002234, 0.000757, 0.001926],\n",
       "       [0.001185, 0.002013, 0.000936, ..., 0.000707, 0.001336, 0.000679],\n",
       "       [0.001286, 0.002495, 0.001249, ..., 0.001368, 0.001335, 0.001297]])</pre></div></li><li class='xr-var-item'><div class='xr-var-name'><span>step_size_bar</span></div><div class='xr-var-dims'>(chain, draw)</div><div class='xr-var-dtype'>float64</div><div class='xr-var-preview xr-preview'>1.303 1.303 1.303 ... 1.224 1.224</div><input id='attrs-2aa542f5-a396-4348-9312-77fdcf7c87f0' class='xr-var-attrs-in' type='checkbox' disabled><label for='attrs-2aa542f5-a396-4348-9312-77fdcf7c87f0' title='Show/Hide attributes'><svg class='icon xr-icon-file-text2'><use xlink:href='#icon-file-text2'></use></svg></label><input id='data-088607ca-a6af-4282-8ffd-ad5683d0eeb8' class='xr-var-data-in' type='checkbox'><label for='data-088607ca-a6af-4282-8ffd-ad5683d0eeb8' title='Show/Hide data repr'><svg class='icon xr-icon-database'><use xlink:href='#icon-database'></use></svg></label><div class='xr-var-attrs'><dl class='xr-attrs'></dl></div><div class='xr-var-data'><pre>array([[1.30292749, 1.30292749, 1.30292749, ..., 1.30292749, 1.30292749,\n",
       "        1.30292749],\n",
       "       [1.58280698, 1.58280698, 1.58280698, ..., 1.58280698, 1.58280698,\n",
       "        1.58280698],\n",
       "       [1.29443062, 1.29443062, 1.29443062, ..., 1.29443062, 1.29443062,\n",
       "        1.29443062],\n",
       "       [1.2240227 , 1.2240227 , 1.2240227 , ..., 1.2240227 , 1.2240227 ,\n",
       "        1.2240227 ]])</pre></div></li></ul></div></li><li class='xr-section-item'><input id='section-ac8629eb-8a5c-4877-8eec-0020d845ab7a' class='xr-section-summary-in' type='checkbox'  ><label for='section-ac8629eb-8a5c-4877-8eec-0020d845ab7a' class='xr-section-summary' >Indexes: <span>(2)</span></label><div class='xr-section-inline-details'></div><div class='xr-section-details'><ul class='xr-var-list'><li class='xr-var-item'><div class='xr-index-name'><div>chain</div></div><div class='xr-index-preview'>PandasIndex</div><div></div><input id='index-3d6751dd-1400-4a60-81df-5fc0a74cc070' class='xr-index-data-in' type='checkbox'/><label for='index-3d6751dd-1400-4a60-81df-5fc0a74cc070' title='Show/Hide index repr'><svg class='icon xr-icon-database'><use xlink:href='#icon-database'></use></svg></label><div class='xr-index-data'><pre>PandasIndex(Int64Index([0, 1, 2, 3], dtype=&#x27;int64&#x27;, name=&#x27;chain&#x27;))</pre></div></li><li class='xr-var-item'><div class='xr-index-name'><div>draw</div></div><div class='xr-index-preview'>PandasIndex</div><div></div><input id='index-cad57cf7-f208-4b3c-8e7c-656ba10d1037' class='xr-index-data-in' type='checkbox'/><label for='index-cad57cf7-f208-4b3c-8e7c-656ba10d1037' title='Show/Hide index repr'><svg class='icon xr-icon-database'><use xlink:href='#icon-database'></use></svg></label><div class='xr-index-data'><pre>PandasIndex(Int64Index([   0,    1,    2,    3,    4,    5,    6,    7,    8,    9,\n",
       "            ...\n",
       "            1990, 1991, 1992, 1993, 1994, 1995, 1996, 1997, 1998, 1999],\n",
       "           dtype=&#x27;int64&#x27;, name=&#x27;draw&#x27;, length=2000))</pre></div></li></ul></div></li><li class='xr-section-item'><input id='section-61116774-b3be-4dc6-a8cd-2aae377ced78' class='xr-section-summary-in' type='checkbox'  checked><label for='section-61116774-b3be-4dc6-a8cd-2aae377ced78' class='xr-section-summary' >Attributes: <span>(6)</span></label><div class='xr-section-inline-details'></div><div class='xr-section-details'><dl class='xr-attrs'><dt><span>created_at :</span></dt><dd>2024-01-30T22:16:53.189155</dd><dt><span>arviz_version :</span></dt><dd>0.17.0</dd><dt><span>inference_library :</span></dt><dd>pymc</dd><dt><span>inference_library_version :</span></dt><dd>5.10.3</dd><dt><span>sampling_time :</span></dt><dd>88.75693082809448</dd><dt><span>tuning_steps :</span></dt><dd>1000</dd></dl></div></li></ul></div></div><br></div>\n",
       "                      </ul>\n",
       "                  </div>\n",
       "            </li>\n",
       "            \n",
       "            <li class = \"xr-section-item\">\n",
       "                  <input id=\"idata_observed_dataf6b8ebbd-491a-4e18-839b-8f69c5dbb142\" class=\"xr-section-summary-in\" type=\"checkbox\">\n",
       "                  <label for=\"idata_observed_dataf6b8ebbd-491a-4e18-839b-8f69c5dbb142\" class = \"xr-section-summary\">observed_data</label>\n",
       "                  <div class=\"xr-section-inline-details\"></div>\n",
       "                  <div class=\"xr-section-details\">\n",
       "                      <ul id=\"xr-dataset-coord-list\" class=\"xr-var-list\">\n",
       "                          <div style=\"padding-left:2rem;\"><div><svg style=\"position: absolute; width: 0; height: 0; overflow: hidden\">\n",
       "<defs>\n",
       "<symbol id=\"icon-database\" viewBox=\"0 0 32 32\">\n",
       "<path d=\"M16 0c-8.837 0-16 2.239-16 5v4c0 2.761 7.163 5 16 5s16-2.239 16-5v-4c0-2.761-7.163-5-16-5z\"></path>\n",
       "<path d=\"M16 17c-8.837 0-16-2.239-16-5v6c0 2.761 7.163 5 16 5s16-2.239 16-5v-6c0 2.761-7.163 5-16 5z\"></path>\n",
       "<path d=\"M16 26c-8.837 0-16-2.239-16-5v6c0 2.761 7.163 5 16 5s16-2.239 16-5v-6c0 2.761-7.163 5-16 5z\"></path>\n",
       "</symbol>\n",
       "<symbol id=\"icon-file-text2\" viewBox=\"0 0 32 32\">\n",
       "<path d=\"M28.681 7.159c-0.694-0.947-1.662-2.053-2.724-3.116s-2.169-2.030-3.116-2.724c-1.612-1.182-2.393-1.319-2.841-1.319h-15.5c-1.378 0-2.5 1.121-2.5 2.5v27c0 1.378 1.122 2.5 2.5 2.5h23c1.378 0 2.5-1.122 2.5-2.5v-19.5c0-0.448-0.137-1.23-1.319-2.841zM24.543 5.457c0.959 0.959 1.712 1.825 2.268 2.543h-4.811v-4.811c0.718 0.556 1.584 1.309 2.543 2.268zM28 29.5c0 0.271-0.229 0.5-0.5 0.5h-23c-0.271 0-0.5-0.229-0.5-0.5v-27c0-0.271 0.229-0.5 0.5-0.5 0 0 15.499-0 15.5 0v7c0 0.552 0.448 1 1 1h7v19.5z\"></path>\n",
       "<path d=\"M23 26h-14c-0.552 0-1-0.448-1-1s0.448-1 1-1h14c0.552 0 1 0.448 1 1s-0.448 1-1 1z\"></path>\n",
       "<path d=\"M23 22h-14c-0.552 0-1-0.448-1-1s0.448-1 1-1h14c0.552 0 1 0.448 1 1s-0.448 1-1 1z\"></path>\n",
       "<path d=\"M23 18h-14c-0.552 0-1-0.448-1-1s0.448-1 1-1h14c0.552 0 1 0.448 1 1s-0.448 1-1 1z\"></path>\n",
       "</symbol>\n",
       "</defs>\n",
       "</svg>\n",
       "<style>/* CSS stylesheet for displaying xarray objects in jupyterlab.\n",
       " *\n",
       " */\n",
       "\n",
       ":root {\n",
       "  --xr-font-color0: var(--jp-content-font-color0, rgba(0, 0, 0, 1));\n",
       "  --xr-font-color2: var(--jp-content-font-color2, rgba(0, 0, 0, 0.54));\n",
       "  --xr-font-color3: var(--jp-content-font-color3, rgba(0, 0, 0, 0.38));\n",
       "  --xr-border-color: var(--jp-border-color2, #e0e0e0);\n",
       "  --xr-disabled-color: var(--jp-layout-color3, #bdbdbd);\n",
       "  --xr-background-color: var(--jp-layout-color0, white);\n",
       "  --xr-background-color-row-even: var(--jp-layout-color1, white);\n",
       "  --xr-background-color-row-odd: var(--jp-layout-color2, #eeeeee);\n",
       "}\n",
       "\n",
       "html[theme=dark],\n",
       "body[data-theme=dark],\n",
       "body.vscode-dark {\n",
       "  --xr-font-color0: rgba(255, 255, 255, 1);\n",
       "  --xr-font-color2: rgba(255, 255, 255, 0.54);\n",
       "  --xr-font-color3: rgba(255, 255, 255, 0.38);\n",
       "  --xr-border-color: #1F1F1F;\n",
       "  --xr-disabled-color: #515151;\n",
       "  --xr-background-color: #111111;\n",
       "  --xr-background-color-row-even: #111111;\n",
       "  --xr-background-color-row-odd: #313131;\n",
       "}\n",
       "\n",
       ".xr-wrap {\n",
       "  display: block !important;\n",
       "  min-width: 300px;\n",
       "  max-width: 700px;\n",
       "}\n",
       "\n",
       ".xr-text-repr-fallback {\n",
       "  /* fallback to plain text repr when CSS is not injected (untrusted notebook) */\n",
       "  display: none;\n",
       "}\n",
       "\n",
       ".xr-header {\n",
       "  padding-top: 6px;\n",
       "  padding-bottom: 6px;\n",
       "  margin-bottom: 4px;\n",
       "  border-bottom: solid 1px var(--xr-border-color);\n",
       "}\n",
       "\n",
       ".xr-header > div,\n",
       ".xr-header > ul {\n",
       "  display: inline;\n",
       "  margin-top: 0;\n",
       "  margin-bottom: 0;\n",
       "}\n",
       "\n",
       ".xr-obj-type,\n",
       ".xr-array-name {\n",
       "  margin-left: 2px;\n",
       "  margin-right: 10px;\n",
       "}\n",
       "\n",
       ".xr-obj-type {\n",
       "  color: var(--xr-font-color2);\n",
       "}\n",
       "\n",
       ".xr-sections {\n",
       "  padding-left: 0 !important;\n",
       "  display: grid;\n",
       "  grid-template-columns: 150px auto auto 1fr 20px 20px;\n",
       "}\n",
       "\n",
       ".xr-section-item {\n",
       "  display: contents;\n",
       "}\n",
       "\n",
       ".xr-section-item input {\n",
       "  display: none;\n",
       "}\n",
       "\n",
       ".xr-section-item input + label {\n",
       "  color: var(--xr-disabled-color);\n",
       "}\n",
       "\n",
       ".xr-section-item input:enabled + label {\n",
       "  cursor: pointer;\n",
       "  color: var(--xr-font-color2);\n",
       "}\n",
       "\n",
       ".xr-section-item input:enabled + label:hover {\n",
       "  color: var(--xr-font-color0);\n",
       "}\n",
       "\n",
       ".xr-section-summary {\n",
       "  grid-column: 1;\n",
       "  color: var(--xr-font-color2);\n",
       "  font-weight: 500;\n",
       "}\n",
       "\n",
       ".xr-section-summary > span {\n",
       "  display: inline-block;\n",
       "  padding-left: 0.5em;\n",
       "}\n",
       "\n",
       ".xr-section-summary-in:disabled + label {\n",
       "  color: var(--xr-font-color2);\n",
       "}\n",
       "\n",
       ".xr-section-summary-in + label:before {\n",
       "  display: inline-block;\n",
       "  content: '►';\n",
       "  font-size: 11px;\n",
       "  width: 15px;\n",
       "  text-align: center;\n",
       "}\n",
       "\n",
       ".xr-section-summary-in:disabled + label:before {\n",
       "  color: var(--xr-disabled-color);\n",
       "}\n",
       "\n",
       ".xr-section-summary-in:checked + label:before {\n",
       "  content: '▼';\n",
       "}\n",
       "\n",
       ".xr-section-summary-in:checked + label > span {\n",
       "  display: none;\n",
       "}\n",
       "\n",
       ".xr-section-summary,\n",
       ".xr-section-inline-details {\n",
       "  padding-top: 4px;\n",
       "  padding-bottom: 4px;\n",
       "}\n",
       "\n",
       ".xr-section-inline-details {\n",
       "  grid-column: 2 / -1;\n",
       "}\n",
       "\n",
       ".xr-section-details {\n",
       "  display: none;\n",
       "  grid-column: 1 / -1;\n",
       "  margin-bottom: 5px;\n",
       "}\n",
       "\n",
       ".xr-section-summary-in:checked ~ .xr-section-details {\n",
       "  display: contents;\n",
       "}\n",
       "\n",
       ".xr-array-wrap {\n",
       "  grid-column: 1 / -1;\n",
       "  display: grid;\n",
       "  grid-template-columns: 20px auto;\n",
       "}\n",
       "\n",
       ".xr-array-wrap > label {\n",
       "  grid-column: 1;\n",
       "  vertical-align: top;\n",
       "}\n",
       "\n",
       ".xr-preview {\n",
       "  color: var(--xr-font-color3);\n",
       "}\n",
       "\n",
       ".xr-array-preview,\n",
       ".xr-array-data {\n",
       "  padding: 0 5px !important;\n",
       "  grid-column: 2;\n",
       "}\n",
       "\n",
       ".xr-array-data,\n",
       ".xr-array-in:checked ~ .xr-array-preview {\n",
       "  display: none;\n",
       "}\n",
       "\n",
       ".xr-array-in:checked ~ .xr-array-data,\n",
       ".xr-array-preview {\n",
       "  display: inline-block;\n",
       "}\n",
       "\n",
       ".xr-dim-list {\n",
       "  display: inline-block !important;\n",
       "  list-style: none;\n",
       "  padding: 0 !important;\n",
       "  margin: 0;\n",
       "}\n",
       "\n",
       ".xr-dim-list li {\n",
       "  display: inline-block;\n",
       "  padding: 0;\n",
       "  margin: 0;\n",
       "}\n",
       "\n",
       ".xr-dim-list:before {\n",
       "  content: '(';\n",
       "}\n",
       "\n",
       ".xr-dim-list:after {\n",
       "  content: ')';\n",
       "}\n",
       "\n",
       ".xr-dim-list li:not(:last-child):after {\n",
       "  content: ',';\n",
       "  padding-right: 5px;\n",
       "}\n",
       "\n",
       ".xr-has-index {\n",
       "  font-weight: bold;\n",
       "}\n",
       "\n",
       ".xr-var-list,\n",
       ".xr-var-item {\n",
       "  display: contents;\n",
       "}\n",
       "\n",
       ".xr-var-item > div,\n",
       ".xr-var-item label,\n",
       ".xr-var-item > .xr-var-name span {\n",
       "  background-color: var(--xr-background-color-row-even);\n",
       "  margin-bottom: 0;\n",
       "}\n",
       "\n",
       ".xr-var-item > .xr-var-name:hover span {\n",
       "  padding-right: 5px;\n",
       "}\n",
       "\n",
       ".xr-var-list > li:nth-child(odd) > div,\n",
       ".xr-var-list > li:nth-child(odd) > label,\n",
       ".xr-var-list > li:nth-child(odd) > .xr-var-name span {\n",
       "  background-color: var(--xr-background-color-row-odd);\n",
       "}\n",
       "\n",
       ".xr-var-name {\n",
       "  grid-column: 1;\n",
       "}\n",
       "\n",
       ".xr-var-dims {\n",
       "  grid-column: 2;\n",
       "}\n",
       "\n",
       ".xr-var-dtype {\n",
       "  grid-column: 3;\n",
       "  text-align: right;\n",
       "  color: var(--xr-font-color2);\n",
       "}\n",
       "\n",
       ".xr-var-preview {\n",
       "  grid-column: 4;\n",
       "}\n",
       "\n",
       ".xr-index-preview {\n",
       "  grid-column: 2 / 5;\n",
       "  color: var(--xr-font-color2);\n",
       "}\n",
       "\n",
       ".xr-var-name,\n",
       ".xr-var-dims,\n",
       ".xr-var-dtype,\n",
       ".xr-preview,\n",
       ".xr-attrs dt {\n",
       "  white-space: nowrap;\n",
       "  overflow: hidden;\n",
       "  text-overflow: ellipsis;\n",
       "  padding-right: 10px;\n",
       "}\n",
       "\n",
       ".xr-var-name:hover,\n",
       ".xr-var-dims:hover,\n",
       ".xr-var-dtype:hover,\n",
       ".xr-attrs dt:hover {\n",
       "  overflow: visible;\n",
       "  width: auto;\n",
       "  z-index: 1;\n",
       "}\n",
       "\n",
       ".xr-var-attrs,\n",
       ".xr-var-data,\n",
       ".xr-index-data {\n",
       "  display: none;\n",
       "  background-color: var(--xr-background-color) !important;\n",
       "  padding-bottom: 5px !important;\n",
       "}\n",
       "\n",
       ".xr-var-attrs-in:checked ~ .xr-var-attrs,\n",
       ".xr-var-data-in:checked ~ .xr-var-data,\n",
       ".xr-index-data-in:checked ~ .xr-index-data {\n",
       "  display: block;\n",
       "}\n",
       "\n",
       ".xr-var-data > table {\n",
       "  float: right;\n",
       "}\n",
       "\n",
       ".xr-var-name span,\n",
       ".xr-var-data,\n",
       ".xr-index-name div,\n",
       ".xr-index-data,\n",
       ".xr-attrs {\n",
       "  padding-left: 25px !important;\n",
       "}\n",
       "\n",
       ".xr-attrs,\n",
       ".xr-var-attrs,\n",
       ".xr-var-data,\n",
       ".xr-index-data {\n",
       "  grid-column: 1 / -1;\n",
       "}\n",
       "\n",
       "dl.xr-attrs {\n",
       "  padding: 0;\n",
       "  margin: 0;\n",
       "  display: grid;\n",
       "  grid-template-columns: 125px auto;\n",
       "}\n",
       "\n",
       ".xr-attrs dt,\n",
       ".xr-attrs dd {\n",
       "  padding: 0;\n",
       "  margin: 0;\n",
       "  float: left;\n",
       "  padding-right: 10px;\n",
       "  width: auto;\n",
       "}\n",
       "\n",
       ".xr-attrs dt {\n",
       "  font-weight: normal;\n",
       "  grid-column: 1;\n",
       "}\n",
       "\n",
       ".xr-attrs dt:hover span {\n",
       "  display: inline-block;\n",
       "  background: var(--xr-background-color);\n",
       "  padding-right: 10px;\n",
       "}\n",
       "\n",
       ".xr-attrs dd {\n",
       "  grid-column: 2;\n",
       "  white-space: pre-wrap;\n",
       "  word-break: break-all;\n",
       "}\n",
       "\n",
       ".xr-icon-database,\n",
       ".xr-icon-file-text2,\n",
       ".xr-no-icon {\n",
       "  display: inline-block;\n",
       "  vertical-align: middle;\n",
       "  width: 1em;\n",
       "  height: 1.5em !important;\n",
       "  stroke-width: 0;\n",
       "  stroke: currentColor;\n",
       "  fill: currentColor;\n",
       "}\n",
       "</style><pre class='xr-text-repr-fallback'>&lt;xarray.Dataset&gt;\n",
       "Dimensions:  (x_dim_0: 20)\n",
       "Coordinates:\n",
       "  * x_dim_0  (x_dim_0) int64 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19\n",
       "Data variables:\n",
       "    x        (x_dim_0) int64 9 15 4 7 7 1 3 5 8 7 9 8 4 3 0 4 6 9 2 4\n",
       "Attributes:\n",
       "    created_at:                 2024-01-30T22:16:53.206718\n",
       "    arviz_version:              0.17.0\n",
       "    inference_library:          pymc\n",
       "    inference_library_version:  5.10.3</pre><div class='xr-wrap' style='display:none'><div class='xr-header'><div class='xr-obj-type'>xarray.Dataset</div></div><ul class='xr-sections'><li class='xr-section-item'><input id='section-46e7ce87-9dff-4121-972d-7b138a019520' class='xr-section-summary-in' type='checkbox' disabled ><label for='section-46e7ce87-9dff-4121-972d-7b138a019520' class='xr-section-summary'  title='Expand/collapse section'>Dimensions:</label><div class='xr-section-inline-details'><ul class='xr-dim-list'><li><span class='xr-has-index'>x_dim_0</span>: 20</li></ul></div><div class='xr-section-details'></div></li><li class='xr-section-item'><input id='section-85969286-c2d7-41f4-96db-c87910be1a09' class='xr-section-summary-in' type='checkbox'  checked><label for='section-85969286-c2d7-41f4-96db-c87910be1a09' class='xr-section-summary' >Coordinates: <span>(1)</span></label><div class='xr-section-inline-details'></div><div class='xr-section-details'><ul class='xr-var-list'><li class='xr-var-item'><div class='xr-var-name'><span class='xr-has-index'>x_dim_0</span></div><div class='xr-var-dims'>(x_dim_0)</div><div class='xr-var-dtype'>int64</div><div class='xr-var-preview xr-preview'>0 1 2 3 4 5 6 ... 14 15 16 17 18 19</div><input id='attrs-2d56e850-a4fc-4b96-adb4-2e5ce7b78f26' class='xr-var-attrs-in' type='checkbox' disabled><label for='attrs-2d56e850-a4fc-4b96-adb4-2e5ce7b78f26' title='Show/Hide attributes'><svg class='icon xr-icon-file-text2'><use xlink:href='#icon-file-text2'></use></svg></label><input id='data-cdfbce17-2c9f-453e-ae59-af108e9ace00' class='xr-var-data-in' type='checkbox'><label for='data-cdfbce17-2c9f-453e-ae59-af108e9ace00' title='Show/Hide data repr'><svg class='icon xr-icon-database'><use xlink:href='#icon-database'></use></svg></label><div class='xr-var-attrs'><dl class='xr-attrs'></dl></div><div class='xr-var-data'><pre>array([ 0,  1,  2,  3,  4,  5,  6,  7,  8,  9, 10, 11, 12, 13, 14, 15, 16, 17,\n",
       "       18, 19])</pre></div></li></ul></div></li><li class='xr-section-item'><input id='section-3290948b-22f7-480e-9df7-fe6f0c77b9e6' class='xr-section-summary-in' type='checkbox'  checked><label for='section-3290948b-22f7-480e-9df7-fe6f0c77b9e6' class='xr-section-summary' >Data variables: <span>(1)</span></label><div class='xr-section-inline-details'></div><div class='xr-section-details'><ul class='xr-var-list'><li class='xr-var-item'><div class='xr-var-name'><span>x</span></div><div class='xr-var-dims'>(x_dim_0)</div><div class='xr-var-dtype'>int64</div><div class='xr-var-preview xr-preview'>9 15 4 7 7 1 3 5 ... 3 0 4 6 9 2 4</div><input id='attrs-1fc691b9-a3a2-446a-83c3-5d10b93462e5' class='xr-var-attrs-in' type='checkbox' disabled><label for='attrs-1fc691b9-a3a2-446a-83c3-5d10b93462e5' title='Show/Hide attributes'><svg class='icon xr-icon-file-text2'><use xlink:href='#icon-file-text2'></use></svg></label><input id='data-48f60d83-5858-4f7f-8e57-775d3c0aa53c' class='xr-var-data-in' type='checkbox'><label for='data-48f60d83-5858-4f7f-8e57-775d3c0aa53c' title='Show/Hide data repr'><svg class='icon xr-icon-database'><use xlink:href='#icon-database'></use></svg></label><div class='xr-var-attrs'><dl class='xr-attrs'></dl></div><div class='xr-var-data'><pre>array([ 9, 15,  4,  7,  7,  1,  3,  5,  8,  7,  9,  8,  4,  3,  0,  4,  6,\n",
       "        9,  2,  4])</pre></div></li></ul></div></li><li class='xr-section-item'><input id='section-78246ded-ca77-46ee-bf43-2bd5df2233f7' class='xr-section-summary-in' type='checkbox'  ><label for='section-78246ded-ca77-46ee-bf43-2bd5df2233f7' class='xr-section-summary' >Indexes: <span>(1)</span></label><div class='xr-section-inline-details'></div><div class='xr-section-details'><ul class='xr-var-list'><li class='xr-var-item'><div class='xr-index-name'><div>x_dim_0</div></div><div class='xr-index-preview'>PandasIndex</div><div></div><input id='index-029175b8-caaf-4728-a9e5-71c421ae574d' class='xr-index-data-in' type='checkbox'/><label for='index-029175b8-caaf-4728-a9e5-71c421ae574d' title='Show/Hide index repr'><svg class='icon xr-icon-database'><use xlink:href='#icon-database'></use></svg></label><div class='xr-index-data'><pre>PandasIndex(Int64Index([0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18,\n",
       "            19],\n",
       "           dtype=&#x27;int64&#x27;, name=&#x27;x_dim_0&#x27;))</pre></div></li></ul></div></li><li class='xr-section-item'><input id='section-2f8fe9d3-8ca7-485b-acda-672a7c7ecdae' class='xr-section-summary-in' type='checkbox'  checked><label for='section-2f8fe9d3-8ca7-485b-acda-672a7c7ecdae' class='xr-section-summary' >Attributes: <span>(4)</span></label><div class='xr-section-inline-details'></div><div class='xr-section-details'><dl class='xr-attrs'><dt><span>created_at :</span></dt><dd>2024-01-30T22:16:53.206718</dd><dt><span>arviz_version :</span></dt><dd>0.17.0</dd><dt><span>inference_library :</span></dt><dd>pymc</dd><dt><span>inference_library_version :</span></dt><dd>5.10.3</dd></dl></div></li></ul></div></div><br></div>\n",
       "                      </ul>\n",
       "                  </div>\n",
       "            </li>\n",
       "            \n",
       "              </ul>\n",
       "            </div>\n",
       "            <style> /* CSS stylesheet for displaying InferenceData objects in jupyterlab.\n",
       " *\n",
       " */\n",
       "\n",
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       "  --xr-disabled-color: var(--jp-layout-color3, #bdbdbd);\n",
       "  --xr-background-color: var(--jp-layout-color0, white);\n",
       "  --xr-background-color-row-even: var(--jp-layout-color1, white);\n",
       "  --xr-background-color-row-odd: var(--jp-layout-color2, #eeeeee);\n",
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       "  --xr-background-color-row-even: #111111;\n",
       "  --xr-background-color-row-odd: #313131;\n",
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       "\n",
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       "  display: block;\n",
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       "  max-width: 700px;\n",
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       "\n",
       ".xr-text-repr-fallback {\n",
       "  /* fallback to plain text repr when CSS is not injected (untrusted notebook) */\n",
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       "\n",
       ".xr-header {\n",
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       "  padding-bottom: 6px;\n",
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       "}\n",
       "\n",
       ".xr-header > div,\n",
       ".xr-header > ul {\n",
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       "\n",
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       "\n",
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       "\n",
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       "\n",
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       "\n",
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       "\n",
       ".xr-section-summary-in + label:before {\n",
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       "\n",
       ".xr-section-summary-in:disabled + label:before {\n",
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       "\n",
       ".xr-section-summary-in:checked + label:before {\n",
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       "\n",
       ".xr-section-summary-in:checked + label > span {\n",
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       "\n",
       ".xr-section-summary,\n",
       ".xr-section-inline-details {\n",
       "  padding-top: 4px;\n",
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       "\n",
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       "\n",
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       "\n",
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       "\n",
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       "\n",
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       "\n",
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       "\n",
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       "\n",
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       "\n",
       ".xr-array-in:checked ~ .xr-array-data,\n",
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       "\n",
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       "\n",
       ".xr-dim-list li {\n",
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       "\n",
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       "\n",
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       "\n",
       ".xr-dim-list li:not(:last-child):after {\n",
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       "\n",
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       "\n",
       ".xr-var-list,\n",
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       "\n",
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       "\n",
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       ".xr-attrs dt:hover {\n",
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       "\n",
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       "\n",
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       "\n",
       ".xr-attrs dt {\n",
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       "\n",
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       "\n",
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       "  white-space: pre-wrap;\n",
       "  word-break: break-all;\n",
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       "\n",
       ".xr-icon-database,\n",
       ".xr-icon-file-text2 {\n",
       "  display: inline-block;\n",
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       "  stroke-width: 0;\n",
       "  stroke: currentColor;\n",
       "  fill: currentColor;\n",
       "}\n",
       ".xr-wrap{width:700px!important;} </style>"
      ],
      "text/plain": [
       "Inference data with groups:\n",
       "\t> posterior\n",
       "\t> sample_stats\n",
       "\t> observed_data"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Setting up the model using pm.Model(). Code is modified from CS146 Session 3\n",
    "with pm.Model() as model:\n",
    "    # Prior\n",
    "    p = pm.Beta('p', alpha = 2, beta = 2)\n",
    "    # Likelihood\n",
    "    pm.NegativeBinomial('x', n = 3, p = p, observed = data)\n",
    "    # Number of trials\n",
    "    inference = pm.sample(2000)\n",
    "inference"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "af6f5bbf",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>mean</th>\n",
       "      <th>sd</th>\n",
       "      <th>hdi_3%</th>\n",
       "      <th>hdi_97%</th>\n",
       "      <th>mcse_mean</th>\n",
       "      <th>mcse_sd</th>\n",
       "      <th>ess_bulk</th>\n",
       "      <th>ess_tail</th>\n",
       "      <th>r_hat</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>p</th>\n",
       "      <td>0.346</td>\n",
       "      <td>0.035</td>\n",
       "      <td>0.281</td>\n",
       "      <td>0.41</td>\n",
       "      <td>0.001</td>\n",
       "      <td>0.0</td>\n",
       "      <td>3089.0</td>\n",
       "      <td>5450.0</td>\n",
       "      <td>1.0</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "    mean     sd  hdi_3%  hdi_97%  mcse_mean  mcse_sd  ess_bulk  ess_tail  \\\n",
       "p  0.346  0.035   0.281     0.41      0.001      0.0    3089.0    5450.0   \n",
       "\n",
       "   r_hat  \n",
       "p    1.0  "
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "az.summary(inference)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "59572432",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<Axes: title={'center': 'p'}, xlabel='Rank (all chains)', ylabel='Chain'>"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "az.plot_rank(inference)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "93a0b5b1",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[<Axes: title={'center': 'p'}>, <Axes: title={'center': 'p'}>]],\n",
       "      dtype=object)"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 1200x200 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "az.plot_trace(inference)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "774bc1bf",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "az.plot_posterior(inference, var_names=['p'])\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "faab6bdb",
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 800x400 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Analytical mean = 0.343\n",
      "Sample mean = 0.346\n",
      "95% Credible interval of the sample= [0.279 0.414]\n"
     ]
    }
   ],
   "source": [
    "# Code adopted and modified appropriately from CS146 Sessions 2 and 4\n",
    "all_p_samples = inference.posterior.p.values.flatten()\n",
    "# Hyperparameters of the prior \n",
    "alpha = 2\n",
    "beta = 2\n",
    "# Known parameter of the likelihood\n",
    "r = 3 \n",
    "# Visualize comparison between approximation and the exact posterior\n",
    "\n",
    "# Plot the histogram of the sample distribution\n",
    "plt.figure(figsize = (8, 4))\n",
    "plt.title('Comparison of the sampling approximation and the exact posterior')\n",
    "plt.xlabel('p')\n",
    "plt.ylabel('probability density')\n",
    "plt.hist(\n",
    "    all_p_samples, bins = 20, density = True,\n",
    "    edgecolor='white', color = 'skyblue', label='approximation')\n",
    "# 95% credible interval\n",
    "cred_interval = np.quantile(all_p_samples, [0.025, 0.975])\n",
    "# Plot the 95% credible interval of the sample distribution\n",
    "plt.axvline(x = cred_interval[0], color = 'orange',  label = '95% CI')\n",
    "plt.axvline(x = cred_interval[1], color = 'orange')\n",
    "\n",
    "# Exact posterior\n",
    "x = np.linspace(0.15, 0.55, 500) # For better clarity\n",
    "y = sts.beta.pdf(x, alpha+len(data)*r, beta+sum(data)) # Analytical Solution\n",
    "plt.plot(x, y, label = 'exact', color = 'black', linestyle = '--')\n",
    "plt.legend()\n",
    "plt.grid(linestyle = 'solid')\n",
    "plt.show()\n",
    "\n",
    "# Exact mean from analytical solution\n",
    "analytical_mean = len(data)*r / (len(data)*r + sum(data))\n",
    "\n",
    "\n",
    "# Extract approximate posterior mean value from pm.summary table\n",
    "summary = pm.summary(inference)\n",
    "# Sample Mean\n",
    "sample_mean = float(summary['mean'].values)\n",
    "\n",
    "# Print the results\n",
    "print(f'Analytical mean = {round(analytical_mean,3)}')\n",
    "print(f'Sample mean = {sample_mean}')\n",
    "print(f'95% Credible interval of the sample= {np.round(cred_interval,3)}')"
   ]
  },
  {
   "attachments": {
    "model.png": {
     "image/png": 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"
    }
   },
   "cell_type": "markdown",
   "id": "a192d718",
   "metadata": {},
   "source": [
    "### Exact and Sampled Posterior Discussion and Interpretation\n",
    "![model.png](attachment:model.png)\n",
    "<t><center>Figure 1. Model.</center></t>\n",
    "\n",
    "#### Prior\n",
    "$$p \\sim \\text{Beta}(\\alpha=2,\\beta=2)$$\n",
    "#### Likelihood\n",
    "$$x_i \\sim \\text{Negative-Binomial}(r=3,p) \\quad i=1,\\ldots,20$$\n",
    "\n",
    "The model/data story shows that the parameter $p$ follows beta distribution, and the likelihood function follows negative binomial distribution. Our prior distribution is beta with specified hyperparameters $\\alpha = \\beta = 2$. The likelihood function follows a negative binomial distribution with parameters $ r=3 $ and an unknown $p$. Negatve-binomial distribution is a probability distribution that describes the number of independent and identically distributed Bernoulli trials needed for a specified number of successes to occur. In the likelihood function, the unknown/unobserved variable is $p$, the probability of success. Meanwhile, the known/observed variable is $r$, a specified number of successes. Another piece of information is 20 data points, which were provided and will be used in the Bayesian process of updating our beliefs to find the value of unknown parameter $p$ (McElreath, 2020, p. 31). This value representing twenty data points is also displayed in figure 1 above. \n",
    " \n",
    "Given this information to find posterior distribution, we can use Bayes' formula to fit a posterior. \n",
    "\n",
    "<t><center>$f_{posterior}\\propto f_{likelihood}\\times f_{prior}$</center></t>\n",
    "<t><center>$p(\\theta|x)\\propto p(x|\\theta)\\times p(\\theta)$</center></t>\n",
    "\n",
    "Given that the prior is a beta distribution the posterior distribution will also be a Beta distribution because of conjugacy. However, the $\\alpha$ and $\\beta$ values of the posterior distribution will be different.  \n",
    "#### Posterior\n",
    "$$(p|s,f) \\sim \\text{Beta}(\\alpha,\\beta)$$\n",
    "\n",
    "Here $s$ represents success where $f$ represents failure. However, these values are unknown and can be approximated using a sampling process. Calculating $p$ will help us in this process, and then we can find expected success, $s$ = $p\\times n$, and expected failure $f$ = $(1-p)\\times n$. Where $n$ is the total number of trials. We will talk about finding exact $\\alpha$ and $\\beta$ values analytically below. \n",
    "\n",
    "We will use two approaches to fit the posterior. First, we will use PyMC and approximate the posterior using inference by sampling. To do this, the model was defined with the following known variables: prior distribution, its hyperparameters, and the likelihood function. Next, we ran the NUTS sampler and stored the results in the variable called inference. To check the results, we called $az.summary()$ to look at how the sampling process went. "
   ]
  },
  {
   "attachments": {
    "az.summary%28inference%29.png": {
     "image/png": 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"
    }
   },
   "cell_type": "markdown",
   "id": "8177caa9",
   "metadata": {},
   "source": [
    "![az.summary%28inference%29.png](attachment:az.summary%28inference%29.png)\n",
    "<t><center>Figure 2. Sampling Summary Statistics.</center></t>\n",
    "Sampling summary statistics provide us with a quick glimpse of what happened in the chains of samples that were generated by the NUTS algorithm. It shows the information about the posterior distributions over all the model parameters and gives us statistics values that reflect the quality of the sampling process (CS146, 2024). Let's evaluate how the sampling process went. \n",
    "#### Overview of the Summary\n",
    "1. $\\hat{R}$ We wanted an r hat value to be very close to 1. We see from the summary table that $\\hat{R}=1.0$, which is exactly what we wanted. Anything greater than 1.01 would not have been okay. $\\hat{R}$ Rhat diagnostic is basically a comparison of within and between chain variances. If all chains are sampling the same distribution it will necessarily be close to 1 as within and between chain variances will be the same. Since our $\\hat{R}=1.0$ This is the indicator that sampling has converged and works well. \n",
    "2. Next are two effective sample size (ESS) columns. The sampling algorithm is more accurate if these values are large: at least a few hundred. From the summary, we see that $ESS_{tail}$ and $ESS_{bulk}$ values are 3318.0 and 5244.0, respectively. The ESS measures how successful the sampling algorithm was in ensuring that consecutive samples are uncorrelated. As a rule of thumb, we want greater than 10% of our sampling size, which was set to 2000. We see that our values are quite large, which indicates that our model is successful and samples are random from all the chains. \n",
    "3. $MCSE_{mean}$ and $MCSE_{sd}$ show how much sampling error there is in the estimates in the mean and SD columns. Our errors are very low, indicating that there is a low correlation in a Markow chain.\n",
    "4. $Mean$ is the sample mean of the parameter $p$. Our sample has approximated the expected value to be $p=0.345$. Meaning that the approximate probability of success is $p=0.345$ after using inference by sampling.\n",
    "5. $SD$ is the sample standard deviation of the parameter. \n",
    "6. $hdi_{3\\%}$ and $hdi_{97\\%}$ are the left and right boundaries of the 94% highest density interval of the distribution. "
   ]
  },
  {
   "attachments": {
    "rank_plot.png": {
     "image/png": 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QC8Xlcik1NbVe2ZKSEhljgmYty1JaWlq9sqWlpfL7/SH7kZ6eXq9sWVmZfL7QJwJGk01LS5NlWZKk8vJyVVVVSZK27t2qLT9sCchaHsvO+iv9Uujuykq2ZLkOZSsqKlRZWRkym5qaKpfLFVE22ZMsT7InomxKSor9vqqsrFRFRUWtTPVfJl6vV0lJSWGz1Wpmq6qqVF5eHvB8zXVnuS1ZSYfWg/EZmarg751g2XDv4eTkZHk8h9aDz+dTWVlZRFm/36/S0tKYZJOSkuT1eg/11xiVlJTEJBvNfh8uW+s9bEkuz5HrIfzl4d7Ah7I9M3tKkqrKq8LmXd7I2q0qrwr43cljREOz0ez30WRr7vexGCOq1TVGVJUdeY9YSZYsd/32+4rSCh08eDD4GFwz6zcylaHblVtyJR1aZ401RkTMJKDCwkIjKeTP2LFjA/JpaWkhs6NGjQrIZmVlhczm5OQEZLt37x4ym52dHZDNzs4Ome3evXtANicnJ2Q2KysrIDtq1KiQ2bS0tIDs2LFjw663msaPHx82W1xcbGcnTZoUNtv/T/3NwAUDzcAFA02bH7UJm+37UF8zcMFAM+GlCWbGjBlhs3l5eXYfcnNzw2bXr19v7lp7l5nw0gRz0uSTwmZH/WaUmfDSBDPhpQlm8E8Hh82ecc8ZdvbU208Nmz191ul29vRZp4fNdrmpi73Ouk8P/T6TZDpd18nOjvpN6PeDJDN37lx7na1fvz5sNjc3187m5eWFzc6YMcPO5ufnh81OnTrVzhYUFITNTpo0yc4WFxeHzY4fPz7gPRwuG80YkdYvzV6/AxcMNO6W7pDZ1J6pZuCCgWbW2lmH2m0ful1vZ29Au97O3tB9aB+4LyfaGFFQUGBnp06dGjabn59vZyMZI6p8VcaYyMaIanPnzg2bXb16tZ197LHHwmaXLl1qZ+fPnx8223VqV/v90HVq17DZ+o4RPe7qETbb4YoO9hjcGGNE9ed3YWGhqUtCH4EBolF9qPbbkm/D5r4s+lLf7/tekvT9we/DZnce2Kn9+/ZLkn4o/iFs9pvib1S8r1iSVFhcGGGvE8/bu97WFS9fIUkqLywPm12zc42drSoL/Vd5onNZrmY/HyFeTPvvNKV3OHQk6MPPPwybfXjDw3p6wNNN0S00AsuYEPMWDlZUVKTMzEzt2rVLGRkZtZ5v6BRSqIGiPlNI1W3FagrJ5/cpo2VGRFmp6Q8PX//q9TGZQjqhzQl69vxnY3p4+OpXr9bmfZvlr/JLYW6pUXMay1QZGV/gdjuv+3l64IwHdP2r12vrga1HDvkGyQa0G+LwcM32GjqFNLzjcD00/KGQH3T1mULy+X2yZMVsCmniaxO19cDWQ8tmjExFmCHKJbmSXUGzwzoN08NnPWwva6ymkGq9h+sxhTS251j97szf6fLnL9eWfVtCxiOdQjq/x/l6+LyH7fMbfOW+kOOJJCWlHPnb9ejsoHaDdMeQO+z1FosxItiY2dAppGBjiRS4f9a1L2d3yNZzlzwnKX6nkAL2+wZMIZ3b5dxa40jQbIRTSCe0OUELxy6M+RRS9ed3YWFh0M/vmhL6CEx6enrADhUuF02bkmJ6Il9jnlRVs6CqS80BO5ZZr9drn6eQlJIUMCgfrfrDKBIejyfiOdNosq4kV8R7hpV0ZMe3XyvVo/T0dCWlJMkqscJmQ7brPjJQ1Wwv2Lqrma1Lq9RWymiZ0SjvuUj3I5fLFTbrTj7yQWdZlixvhOvsqGzbzLYxXdbq/bXO93CY546W5A3fVqTtJqckS4rihM/Qpwqpj6tPo71HQqk5RtSlOlvXdpDq3perCx0pduPJ0cVacnKykpOTI2o3WDYW+73ltuocR+ysK/J9zu12x2y/r4+ELmAaUyzODK8+kY97QUSvbWpbDpk3wLH0novlVRzHklitt2NtX+VKtaZDAZNAGmOgiNeBJ8OTwUABOEAs91XJGftrLP/ARWgUMAkk1gNFPFznXxcGiuZ1rP11jfrjSBhijQImAR1L0wNoXhwJA9BcKGAANBhHwuBEHEF0NgoYhMTODSCRHYvn5yQSChiExPQAgGMB5+c4EwUM6sT0AAAg3kR+xyUAAIA4QQEDAAAchwIGAAA4DgUMAABwHAoYAADgOBQwAADAcShgAACA41DAAAAAx6GAAQAAjkMBAwAAHIcCBgAAOA4FDAAAcBwKGAAA4DgUMAAAwHEoYAAAgONQwAAAAMehgAEAAI5DAQMAAByHAgYAADgOBQwAAHAcChgAAOA4FDAAAMBxkhrawJo1a7Ru3Trt3r1b5eXlQTOWZenpp59u6EsBAABIakABU1hYqEsuuURvvPGGjDFhsxQwAAAglupdwNx1111at26devfurSlTpqhv375q2bJlLPsGAAAQVL0LmBdffFEdOnTQO++8ozZt2sSyTwAAAGHV+yTewsJCjRgxguIFAAA0uXoXMH369NHBgwdj2RcAAICI1LuA+dnPfqY1a9Zo+/btsewPAABAnepdwNx88836+c9/rlGjRmn+/Pn6+uuvY9kvAACAkOp9Eq/b7ZYkGWN08803h81alqWqqqr6vhQAAECAehcwXbt2lWVZsewLAABAROpdwHzxxRcx7AYAAEDk4vK7kB588EGdeuqpatmypdq3b69LL71UW7Zsae5uAQCAOBGXBczatWs1bdo0vfPOO1qxYoUqKyt13nnncdk2AACQFMUU0rp16yRJp512mlJSUuzfI3XmmWdGnF2+fHnA7wsWLFD79u21cePGqNoBAACJKeIC5qyzzpJlWdq8ebP69u1r/x4pn89Xrw5Kh+76K4m7/gIAAElRFDATJ06UZVnKzMwM+L2x+f1+TZ8+XSNGjNDAgQODZsrLy1VeXm7/XlRU1Oj96pXZq8FtdGnRJWZtxXt79C0+2qNv8dEefYuP9uhb/cWqnYawjDGmuTsRzq233qply5bpzTff1HHHHRc0c++99+q+++6r9XhhYaEyMjJi3ief3ye3yx13bcV7e/QtPtqjb/HRHn2Lj/boW/y0Jx06AJGZmRnR53dcFzC33XabXnzxRa1bt049e/YMmQt2BKZr166NVsAAAIDYi6aAqfd9YBqTMUY/+9nPtGTJEq1ZsyZs8SJJXq9XXq+3iXoHAACaW4MLmJKSEq1evVrbtm3TgQMHFOyAjmVZuueeeyJuc9q0afrnP/+pF198US1bttSePXskSZmZmUpNTW1olwEAgMM1aAppwYIFuuOOOwJOmjXGBJzcW/17NFchhTo5eP78+Zo8eXKd/z+aQ1AAACA+NMkU0n//+1/ddNNNyszM1C9/+UutXr1ab7/9tp588kl9/vnnWrJkibZt26bbbrtNQ4YMiartOD4tBwAAxIF634n3D3/4gyzL0urVq3X//ferT58+kqRbbrlFc+bM0SeffKLp06frmWeeibqAAQAACKfeBcx7772n008/XYMGDQr6fFJSkn7/+9+rffv2ys3NrXcHAQAAjlbvAqa4uFjdunWzf6++CujAgQNHGne5NHToUL3xxhsN6CIAAECgehcwHTt21L59++zfO3XqJEnaunVrQG7fvn0qLS2t78sAAADUUu8Cpn///tq2bZv9+/Dhw2WM0dy5c+2TcN966y2tWrVK/fr1a3hPAQAADqt3ATNu3Djl5+dr/fr1kqRzzjlHJ510kp5//nl16dJFQ4YM0dlnn21/lxEAAECs1LuAmThxopYtW6YOHTocasjl0iuvvKJzzz1XBQUF+uCDD5SWlqYHHnhA1113Xcw6DAAA0CjfhVRSUqLCwkK1b99ebndsv+gpEtzIDgAA52n270JKS0tTWlpaYzQNAABQ/ykkAACA5tKgIzAFBQV6/PHHtW7dOu3evVvl5eVBc5Zl6fPPP2/ISwEAANjqXcBs3rxZo0aN0vfff893FwEAgCZV7ymkmTNn6rvvvtPll1+uDRs2qKioSH6/P+QPAABArNT7CMwbb7yhfv36afHixbIsK5Z9AgAACKveR2CMMTr55JMpXgAAQJOrdwGTk5OjL7/8MpZ9AQAAiEi9C5h7771X7733nl5++eVY9gcAAKBOEZ8Ds27dulqP3X777br88st1zTXX6Nxzz9Vxxx0nlyt4TXTmmWfWv5cAAAA1RPxVAi6XK+j5LtX/va5zYXw+Xz26Vz98lQAAAM7TKF8lMHHiRE7YBQAAcSHiAmbBggWN2A0AAIDIRXUfmFWrVunrr79WTk6OsrOzw2Y//fRTbdiwQV27dtXZZ5/doE4CAADUFHEBs3PnTo0bN05du3bVxo0b68x37dpVl112mb7++mtt27ZNnTt3blBHAQAAqkV8GfVTTz2liooKzZ07Vy1btqwz37JlSz300EMqLS3V008/3aBOAgAA1BRxAbNixQq1a9dOl156acSNX3zxxerQoYOWLVtWn74BAAAEFXEB89lnn+nUU0+N+gVycnK0ZcuWqP8fAABAKBEXMAcPHlRmZmbUL5CZmani4uKo/x8AAEAoERcwrVu31t69e6N+gb1796p169ZR/z8AAIBQIi5gsrOz9c4776i0tDTixktKSvT222/Xeck1AABANCIuYC688EIdPHhQDzzwQMSNP/DAAyotLdVFF11Ur84BAAAEE3EBM2XKFHXo0EFz5szRAw88IL/fHzLr9/t1//33a86cOerQoYN++tOfxqSzAAAAUhRf5ihJb731lkaPHq3y8nIdd9xxmjBhgk455RS1a9dOkvTtt9/q/fff13PPPaevv/5aXq9XK1eu1LBhwxptAYLhyxwBAHCeaD6/oypgJGnTpk26/vrr9cknn4T9duoBAwbo2Wef1aBBg6JpPiYoYAAAcJ5G+TbqaieffLI+/vhjLV++XK+88oo2bdqk77//XpLUtm1bnXzyyRo3bpwuuOCC+vUeAACgDlEfgXECjsAgan6f5HLHb3uoH7Yr4CiNegQGSEgut/Tvm6Xvtja8ray+0o+fang7aDi2K5CwKGCAat9tlXZ/2Ny9QKyxXYFDEuyIJAUMAADHggQ7IkkBk2gSrMIGAMRQAh2RpIBJNLGssLueLl3wYMPbqUYxlJhiuV15jwCIUEIXMAcPHpTbXXswdLvdSklJCciF4nK5lJqaGpgNMcgenS0pKVGoi7wsy1JaWprdVkTZw0pLS8PeCTm9RoVdWmnkD3OdWbrnyL18yqqMfDWbbdFTKi2TXpgqfb9d6d4jy1xW6ZcvTMNpHpd9n6DySr+qWh8vXfp48Gxa2pFsebmqqqpCtpuamiqX69ANpCsqKlRZWRmTbEpKiqqXrsJnVOkLGVVKkuR2Hepvpc+o4uhsuU86/J7yer1KSjq0m1VWVqqioiJkuzWzVVVVKi8vD5n1eDxKTk6OOuvz+VRWcjBkkZCcnCyPx3MkW1YWsl0763LL/9xNKt39Weis25In6dC28PuNSiuDvH/b9pYufVxJSUnyer2SDt1XqqSkJGS7EWXLfVKFkdslpSQdeb8frAj9/g2arbFdawo6RoRQrzGiHtk6x4j09Hply8rK5POF3jmiyUaz39fKVpSHfA9HPUbISC53ZGPE4c+TsFm/Tylp6XY2mv2+Vvaoz5qYjBGH94eArPvQPipJPr9RWehNoWS35KnORjpG6NAd+sN9l2LNbMRMAiosLDSSQv6MHTs2IJ+WlhYyO2rUqIBsVlZWyGxO9xbGPDHS/unexhsym90pzZjnb7Lbzc7ODpnt3r17QB9ycnJCZrOysg69fm6GMbkZZlR3d8hsWrLsnMnNMGP7JIVdbzWz47PDZ4tnt7SzkwYlh80WFBTYyzZ16tSw2fz8fDs7Y8aMsNm8vDw7m5ubGza7fv16e73NHR16u0kyqyel2cv22JiUsNmlS5fafZg/f37Y7OLFi+3s4sWLw2bnz59vZ5cuXRo2+9hjj9nZ1atXh83Ovbyn/f5df/fJYbO547oZ89/7jDHG5P36lLDZGcM89jrLv71F2OzUqVPt/hYUFITNTpo0yc4WFxeHzY7PTgp4D4fLju0TmE1LDp2NaozIyQnIdu/ePWQ2Ozs7IBvTMaKGUaNGhcympaUFZMeOHRt2vdU0fvz4sNni4mI7O2nSpLDZqMaIB06138Mzzu0SNpv3+A3G+KqMMRGOEYfNnTs3bHb1vWPtPjx21fFhs0unDbCz8yf2DZtdfEt/O7v4lv5hs/Mn9rWzS6cNCJt9bEyK/V5fPSn056EkM3e091D2iZFm/fr1YbO5ubn2OsvLywubnTFjhjHmyOd3YWGhqUtCH4FpcpUlgXOLvtBVt6rKYjPNA8RS0S5p96EbU+q7MIehJKl4j7T/q8bvExCNbzdLlYe/5q849NEBSVJ54ZFp9w0rwmf/8xPp/ZaH/v3O1+GzhTsl8+Xhf4f5HJCkfTuk3Tsjy/7wpbR71+F/hz5adKitr6Tdew6/Rh1Zh0roG9nt2rUr6I1wGjyFJElPnyft+Tgwa0mpyUcOO5dUGoVau5YlpWWfJ139r9hPIT07JjZTSAMuOzTtc3hZw2aPkpasI4d8q4yq2p8o3fR68Gy8TCE9dba0+8OGTyF1PLKscTmFVFYW9P0rHXV4OJJDySdfIf34KfnnjVTpztAnBtZs12+MSoNtisPrLeZTSIeXtcFTSB2Dv4eZQqpftkFTSFVVId/DqcmS63C2rn05dfAEuSY8LT15piq+3hTxfh+y3cNjZsr/XSD33o8khRgjavAmSUnBxpOjxt+js1V+o/Iw+2fNaaEqv1F5v9rtBctGPIXUaZB8N6+O+RQSN7I7LD09PWCHCpeLpk1Jktct1fhADyYtOfzzSmllV/9pURyNSQ31RO/R0jm/DszW1Yea3Uk6KpuSLKWnB13WWtkwvEmWvF73obbqynq99gdSXTweT8RzplFl3ZY8EZ5Hmuy2lHx0NsSyJicn24VEXZKSkuxiJpZZt9t96D0cwfvX7bKUHuGUtMtlBRS4YbNWiHaDrDfLsiLeP0NmQyxrpP21sxG+h6MZT2oWHbHM1iyS6pUNcZ5fzT/86hKQrePk7Gj2ezsbwXu4zn3ZZUWejaTd6jGzRrtBx4gQArJhxl/pUCGTFOH+meSylFRHe9Wi2e/t8SQCLpcrqn0jEgldwDhGrC5ry+rb8DYaS4v2XOINZ4v1ezie37+xvJqx+g+rWLeHYx4FDJpGjaNNcXmJN1CXWL6HG+MmYLEuiGL9h9Wx8IcamhQFDJpWLAexWH2YOOEvunj+a/1YE4v3cGMckTyW9gdAFDBwulh8mDjhLzo+nBJLrI9IVm/XY2V/AEQBA8ReY/x1LSX+h1Njrbd4xrQKUG8UMECsNdZf14mO9QYgChQwQGPhr+v6Yb0BiICruTsAAAAQLQoYAADgOBQwAADAcShgAACA41DAAAAAx6GAAQAAjkMBAwAAHIcCBgAAOA4FDAAAcBwKGAAA4DgUMAAAwHEoYAAAgONQwAAAAMehgAEAAI5DAQMAAByHAgYAADgOBQwAAHAcChgAAOA4FDAAAMBxKGAAAIDjUMAAAADHoYABAACOQwEDAAAchwIGAAA4DgUMAABwHAoYAADgOBQwAADAcShgAACA41DAAAAAx6GAAQAAjkMBAwAAHIcCBgAAOA4FDAAAcBwKGAAA4DhxWcCsW7dOF110kTp37izLsvTCCy80d5cAAEAcicsC5uDBgxo0aJD+8pe/NHdXAABAHEpq7g4EM2bMGI0ZM6a5uwEAAOJUXB6BAQAACCcuj8BEq7y8XOXl5fbvRUVFjf+iWX0b3karbrFrK97bo2/x0R59i4/26Ft8tEff6i9W7TSAZYwxzd2JcCzL0pIlS3TppZeGzNx777267777aj1eWFiojIyM2HfK75Nc7vhrK97bo2/x0R59i4/26Ft8tEff4qc9HToAkZmZGdHnd0JMIc2ePVuFhYX2z86dOxv3BWO5wWK88eO6PfoWH+3Rt/hoj77FR3v0LX7ai1JCTCF5vV55vd7m7gYAAGgicVnAFBcXa/v27fbv+fn52rRpk9q0aaNu3bo1Y88AAEA8iMsCZsOGDTr77LPt3++8805J0qRJk7RgwYJm6hUAAIgXcVnAnHXWWYrzc4sBAEAzSoiTeAEAwLGFAgYAADgOBQwAAHAcChgAAOA4FDAAAMBxKGAAAIDjUMAAAADHoYABAACOQwEDAAAchwIGAAA4DgUMAABwHAoYAADgOBQwAADAcShgAACA41DAAAAAx6GAAQAAjkMBAwAAHIcCBgAAOA4FDAAAcBwKGAAA4DgUMAAAwHEoYAAAgONQwAAAAMehgAEAAI5DAQMAAByHAgYAADgOBQwAAHAcChgAAOA4FDAAAMBxKGAAAIDjUMAAAADHoYABAACOQwGTYHx+E9ftAUA8Ycx0rqTm7gBiy+2ydPuiD7S9oLjBbfVu30KPXjU4Br0CgPjEmOlcFDDNzOc3crusmLa5vaBYn+wqanA77Vp4Y9q/xlhWAGioWI2ZaFoUMM0sltX/Wf3aaeb5/WPQq0MyUpNi1j/+MgEAxBIFTByIVfV/fLv0GPSmNv46AQDEG07iBQAAjkMBAwAAHIcCBgCAGKi+8CFWuCQ7vIQ+B+bgwYNyu921Hne73UpJSQnIheJyuZSamlqvbElJiYwJ/ga0LEtpaWn27/7KMinUe9WSXMkpNbLlUpB2K8tKa/UvVNbus+dIu6aqQsbvr9VeVXmp/BVlYbO1upzslWVZh7OVqiqv3bdqaWlpdra8vFxVVVUh201NTZXLdajurqioUGVlZUyyKSkp9nslmmxlZaUqKipCZr1er5KSkqLOVlVVqby83H7u6Cu4PB6PkpOTg2aPVjPr8/l0sKQ05NVgycnJ8ng8drasrCxku9VZn9/IklFpaWmdWUny+/0hsz6/kdeTLK/XK0kyxqikpCRku0lJSRFno9nvm2KM8PmNystKIx4j6hpPvCmp9nYtLS2VP8z+mZ5+5Hy5aLJlZWXy+XwxyUaz3zfFGGF8lTJh+mslJctyucNmU61KlZWW6O4XN2vHd4fe435flfxVofvgSkqWy51UK3t8uxZ6aMKggGy4MeJoDRkjItnvo82G2++PzkbMJKDCwkKjQ+VA0J+xY8cG5NPS0kJmR40aFZDNysoKmc3JyQnIdu/ePWQ2Ozvbzo19dJ1JbtstZNad0d50v2up/ePp2CdkNisry4x9dJ2d9XYdGDJrJXsD2k3tlRN2vdXMpvUbETbb9Y7n7Wz6wHPCZgsKCux1MXXq1LDZ/Px8Oztjxoyw2by8PDubm5sbNrt+/Xo7O3fu3LDZ1atX29nHHnssbHbp0qV2dv78+WGzixcvtrOLFy8Omz3pmtlm7KPrzNhH15mcn/wubDZ7/HQ7e/k9fw2bnTt3rt2H9evXh83m5uba2WvnPhc22/NHV9l9OOvX/wqbnTp1qt1uQUFB2OykSZPsbHFxcdjs+PHjA/bPcNmmGiNaZnUKmW3RsYe9zsY+us606NgjZLZlVqeAdnNyQu/LWVlZAdlRo0aFzKalpQVkx44dG3a91TR+/Piw2eLiYjs7adKksNnGHiPGPrrOZI64Omy248SH7TGt1Vk3hM0Ove1RO9vm3Clhs+3G59rZtmOnh81GM0bMnz/fzi5dujRs9rHHHrOzq1evDput7xiRl5cXNjtjxgxjzJHP78LCQlOXhD4CAySqb/aXqvDwlWEl+0IfdZCkPYVlOng42/Fg6L+AGuKrOvrwfXGFfSVbVWHDbxmQKKrCTBGUV/oDrv4rrwx9lCRcO0CisowJM7/gUEVFRcrMzNSuXbuUkZFR6/l4m0Ia96c39PGXBYfq0KDhyKaQxp3YUb+/4mRd8fT79sDXkCmk6vYuf/x/2rz7QIOmkPp3SNN/po4Imk3UKaSZz32o/B/Kgx4eDibUoeQz+2Zp+uh+9naQJMudJOtw1vh9MmHarZnN7piu5245NWS2voeHxz6yVnlffRemD25Z7kOHqI3xy1TWXmcj+2Rp3nVDYjqFVHPqLVZTSDOf+1Cff3ukCLMsl9wer/17VXnoIrE6W33Ppgt+v0KfhrpFQa39PvQ0c3bnDC2fca79ezxOIR293tyeFHu/91VVhJ2+qZnt0dqjuZcPDJmtzxgx7k9vKG/n9w2eQqoeMyf87T19uufg4WyVjC/0mBbY7pFsdVs111uoMSKYo7M9W3trTUlVi6cppOrP78LCwqCf3zUl9BGY9PT0gB0qXC6aNiO9o2zN+eu61Byo6s56gz6enJJaa1lCZYOxkjyquVTV7SV5U+XyVIbNhm83WUne2n0Lxuv12h9IdfF4PBHPmTZWNjk52d7xj/ZlkU+b94Y/MhEo+GDUr0Qht4MkWS63LE/tc72CaZ+RppTUtIjev263O+J9w3K5AgrcsFnLJStItm2rlspo2aLJbuse7X5f7csin7Z8f/R2CH1+QW3l9j2b3J4UuTyhz4uqKdwY4T5qfdb8Q6ou0WRrFnXRZmuvt9AfvrUdybZr0S7i93A0+7LlTraL7Ppmq8fM6oLkUPbIHxB1t3skW91W4Hqr3zqTJJc7KaL3fDT7fTRZl8sV1T4XiYQuYBpLrO5OG+s75wJ1ieXdlaXGeQ9z48ToHUtf+xHL9zBjsLNRwNRTLAbZxrpzLlCXeL/7M6LTGB/q8VzkSozBoIBBE4n1X4hSbP9KjOe/OIFIxfJDnSIX8Y4CBk2isaYu+KJJhNIYRTOA+EEBgyYV67/qOF8CoTjhfB8A9UcBAyChMRUCJCa+CwnHvFh/fwkAoPFxBAbHPKYaAMB5KGCAw5hqAJCo4v1K0PqggAEAIMHF+khzPFy9SQEDAMAxIpGu3OQkXgAA4DgUMAAAwHEoYAAAgONQwAAAAMehgAEAAI5DAQMAAByHAgYAADgOBQwAAHAcChgAAOA4FDAAAMBxKGAAAIDjUMAAAADHoYABAACOQwEDAAAchwIGAAA4DgUMAABwHAoYAADgOBQwAADAcShgAACA41DAAAAAx6GAAQAAjkMBAwAAHIcCBgAAOA4FDAAAcBwKGAAA4DgUMAAAwHEoYAAAgONQwAAAAMehgAEAAI5DAQMAABwnrguYv/zlL+rRo4dSUlI0dOhQrV+/vrm7BAAA4kDcFjD/+te/dOeddyo3N1fvv/++Bg0apPPPP18FBQXN3TUAANDM4raAefjhh3XLLbfohhtuUHZ2tp544gmlpaXpmWeeae6uAQCAZhaXBUxFRYU2btyo0aNH24+5XC6NHj1ab7/9djP2DAAAxIOk5u5AMN999518Pp86dOgQ8HiHDh302Wef1cqXl5ervLzc/r2wsFCSVFRU1Gh97NpCqmzjblAb7bx+FRUVxaSteG+PvsVHe/QtPtqjb/HRHn2rv64tGucztrpNY0zdYROHvvnmGyPJvPXWWwGPz5w505x22mm18rm5uUYSP/zwww8//PCTAD87d+6ss1aIyyMwWVlZcrvd2rt3b8Dje/fuVceOHWvlZ8+erTvvvNP+3e/3a9++fWrbtq0sy4pp34qKitS1a1ft3LlTGRkZMW07HrB8zpfoy5joyycl/jKyfM7XWMtojNGBAwfUuXPnOrNxWcB4PB4NGTJEK1eu1KWXXirpUFGycuVK3XbbbbXyXq9XXq834LFWrVo1ah8zMjIS9o0psXyJINGXMdGXT0r8ZWT5nK8xljEzMzOiXFwWMJJ05513atKkScrJydFpp52mRx55RAcPHtQNN9zQ3F0DAADNLG4LmCuvvFLffvutfv3rX2vPnj06+eSTtXz58lon9gIAgGNP3BYwknTbbbcFnTJqTl6vV7m5ubWmrBIFy+d8ib6Mib58UuIvI8vnfPGwjJYxkVyrBAAAED/i8kZ2AAAA4VDAAAAAx6GAAQAAjkMBAwAAHIcCJgp/+ctf1KNHD6WkpGjo0KFav359c3cpqHXr1umiiy5S586dZVmWXnjhhYDnjTH69a9/rU6dOik1NVWjR4/Wtm3bAjL79u3Ttddeq4yMDLVq1Uo33XSTiouLAzIfffSRRo4cqZSUFHXt2lVz585t7EWTJD344IM69dRT1bJlS7Vv316XXnqptmzZEpApKyvTtGnT1LZtW7Vo0UI//vGPa93Z+auvvtK4ceOUlpam9u3ba+bMmaqqqgrIrFmzRqeccoq8Xq969+6tBQsWNPbiad68eTrppJPsG0QNGzZMy5YtS4hlC2bOnDmyLEvTp0+3H3P6Mt57772yLCvgp3///vbzTl8+Sfrmm2903XXXqW3btkpNTdWJJ56oDRs22M87fZzp0aNHrW1oWZamTZsmyfnb0Ofz6Z577lHPnj2Vmpqq448/Xvfff3/AdxDF/TZs+DcXHRsWLVpkPB6PeeaZZ8wnn3xibrnlFtOqVSuzd+/e5u5aLa+++qr51a9+Zf7zn/8YSWbJkiUBz8+ZM8dkZmaaF154wXz44Yfm4osvNj179jSlpaV25oILLjCDBg0y77zzjnnjjTdM7969zdVXX20/X1hYaDp06GCuvfZak5eXZxYuXGhSU1PNk08+2ejLd/7555v58+ebvLw8s2nTJjN27FjTrVs3U1xcbGemTJliunbtalauXGk2bNhgTj/9dDN8+HD7+aqqKjNw4EAzevRo88EHH5hXX33VZGVlmdmzZ9uZHTt2mLS0NHPnnXeaTz/91Pz5z382brfbLF++vFGX76WXXjKvvPKK2bp1q9myZYv55S9/aZKTk01eXp7jl+1o69evNz169DAnnXSSuf322+3Hnb6Mubm5ZsCAAWb37t32z7fffpswy7dv3z7TvXt3M3nyZPPuu++aHTt2mNdee81s377dzjh9nCkoKAjYfitWrDCSzOrVq40xzt+Gv/nNb0zbtm3N0qVLTX5+vnnuuedMixYtzKOPPmpn4n0bUsBE6LTTTjPTpk2zf/f5fKZz587mwQcfbMZe1e3oAsbv95uOHTuahx56yH5s//79xuv1moULFxpjjPn000+NJPPee+/ZmWXLlhnLssw333xjjDHm8ccfN61btzbl5eV25q677jL9+vVr5CWqraCgwEgya9euNcYcWp7k5GTz3HPP2ZnNmzcbSebtt982xhwq8lwul9mzZ4+dmTdvnsnIyLCXadasWWbAgAEBr3XllVea888/v7EXqZbWrVubp556KqGW7cCBA6ZPnz5mxYoVZtSoUXYBkwjLmJubawYNGhT0uURYvrvuusucccYZIZ9PxHHm9ttvN8cff7zx+/0JsQ3HjRtnbrzxxoDHLr/8cnPttdcaY5yxDZlCikBFRYU2btyo0aNH24+5XC6NHj1ab7/9djP2LHr5+fnas2dPwLJkZmZq6NCh9rK8/fbbatWqlXJycuzM6NGj5XK59O6779qZM888Ux6Px86cf/752rJli3744YcmWppDCgsLJUlt2rSRJG3cuFGVlZUBy9i/f39169YtYBlPPPHEgDs7n3/++SoqKtInn3xiZ2q2UZ1pym3u8/m0aNEiHTx4UMOGDUuoZZs2bZrGjRtXqx+Jsozbtm1T586d1atXL1177bX66quvJCXG8r300kvKycnRhAkT1L59ew0ePFh/+9vf7OcTbZypqKjQs88+qxtvvFGWZSXENhw+fLhWrlyprVu3SpI+/PBDvfnmmxozZowkZ2xDCpgIfPfdd/L5fLW+xqBDhw7as2dPM/Wqfqr7G25Z9uzZo/bt2wc8n5SUpDZt2gRkgrVR8zWagt/v1/Tp0zVixAgNHDjQfn2Px1PrCz2PXsa6+h8qU1RUpNLS0sZYHNvHH3+sFi1ayOv1asqUKVqyZImys7MTYtkkadGiRXr//ff14IMP1nouEZZx6NChWrBggZYvX6558+YpPz9fI0eO1IEDBxJi+Xbs2KF58+apT58+eu2113Trrbfq5z//uf7f//t/AX1MlHHmhRde0P79+zV58mT7tZ2+De+++25dddVV6t+/v5KTkzV48GBNnz5d1157bUAf43kbxvVXCQB1mTZtmvLy8vTmm282d1diql+/ftq0aZMKCwv1/PPPa9KkSVq7dm1zdysmdu7cqdtvv10rVqxQSkpKc3enUVT/FStJJ510koYOHaru3btr8eLFSk1NbcaexYbf71dOTo5++9vfSpIGDx6svLw8PfHEE5o0aVIz9y72nn76aY0ZM0adO3du7q7EzOLFi/WPf/xD//znPzVgwABt2rRJ06dPV+fOnR2zDTkCE4GsrCy53e5aZ5jv3btXHTt2bKZe1U91f8MtS8eOHVVQUBDwfFVVlfbt2xeQCdZGzddobLfddpuWLl2q1atX67jjjrMf79ixoyoqKrR///5a/Yum/6EyGRkZjf4h5PF41Lt3bw0ZMkQPPvigBg0apEcffTQhlm3jxo0qKCjQKaecoqSkJCUlJWnt2rX605/+pKSkJHXo0MHxy3i0Vq1aqW/fvtq+fXtCbMNOnTopOzs74LETTjjBniZLpHHmyy+/1H//+1/dfPPN9mOJsA1nzpxpH4U58cQTdf311+uOO+6wj4o6YRtSwETA4/FoyJAhWrlypf2Y3+/XypUrNWzYsGbsWfR69uypjh07BixLUVGR3n33XXtZhg0bpv3792vjxo12ZtWqVfL7/Ro6dKidWbdunSorK+3MihUr1K9fP7Vu3bpRl8EYo9tuu01LlizRqlWr1LNnz4DnhwwZouTk5IBl3LJli7766quAZfz4448Ddr4VK1YoIyPDHpiHDRsW0EZ1pjm2ud/vV3l5eUIs2znnnKOPP/5YmzZtsn9ycnJ07bXX2v92+jIerbi4WJ9//rk6deqUENtwxIgRtW5dsHXrVnXv3l1SYowz1ebPn6/27dtr3Lhx9mOJsA1LSkrkcgWWAG63W36/X5JDtmGDTwM+RixatMh4vV6zYMEC8+mnn5qf/OQnplWrVgFnmMeLAwcOmA8++MB88MEHRpJ5+OGHzQcffGC+/PJLY8yhS+NatWplXnzxRfPRRx+ZSy65JOilcYMHDzbvvvuuefPNN02fPn0CLo3bv3+/6dChg7n++utNXl6eWbRokUlLS2uSyxtvvfVWk5mZadasWRNwmWNJSYmdmTJliunWrZtZtWqV2bBhgxk2bJgZNmyY/Xz1JY7nnXee2bRpk1m+fLlp165d0EscZ86caTZv3mz+8pe/NMkljnfffbdZu3atyc/PNx999JG5++67jWVZ5vXXX3f8soVS8yokY5y/jL/4xS/MmjVrTH5+vvnf//5nRo8ebbKyskxBQUFCLN/69etNUlKS+c1vfmO2bdtm/vGPf5i0tDTz7LPP2hmnjzPGHLratFu3buauu+6q9ZzTt+GkSZNMly5d7Muo//Of/5isrCwza9YsOxPv25ACJgp//vOfTbdu3YzH4zGnnXaaeeedd5q7S0GtXr3aSKr1M2nSJGPMocvj7rnnHtOhQwfj9XrNOeecY7Zs2RLQxvfff2+uvvpq06JFC5ORkWFuuOEGc+DAgYDMhx9+aM444wzj9XpNly5dzJw5c5pk+YItmyQzf/58O1NaWmqmTp1qWrdubdLS0sxll11mdu/eHdDOF198YcaMGWNSU1NNVlaW+cUvfmEqKysDMqtXrzYnn3yy8Xg8plevXgGv0VhuvPFG0717d+PxeEy7du3MOeecYxcvTl+2UI4uYJy+jFdeeaXp1KmT8Xg8pkuXLubKK68MuEeK05fPGGNefvllM3DgQOP1ek3//v3NX//614DnnT7OGGPMa6+9ZiTV6rcxzt+GRUVF5vbbbzfdunUzKSkpplevXuZXv/pVwOXO8b4NLWNq3HYPAADAATgHBgAAOA4FDAAAcBwKGAAA4DgUMAAAwHEoYAAAgONQwAAAAMehgAEAAI5DAQM0AcuyAn5cLpcyMzN1+umn65FHHgm4zXZTW7BggSzL0r333huzNrdv3y6Px6OZM2c2uK2zzjpLlmXpiy++CHi8R48esiyrwe2HYlmWevTo0WjtN/Xr1PTBBx/IsizNnTu3SV8XiCW+jRpoQtXf8urz+fTFF1/orbfe0rvvvqulS5dq+fLlSkpKjF1y9uzZ8ng8mjVrVnN3BUEMHjxYF198sR588EHdfPPNatOmTXN3CYgaR2CAJrRgwQItWLBAf//73/XGG2/orbfeUkpKilauXKlFixY1d/di4v3339fzzz+vm266Se3atWvu7sS9zZs31/pCv6Ywe/Zs7d+/X7/73e+a/LWBWKCAAZrR0KFDNXnyZEnSa6+91rydiZF58+ZJkiZOnNjMPXGG/v376/jjj2/y1z399NPVu3dvPfPMM6qoqGjy1wcaigIGaGYDBgyQJBUUFAQ8bozRwoULddVVV6lv375KT09Xy5Ytddppp+nxxx+3v/a+pnvvvVeWZWnBggX6+OOPdfHFF6t169ZKT0/XqFGj9NZbb0XVtz/84Q9yuVzq37+/du7cWWe+uLhYixYtUp8+fTRkyJBaz+/evVtz587VqFGj1KVLF3k8HnXs2FGXX3653nvvvaj6Vl/Lly/XxRdfrA4dOsjr9apr16668MIL9e9//zto3ufz6Xe/+5369u1r5++66y6Vl5fXym7atEmzZs3SkCFD1K5dO3m9XvXq1UtTp07Vrl27grYf7ByYNWvWyLIsTZ48Wfv27dOtt96qTp06yev1auDAgXrmmWeCtpWXl6frrrtOvXr1UkpKitq1a6eTTz5Z06dP1+7du2vlr776an333XdasmRJHWsNiD8UMEAzO3DggCSpffv2AY+Xl5frmmuu0X//+1917NhRF110kU4//XR98sknmjZtmm688caQbW7YsEGnn366vvjiC51//vnq06eP1q1bp3POOUd5eXkR9euXv/ylZsyYoSFDhujNN99U165d6/w/a9euVXFxsc4666ygz7/44ou66667tHfvXp100km67LLL1LlzZy1ZskQjRozQ66+/HlHf6usXv/iFxowZo1deeUV9+vTRj3/8Yx1//PH63//+p/vvvz/o/7nmmmv0wAMPqF+/fjrvvPN04MABzZ07VzfddFOt7Jw5c/THP/5RknTGGWdo7NixMsZo3rx5ysnJCVnEhLJ//34NGzZML730kkaOHKkRI0bos88+00033aSnnnoqILtx40adeuqp+sc//qGWLVvqkksu0emnn67Kyko9+uij2rJlS632q7fTK6+8ElW/gLgQk++0BhCWJBNqdzvzzDONJPPss88GPF5ZWWmWLFliKioqAh4vKCgwOTk5RpJZu3ZtwHO5ubn2az366KMBz02fPt1IMtdff33A4/PnzzeSTG5urjHGGJ/PZ37yk58YSebss882RUVFES/nXXfdZSSZv/71r0Gf/+ijj0xeXl6tx5cvX248Ho85/vjjjd/vD3hu1KhRRpLJz88PeLx79+4h12kwf//7340k07lzZ/PBBx8EPFdSUmJef/31gMeq1+MJJ5xgdu/ebT++Y8cO06pVKyPJbN++PeD/rFq1yuzZsyfgMZ/PZ+677z4jydxwww21+iXJdO/ePeCx1atX269/1VVXmbKyMvu5JUuWGEmmW7duAf9n4sSJRpL5/e9/X+s1Nm/ebHbt2lXr8cLCQuNyuWq1BTgBBQzQBI4uYHw+n9m+fbuZMmWKkWQuueQSU1lZGXF7K1asMJLMnXfeGfB4dQEzYsSIWv/nu+++C/phWbOAKS8vNxMmTDCSzKWXXhrwwRmJMWPGBC2sInHttdcaSeajjz4KeDxWBcwJJ5xgJJlFixZFlK/eZitWrKj13G233WYkmfnz50f8+l26dDFt27YN+jqhCpiMjAzz3Xff1fo/AwcOrLVOqtf9pk2bIu5Tdb8kmX379kX1/4DmlhjXbAIOEey+JbfccouefPLJkPc02bRpk15//XV9+eWXKikpkTHGnnbatm1b0P9z3nnn1Xqsbdu2atOmTdBzISTp4MGDuvDCC7VixQpNnjxZTz31lNxud6SLJunIeTytW7cOmSkvL9fy5cu1fv16ffvtt/YJpB9//LG9TCeeeGJUr1uXXbt2afPmzWrVqpWuuOKKiP9fcnKyzj777FqP9+3bV5KCrsvvv/9eL730kvLy8rR//375fD5JUmVlpb7//nvt27cv4suWhwwZorZt2wZ9/by8PO3evds+f2bIkCFatmyZpk2bpgceeEBnnHFGRJflt2nTRt98842+/fbbsNsNiDcUMEATqr4PTFlZmT788EN99tln+tvf/qbhw4fbVyNVq6io0OTJk7Vw4cKQ7VUXMkc77rjjgj7esmVL7du3L+hzjzzyiKqqqjR27Fg988wz9bpJXGFhof06wVSfWHz0TelqCrVMDVF9AnKvXr2iWq6OHTsGLeKql+/oE3kXLlyon/zkJyouLg7Z5oEDByIuYMJtx6Nff+bMmXrzzTe1Zs0anX322WrRooWGDRumcePGafLkycrMzAzaVkZGhqRD59sATsJJvEATqr4PzKJFi7R582b7TqjTpk3Tl19+GZB9+OGHtXDhQp144olatmyZ9u7dq4qKChlj7BMyjTFBX8flin7XHjNmjDIzM/X666+HvCKnLtUfksGKEGOMrrjiCn3xxReaMmWKNm3apKKiIvn9fhljNHv2bDsXL6JZj19++aUmT56siooKPfLII9q2bZt9xMwYo2HDhkmKbvmief2MjAytWrVKb7zxhmbNmqXs7GytWrVK06dPV79+/UIerasuOlu1ahXxawHxgAIGaEYzZ87Ueeedp5KSEt13330Bz1Vf2rpw4UJdcMEFat++vZKTkyVJO3bsiHlfTjnlFL322mtKS0vT1Vdfrf/85z9Rt1F9JVWwozyfffaZPvvsM+Xk5GjevHkaNGiQWrZsaR8RaYxlqlZ9BdWOHTsarUB69dVXVVFRoZ///Oe6/fbb1bt3b6WmptrPN+byVbMsS2eccYZ+97vf6d1339WuXbt09dVXa+/evfrVr34V9P/88MMPksRNB+E4FDBAM5szZ44k6e9//3vAUZjqD5Zg0wiLFy9ulL4MHTpUy5cvV2pqqq666iq9+OKLUf3/QYMGSVLQS3bDLc8PP/ygFStW1KPHkencubNOOOEE7d+/X88991yjvEa45Vu3bp327t3bKK8bTvv27e3vuAp2+XxRUZF27dqlbt26cf4LHIcCBmhmgwcP1qWXXqqqqqqAL9erPlH0iSeeCMg///zz+r//+79G68+wYcO0fPlyeb1eXXHFFXr55Zcj/r8jR46UpKA3pevdu7dcLpdWrVoVMJ1RVlamKVOmhDw3J1buvvtuSdKdd96pjz76KOC5srKyBhdQ1dvr2Wef1cGDB+3Hv/nmG02ZMqVBbUfiiSeeUH5+fq3HX331VUkKeh+f9957T8YYjRo1qtH7B8QaBQwQB6rvoPvMM89oz549kqRZs2bJ7Xbr7rvvVk5Ojq655hqdeuqpmjBhgu64445G7c/w4cO1bNkyJScna/z48RHf6OzMM89UixYttGbNmlrPtW/fXjfddJOKioo0aNAgXXjhhZowYYJ69OihVatW1TqJOdYmTpyon/3sZ/rmm290yimnaOTIkbrmmmt09tlnq1OnTg3+5uyLL75YAwYM0IYNG9S7d2+NHz9eF154ofr27avWrVtr+PDhMVqS4J544gn16tVLAwYM0Pjx43XVVVfp5JNP1h133KGUlBT9+te/rvV/qrfTuHHjGrVvQGOggAHiwKBBg3TZZZeprKxMDz/8sKRDxcCbb76pH/3oR9qxY4eWLl0qj8ejf//735o2bVqj9+mMM87Qq6++quTkZP34xz/W8uXL6/w/LVq00NVXX63t27cHPQozb948/eEPf1DPnj21cuVKvfHGGxo9erQ2bNig7t27N8ZiBPjTn/6kF198UaNHj9ann36qf//739q+fbvOOOMM5ebmNqhtj8ejN954Q7feeqtSUlK0dOlSbd68WT/72c+0YsUK+/ylxnL//ffrxhtvlGVZWrlypV5++WWVlpbq5ptv1qZNmzRixIha/2fhwoXKysrSZZdd1qh9AxqDZeLplH8Ajrdp0yYNHjxYt912m/785z83d3cQwttvv63hw4dr1qxZfCM1HIkCBkDMXXHFFXrllVeUn59f6zueEB8uueQSrVu3Tp9//nnE96UB4glTSABi7sEHH1RlZWXAScmIHx988IFeeuklzZ49m+IFjsURGAAA4DgcgQEAAI5DAQMAAByHAgYAADgOBQwAAHAcChgAAOA4FDAAAMBxKGAAAIDjUMAAAADHoYABAACOQwEDAAAc5/8D2kklD8qwYHcAAAAASUVORK5CYII="
    }
   },
   "cell_type": "markdown",
   "id": "86b7b904",
   "metadata": {},
   "source": [
    "#### Rank Plots\n",
    "![rank_plot.png](attachment:rank_plot.png)\n",
    "<t><center>Figure 3. Rank plots.</center></t>\n",
    "To quickly tell if our sampler worked correctly, we can look at rank plots, which show us one histogram for each unobserved variable in the model and each chain in the sampler. I ran four chains. Thus, there are four histograms. We are looking to see if the sampler has explored the whole posterior distribution, and if we restarted the sampler from a different initial point, it should also explore the whole posterior distribution. If the sampler is working correctly, we will see a uniform distribution that lies close to the dashed black line. Looking at Figure 3, we observe that all of our four chains are approximately uniform, which means that our sampler explores the whole posterior distribution across all ranks and doesn't get stuck in a particular place of the distribution. "
   ]
  },
  {
   "attachments": {
    "trace_plot.png": {
     "image/png": 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"
    }
   },
   "cell_type": "markdown",
   "id": "f4c787c5",
   "metadata": {},
   "source": [
    "#### Trace Plot\n",
    "![trace_plot.png](attachment:trace_plot.png)\n",
    "<t><center>Figure 4. Trace plot.</center></t>\n",
    "The last thing that we will look at is trace plots that output two plots. On the left, we see all the sample distributions for $p$ value. It is clear from the graph that all four samples are converging and have similar shapes and peaks around $p\\approx0.35.$ This is another indicator that the sampler is working correctly. On the right side, we see the trace plot that represents how each chain sample $p$ values out of 2000 trials. In this graph, we want a lot of fluctuation, which represents that different values of $p$ were sampled by each chain within each trail. This means that the sampler did not get stuck on one particular value of $p$, and it took steps in all directions.\n",
    "$ \\\\ $\n",
    "\n",
    "#### Summary\n",
    "In summary, the posterior distribution indicates that the mean value of $p$ is approximately $p=0.345.$ The $95\\%$ credible interval is $[0.28, 0.417]$  meaning that $95\\%$ mass of all values lay within these two bounds. As a side note, McElreath 2020 uses compatibility intervals instead of credible intervals, and this definition might be more accurate and defines it as \" a range of parameter values compatible with the model and data\" (McElreath, 2020, p. 54). This definition steers away from words such as credibility and confidence since if the model is wrong, so are $95\\%$ intervals, and one cannot be confident about them. However, in the context of this setup and data, I am positive that we can be confident about these intervals. We walked through how different diagnostics tests helpt us with ensuring that sampling procedure has been successful and that Markov Chains have converged. We reported $\\hat{R}$ value, alongside with Effective Sample Sizes and other statistics that are relevant for evaluating sampling process. We display the results of the sampling approximation approach in the figure 6 below."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "904aa33f",
   "metadata": {},
   "source": [
    " \n",
    "\n",
    "The second approach to fit the posterior is finding the posterior analytically. Since we only have twenty data points and are using beta distribution as a prior, it will be easy to use this approach and find the exact value of $p$. However, this approach is not always useful since it is hard to compute the exact posterior if the dataset is large or the prior is not a conjugate. \n",
    "\n",
    "After some research, it was found that given that the prior follows a beta distribution and that given a sample \n",
    "<t><center>$x=(x_1,....x_n)$</center></t> \n",
    "of negative-binomial data. The posterior distribution will be given by: \n",
    "<t><center>$p(\\theta|x) \\sim Beta(\\alpha+rn,\\beta+\\sum_{i=1}^{n}x_i$)</center></t> \n",
    "Where n is the number of data points (Bernardo et al., 1994), in our case, n=20, and r is the number of successes, $r=3$. \n",
    "Thus, we have: \n",
    "<t><center>$p(\\theta|x) \\sim Beta(\\alpha+3\\cdot 20,\\beta+\\sum_{i=1}^{20}x_i$)</center></t> \n",
    "Using this formula and Python, the exact posterior can be easily computed analytically. This calculation is performed above using this code line: \n",
    "\n",
    "<t><center>$y = sts.beta.pdf(x, alpha+len(data)*r, beta+sum(data))$</center></t>\n",
    "\n",
    "The resulting plot comparing the exact posterior and posterior obtained using sampling approximation was coded above and is also given in the figure below.  "
   ]
  },
  {
   "attachments": {
    "exact_and_sample_posterior.png": {
     "image/png": 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"
    }
   },
   "cell_type": "markdown",
   "id": "c86e5ab1",
   "metadata": {},
   "source": [
    "![exact_and_sample_posterior.png](attachment:exact_and_sample_posterior.png)\n",
    "<t><center>Figure 6. Comparison of the sampling approximation and the exact posterior.</center></t>\n",
    "\n",
    "\n",
    "In figure 6, we have superimposed the posterior distribution that was obtained from sampling approximation and the posterior distribution that we have calculated analytically. We also obtained the mean values from these distributions: \n",
    "\n",
    "<t><center>Analytical mean = 0.343</center></t>\n",
    "<t><center>Sample mean = 0.345</center></t>\n",
    "We can see that there is very minimal difference between the plots and expected values. Thus, this comparison further reinforces our belief that sampling has worked well. It has to be mentioned that often, we cannot use the second approach, but it was a nice touch that we could calculate and see the analytical posterior. "
   ]
  },
  {
   "cell_type": "markdown",
   "id": "d76c80f8",
   "metadata": {},
   "source": [
    "## Problem 2. Create a prior\n",
    "\n",
    "We want to model purchasing behavior at an e-commerce company. For each customer, we model the average amount of money they spend per month. Set up an appropriate model (likelihood and prior) such that the median of the average amount of money spent per customer per month is JPY 10,000 (ten thousand Japanese yen) and that 80% of customers have an average spend between JPY 1,000 and JPY 30,000.\n",
    "\n",
    "* Motivate our choices for the prior distribution and likelihood function.\n",
    "* Show that samples from the prior-predictive distribution have the percentiles indicated above. (This can be approximate but you have to quantify how close you are to the desired values.)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "99b2baaf",
   "metadata": {},
   "source": [
    "### Reasoning for Prior\n",
    "Given the information above and some common sense we can infer several things. Firstly, the domain of the target prior distribution should not contain negative values. The reasoning behind this is that one cannot spend negative amount of money. Secondly, from simple supply-demand and the way wealth is distributed in Japan, we know that the quantity demanded decreases as the items get more expensive. This would mean that the average monthly expenditure would be assymetric and left-skewed. Finally, we know that the median of the average amount of money spent per costumer per month is JPY 10000 and that $80\\%$ of costumers have an average monthly spend between JPY $[1000,30000]$. \n",
    "\n",
    "#### Likelihood \n",
    "<t><center>$x_i \\sim TruncatedNormal(µ,\\sigma^2,\\alpha,\\beta)$</center></t>\n",
    "With the assumptions above and information provided in the prompt it can be argued that the likelihood function which describes the average monthly consumer spending can follow truncated normal distribution. Truncated normal distribution is quite convenient since we can define upper and lower bounds accordingly following the support: $x\\in[0,150000]$. This is convenient for two reasons. First, the resulting distribution will not include negative values, since one cannot spend $-x$ amount of money and secondly, since it is an e-commerce company we make an assumption that a given costumer can not spend above 150000 JPY per month on average. This assumption is justified by the fact that people do not tend to spend large sums of money online and they would rather spend more in-person. Thus, an arbitrary cap at 150000 JPY was created that is approximately equivalent to 1000 US. \n",
    "\n",
    "The likelihood function is as follows \n",
    "<t><center>$x_i \\sim TruncatedNormal(µ,\\sigma^2,\\alpha=\\frac{0-µ}{\\sigma},\\beta=\\frac{150000-µ}{\\sigma})$</center></t>\n",
    "#### Prior\n",
    "<t><center>$ \\sigma^2 \\sim Uniform (0,10)$</center></t>\n",
    "<t><center>$ \\mu \\sim LogNormal (µ,\\sigma^2)$</center></t>\n",
    "We chose two prior distribution over two unknown parameters in the likelihood function: $\\mu$ and $\\sigma^2$. In the Truncated-normal distribution $\\mu$ represents the mean while $\\sigma^2$ represents variance. We chose these distributions for the priors since $\\mu$ represents the average monthly spending in JPY and cannot take negative values and has a left skew. LogNormal distribution satisfies all of these requirements. The prior distribution over sigma parameter was more of an arbitrary choice since sigma can take many different values and will only impact the spread of the distribution. Thus, unifrom distribution was chosen to assign same probability for all values between 0 and 10. \n",
    "\n",
    "#### Optimizing Hyperparameters \n",
    "\n",
    "To optimize the prior hyperparameters within LogNormal distribution several equations were employed. \n",
    "Firstly we used median = 10000 to find $\\mu:$\n",
    "<t><center>$ median = exp(\\mu) $</center></t>\n",
    "<t><center>$ \\mu = \\log(median) $</center></t>\n",
    "<t><center>$ \\mu = \\log(10000) $</center></t>\n",
    "<t><center>$ \\mu \\approx 9.21 $</center></t>\n",
    "\n",
    "We also calculated $\\sigma^2$ using maximum likelihood formula: \n",
    "<t><center>$ Z = \\frac{x-\\mu}{\\sigma}$</center></t>\n",
    "and used $\\log(median)$ and $90\\%$th percentile upper bound which is 30000 JPY: \n",
    "<t><center>$ \\sigma = \\frac{x-\\mu}{Z}$</center></t>\n",
    "<t><center>$ \\sigma = \\frac{30000-\\log(10000)}{1.28}$</center></t>\n",
    "Finally, we will take $\\frac{30000-\\log(10000)}{1.28}$ and square it to obtain $\\sigma^2.$\n",
    "The calculations are shown below. \n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "a10173a5",
   "metadata": {},
   "outputs": [],
   "source": [
    "# Known Variables\n",
    "from scipy.stats import norm\n",
    "median = 10000\n",
    "lower_bound = 1000\n",
    "upper_bound = 30000\n",
    "Z = norm.ppf(0.9)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "id": "646bb423",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<IPython.core.display.Image object>"
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Defining the model\n",
    "with pm.Model() as eccomerce_model:\n",
    "    # Prior\n",
    "    σ = pm.Uniform('σ',0,1)\n",
    "    µ = pm.Lognormal('µ', \n",
    "                           # Find mu  \n",
    "                           mu = np.log(median), \n",
    "                           # Find sigma using formula σ = (x-µ)/z. x = 30000 (upper bound)\n",
    "                           sigma = (np.log(upper_bound) - np.log(median)) / norm.ppf(0.9))**2 \n",
    "    \n",
    "    # Truncated Normal likelihood\n",
    "    pm.TruncatedNormal('x', mu=µ, sigma=np.sqrt(σ), lower = (0-10000)/σ, \n",
    "                       upper = (150000-10000)/σ, observed = 1) # Set observed to an arbitrary value\n",
    "\n",
    "from IPython.display import Image\n",
    "Image(pm.model_to_graphviz(eccomerce_model).render(format='png'))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "id": "4b29bfdb",
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Sampling: [x, µ, σ]\n"
     ]
    },
    {
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       "  --xr-disabled-color: var(--jp-layout-color3, #bdbdbd);\n",
       "  --xr-background-color: var(--jp-layout-color0, white);\n",
       "  --xr-background-color-row-even: var(--jp-layout-color1, white);\n",
       "  --xr-background-color-row-odd: var(--jp-layout-color2, #eeeeee);\n",
       "}\n",
       "\n",
       "html[theme=dark],\n",
       "body[data-theme=dark],\n",
       "body.vscode-dark {\n",
       "  --xr-font-color0: rgba(255, 255, 255, 1);\n",
       "  --xr-font-color2: rgba(255, 255, 255, 0.54);\n",
       "  --xr-font-color3: rgba(255, 255, 255, 0.38);\n",
       "  --xr-border-color: #1F1F1F;\n",
       "  --xr-disabled-color: #515151;\n",
       "  --xr-background-color: #111111;\n",
       "  --xr-background-color-row-even: #111111;\n",
       "  --xr-background-color-row-odd: #313131;\n",
       "}\n",
       "\n",
       ".xr-wrap {\n",
       "  display: block !important;\n",
       "  min-width: 300px;\n",
       "  max-width: 700px;\n",
       "}\n",
       "\n",
       ".xr-text-repr-fallback {\n",
       "  /* fallback to plain text repr when CSS is not injected (untrusted notebook) */\n",
       "  display: none;\n",
       "}\n",
       "\n",
       ".xr-header {\n",
       "  padding-top: 6px;\n",
       "  padding-bottom: 6px;\n",
       "  margin-bottom: 4px;\n",
       "  border-bottom: solid 1px var(--xr-border-color);\n",
       "}\n",
       "\n",
       ".xr-header > div,\n",
       ".xr-header > ul {\n",
       "  display: inline;\n",
       "  margin-top: 0;\n",
       "  margin-bottom: 0;\n",
       "}\n",
       "\n",
       ".xr-obj-type,\n",
       ".xr-array-name {\n",
       "  margin-left: 2px;\n",
       "  margin-right: 10px;\n",
       "}\n",
       "\n",
       ".xr-obj-type {\n",
       "  color: var(--xr-font-color2);\n",
       "}\n",
       "\n",
       ".xr-sections {\n",
       "  padding-left: 0 !important;\n",
       "  display: grid;\n",
       "  grid-template-columns: 150px auto auto 1fr 20px 20px;\n",
       "}\n",
       "\n",
       ".xr-section-item {\n",
       "  display: contents;\n",
       "}\n",
       "\n",
       ".xr-section-item input {\n",
       "  display: none;\n",
       "}\n",
       "\n",
       ".xr-section-item input + label {\n",
       "  color: var(--xr-disabled-color);\n",
       "}\n",
       "\n",
       ".xr-section-item input:enabled + label {\n",
       "  cursor: pointer;\n",
       "  color: var(--xr-font-color2);\n",
       "}\n",
       "\n",
       ".xr-section-item input:enabled + label:hover {\n",
       "  color: var(--xr-font-color0);\n",
       "}\n",
       "\n",
       ".xr-section-summary {\n",
       "  grid-column: 1;\n",
       "  color: var(--xr-font-color2);\n",
       "  font-weight: 500;\n",
       "}\n",
       "\n",
       ".xr-section-summary > span {\n",
       "  display: inline-block;\n",
       "  padding-left: 0.5em;\n",
       "}\n",
       "\n",
       ".xr-section-summary-in:disabled + label {\n",
       "  color: var(--xr-font-color2);\n",
       "}\n",
       "\n",
       ".xr-section-summary-in + label:before {\n",
       "  display: inline-block;\n",
       "  content: '►';\n",
       "  font-size: 11px;\n",
       "  width: 15px;\n",
       "  text-align: center;\n",
       "}\n",
       "\n",
       ".xr-section-summary-in:disabled + label:before {\n",
       "  color: var(--xr-disabled-color);\n",
       "}\n",
       "\n",
       ".xr-section-summary-in:checked + label:before {\n",
       "  content: '▼';\n",
       "}\n",
       "\n",
       ".xr-section-summary-in:checked + label > span {\n",
       "  display: none;\n",
       "}\n",
       "\n",
       ".xr-section-summary,\n",
       ".xr-section-inline-details {\n",
       "  padding-top: 4px;\n",
       "  padding-bottom: 4px;\n",
       "}\n",
       "\n",
       ".xr-section-inline-details {\n",
       "  grid-column: 2 / -1;\n",
       "}\n",
       "\n",
       ".xr-section-details {\n",
       "  display: none;\n",
       "  grid-column: 1 / -1;\n",
       "  margin-bottom: 5px;\n",
       "}\n",
       "\n",
       ".xr-section-summary-in:checked ~ .xr-section-details {\n",
       "  display: contents;\n",
       "}\n",
       "\n",
       ".xr-array-wrap {\n",
       "  grid-column: 1 / -1;\n",
       "  display: grid;\n",
       "  grid-template-columns: 20px auto;\n",
       "}\n",
       "\n",
       ".xr-array-wrap > label {\n",
       "  grid-column: 1;\n",
       "  vertical-align: top;\n",
       "}\n",
       "\n",
       ".xr-preview {\n",
       "  color: var(--xr-font-color3);\n",
       "}\n",
       "\n",
       ".xr-array-preview,\n",
       ".xr-array-data {\n",
       "  padding: 0 5px !important;\n",
       "  grid-column: 2;\n",
       "}\n",
       "\n",
       ".xr-array-data,\n",
       ".xr-array-in:checked ~ .xr-array-preview {\n",
       "  display: none;\n",
       "}\n",
       "\n",
       ".xr-array-in:checked ~ .xr-array-data,\n",
       ".xr-array-preview {\n",
       "  display: inline-block;\n",
       "}\n",
       "\n",
       ".xr-dim-list {\n",
       "  display: inline-block !important;\n",
       "  list-style: none;\n",
       "  padding: 0 !important;\n",
       "  margin: 0;\n",
       "}\n",
       "\n",
       ".xr-dim-list li {\n",
       "  display: inline-block;\n",
       "  padding: 0;\n",
       "  margin: 0;\n",
       "}\n",
       "\n",
       ".xr-dim-list:before {\n",
       "  content: '(';\n",
       "}\n",
       "\n",
       ".xr-dim-list:after {\n",
       "  content: ')';\n",
       "}\n",
       "\n",
       ".xr-dim-list li:not(:last-child):after {\n",
       "  content: ',';\n",
       "  padding-right: 5px;\n",
       "}\n",
       "\n",
       ".xr-has-index {\n",
       "  font-weight: bold;\n",
       "}\n",
       "\n",
       ".xr-var-list,\n",
       ".xr-var-item {\n",
       "  display: contents;\n",
       "}\n",
       "\n",
       ".xr-var-item > div,\n",
       ".xr-var-item label,\n",
       ".xr-var-item > .xr-var-name span {\n",
       "  background-color: var(--xr-background-color-row-even);\n",
       "  margin-bottom: 0;\n",
       "}\n",
       "\n",
       ".xr-var-item > .xr-var-name:hover span {\n",
       "  padding-right: 5px;\n",
       "}\n",
       "\n",
       ".xr-var-list > li:nth-child(odd) > div,\n",
       ".xr-var-list > li:nth-child(odd) > label,\n",
       ".xr-var-list > li:nth-child(odd) > .xr-var-name span {\n",
       "  background-color: var(--xr-background-color-row-odd);\n",
       "}\n",
       "\n",
       ".xr-var-name {\n",
       "  grid-column: 1;\n",
       "}\n",
       "\n",
       ".xr-var-dims {\n",
       "  grid-column: 2;\n",
       "}\n",
       "\n",
       ".xr-var-dtype {\n",
       "  grid-column: 3;\n",
       "  text-align: right;\n",
       "  color: var(--xr-font-color2);\n",
       "}\n",
       "\n",
       ".xr-var-preview {\n",
       "  grid-column: 4;\n",
       "}\n",
       "\n",
       ".xr-index-preview {\n",
       "  grid-column: 2 / 5;\n",
       "  color: var(--xr-font-color2);\n",
       "}\n",
       "\n",
       ".xr-var-name,\n",
       ".xr-var-dims,\n",
       ".xr-var-dtype,\n",
       ".xr-preview,\n",
       ".xr-attrs dt {\n",
       "  white-space: nowrap;\n",
       "  overflow: hidden;\n",
       "  text-overflow: ellipsis;\n",
       "  padding-right: 10px;\n",
       "}\n",
       "\n",
       ".xr-var-name:hover,\n",
       ".xr-var-dims:hover,\n",
       ".xr-var-dtype:hover,\n",
       ".xr-attrs dt:hover {\n",
       "  overflow: visible;\n",
       "  width: auto;\n",
       "  z-index: 1;\n",
       "}\n",
       "\n",
       ".xr-var-attrs,\n",
       ".xr-var-data,\n",
       ".xr-index-data {\n",
       "  display: none;\n",
       "  background-color: var(--xr-background-color) !important;\n",
       "  padding-bottom: 5px !important;\n",
       "}\n",
       "\n",
       ".xr-var-attrs-in:checked ~ .xr-var-attrs,\n",
       ".xr-var-data-in:checked ~ .xr-var-data,\n",
       ".xr-index-data-in:checked ~ .xr-index-data {\n",
       "  display: block;\n",
       "}\n",
       "\n",
       ".xr-var-data > table {\n",
       "  float: right;\n",
       "}\n",
       "\n",
       ".xr-var-name span,\n",
       ".xr-var-data,\n",
       ".xr-index-name div,\n",
       ".xr-index-data,\n",
       ".xr-attrs {\n",
       "  padding-left: 25px !important;\n",
       "}\n",
       "\n",
       ".xr-attrs,\n",
       ".xr-var-attrs,\n",
       ".xr-var-data,\n",
       ".xr-index-data {\n",
       "  grid-column: 1 / -1;\n",
       "}\n",
       "\n",
       "dl.xr-attrs {\n",
       "  padding: 0;\n",
       "  margin: 0;\n",
       "  display: grid;\n",
       "  grid-template-columns: 125px auto;\n",
       "}\n",
       "\n",
       ".xr-attrs dt,\n",
       ".xr-attrs dd {\n",
       "  padding: 0;\n",
       "  margin: 0;\n",
       "  float: left;\n",
       "  padding-right: 10px;\n",
       "  width: auto;\n",
       "}\n",
       "\n",
       ".xr-attrs dt {\n",
       "  font-weight: normal;\n",
       "  grid-column: 1;\n",
       "}\n",
       "\n",
       ".xr-attrs dt:hover span {\n",
       "  display: inline-block;\n",
       "  background: var(--xr-background-color);\n",
       "  padding-right: 10px;\n",
       "}\n",
       "\n",
       ".xr-attrs dd {\n",
       "  grid-column: 2;\n",
       "  white-space: pre-wrap;\n",
       "  word-break: break-all;\n",
       "}\n",
       "\n",
       ".xr-icon-database,\n",
       ".xr-icon-file-text2,\n",
       ".xr-no-icon {\n",
       "  display: inline-block;\n",
       "  vertical-align: middle;\n",
       "  width: 1em;\n",
       "  height: 1.5em !important;\n",
       "  stroke-width: 0;\n",
       "  stroke: currentColor;\n",
       "  fill: currentColor;\n",
       "}\n",
       "</style><pre class='xr-text-repr-fallback'>&lt;xarray.Dataset&gt;\n",
       "Dimensions:  (chain: 1, draw: 10000)\n",
       "Coordinates:\n",
       "  * chain    (chain) int64 0\n",
       "  * draw     (draw) int64 0 1 2 3 4 5 6 7 ... 9993 9994 9995 9996 9997 9998 9999\n",
       "Data variables:\n",
       "    σ        (chain, draw) float64 9.029 0.9953 9.476 ... 2.273 1.382 7.598\n",
       "    µ        (chain, draw) float64 3.813e+03 8.791e+03 ... 4.472e+03 1.074e+04\n",
       "Attributes:\n",
       "    created_at:                 2024-01-30T22:17:16.346161\n",
       "    arviz_version:              0.17.0\n",
       "    inference_library:          pymc\n",
       "    inference_library_version:  5.10.3</pre><div class='xr-wrap' style='display:none'><div class='xr-header'><div class='xr-obj-type'>xarray.Dataset</div></div><ul class='xr-sections'><li class='xr-section-item'><input id='section-cbba35d8-c2cc-4912-a32e-c14c290e4ca6' class='xr-section-summary-in' type='checkbox' disabled ><label for='section-cbba35d8-c2cc-4912-a32e-c14c290e4ca6' class='xr-section-summary'  title='Expand/collapse section'>Dimensions:</label><div class='xr-section-inline-details'><ul class='xr-dim-list'><li><span class='xr-has-index'>chain</span>: 1</li><li><span class='xr-has-index'>draw</span>: 10000</li></ul></div><div class='xr-section-details'></div></li><li class='xr-section-item'><input id='section-e8ee2631-a85b-4704-8549-a6dd690e2cf2' class='xr-section-summary-in' type='checkbox'  checked><label for='section-e8ee2631-a85b-4704-8549-a6dd690e2cf2' class='xr-section-summary' >Coordinates: <span>(2)</span></label><div class='xr-section-inline-details'></div><div class='xr-section-details'><ul class='xr-var-list'><li class='xr-var-item'><div class='xr-var-name'><span class='xr-has-index'>chain</span></div><div class='xr-var-dims'>(chain)</div><div class='xr-var-dtype'>int64</div><div class='xr-var-preview xr-preview'>0</div><input id='attrs-3124ad77-c5cf-494d-b71f-dc2d4cbd979b' class='xr-var-attrs-in' type='checkbox' disabled><label for='attrs-3124ad77-c5cf-494d-b71f-dc2d4cbd979b' title='Show/Hide attributes'><svg class='icon xr-icon-file-text2'><use xlink:href='#icon-file-text2'></use></svg></label><input id='data-3f47d33a-895e-4fc8-bc48-aa5864bb628d' class='xr-var-data-in' type='checkbox'><label for='data-3f47d33a-895e-4fc8-bc48-aa5864bb628d' title='Show/Hide data repr'><svg class='icon xr-icon-database'><use xlink:href='#icon-database'></use></svg></label><div class='xr-var-attrs'><dl class='xr-attrs'></dl></div><div class='xr-var-data'><pre>array([0])</pre></div></li><li class='xr-var-item'><div class='xr-var-name'><span class='xr-has-index'>draw</span></div><div class='xr-var-dims'>(draw)</div><div class='xr-var-dtype'>int64</div><div class='xr-var-preview xr-preview'>0 1 2 3 4 ... 9996 9997 9998 9999</div><input id='attrs-c09d796e-74e5-4766-a289-e23dc284f004' class='xr-var-attrs-in' type='checkbox' disabled><label for='attrs-c09d796e-74e5-4766-a289-e23dc284f004' title='Show/Hide attributes'><svg class='icon xr-icon-file-text2'><use xlink:href='#icon-file-text2'></use></svg></label><input id='data-4600ffbe-5812-400a-ac3b-8f934b81a6b5' class='xr-var-data-in' type='checkbox'><label for='data-4600ffbe-5812-400a-ac3b-8f934b81a6b5' title='Show/Hide data repr'><svg class='icon xr-icon-database'><use xlink:href='#icon-database'></use></svg></label><div class='xr-var-attrs'><dl class='xr-attrs'></dl></div><div class='xr-var-data'><pre>array([   0,    1,    2, ..., 9997, 9998, 9999])</pre></div></li></ul></div></li><li class='xr-section-item'><input id='section-c5a8d462-5a69-4b17-ac4c-38d0d81ff758' class='xr-section-summary-in' type='checkbox'  checked><label for='section-c5a8d462-5a69-4b17-ac4c-38d0d81ff758' class='xr-section-summary' >Data variables: <span>(2)</span></label><div class='xr-section-inline-details'></div><div class='xr-section-details'><ul class='xr-var-list'><li class='xr-var-item'><div class='xr-var-name'><span>σ</span></div><div class='xr-var-dims'>(chain, draw)</div><div class='xr-var-dtype'>float64</div><div class='xr-var-preview xr-preview'>9.029 0.9953 9.476 ... 1.382 7.598</div><input id='attrs-7810eec8-bf90-45ce-91e4-e9e899a452ac' class='xr-var-attrs-in' type='checkbox' disabled><label for='attrs-7810eec8-bf90-45ce-91e4-e9e899a452ac' title='Show/Hide attributes'><svg class='icon xr-icon-file-text2'><use xlink:href='#icon-file-text2'></use></svg></label><input id='data-14deb9a4-e53c-406b-87ef-a8efb40fa96c' class='xr-var-data-in' type='checkbox'><label for='data-14deb9a4-e53c-406b-87ef-a8efb40fa96c' title='Show/Hide data repr'><svg class='icon xr-icon-database'><use xlink:href='#icon-database'></use></svg></label><div class='xr-var-attrs'><dl class='xr-attrs'></dl></div><div class='xr-var-data'><pre>array([[9.02936294, 0.99533994, 9.4761615 , ..., 2.27322573, 1.38237588,\n",
       "        7.5984923 ]])</pre></div></li><li class='xr-var-item'><div class='xr-var-name'><span>µ</span></div><div class='xr-var-dims'>(chain, draw)</div><div class='xr-var-dtype'>float64</div><div class='xr-var-preview xr-preview'>3.813e+03 8.791e+03 ... 1.074e+04</div><input id='attrs-540f9264-af9f-4cfa-8c01-421f7596b0d3' class='xr-var-attrs-in' type='checkbox' disabled><label for='attrs-540f9264-af9f-4cfa-8c01-421f7596b0d3' title='Show/Hide attributes'><svg class='icon xr-icon-file-text2'><use xlink:href='#icon-file-text2'></use></svg></label><input id='data-99bc30d5-2d79-42c7-b98b-0c1a9edef2b3' class='xr-var-data-in' type='checkbox'><label for='data-99bc30d5-2d79-42c7-b98b-0c1a9edef2b3' title='Show/Hide data repr'><svg class='icon xr-icon-database'><use xlink:href='#icon-database'></use></svg></label><div class='xr-var-attrs'><dl class='xr-attrs'></dl></div><div class='xr-var-data'><pre>array([[ 3813.0687096 ,  8790.50581868,  2636.35934631, ...,\n",
       "        14953.33298383,  4471.77378128, 10735.54873055]])</pre></div></li></ul></div></li><li class='xr-section-item'><input id='section-2a6ba683-4e68-42e3-89df-dd2303ad2bc2' class='xr-section-summary-in' type='checkbox'  ><label for='section-2a6ba683-4e68-42e3-89df-dd2303ad2bc2' class='xr-section-summary' >Indexes: <span>(2)</span></label><div class='xr-section-inline-details'></div><div class='xr-section-details'><ul class='xr-var-list'><li class='xr-var-item'><div class='xr-index-name'><div>chain</div></div><div class='xr-index-preview'>PandasIndex</div><div></div><input id='index-a983a151-6634-43c3-9018-52e90e4ba9d0' class='xr-index-data-in' type='checkbox'/><label for='index-a983a151-6634-43c3-9018-52e90e4ba9d0' title='Show/Hide index repr'><svg class='icon xr-icon-database'><use xlink:href='#icon-database'></use></svg></label><div class='xr-index-data'><pre>PandasIndex(Int64Index([0], dtype=&#x27;int64&#x27;, name=&#x27;chain&#x27;))</pre></div></li><li class='xr-var-item'><div class='xr-index-name'><div>draw</div></div><div class='xr-index-preview'>PandasIndex</div><div></div><input id='index-def5b04f-239c-4f8c-bce5-ce76ba694300' class='xr-index-data-in' type='checkbox'/><label for='index-def5b04f-239c-4f8c-bce5-ce76ba694300' title='Show/Hide index repr'><svg class='icon xr-icon-database'><use xlink:href='#icon-database'></use></svg></label><div class='xr-index-data'><pre>PandasIndex(Int64Index([   0,    1,    2,    3,    4,    5,    6,    7,    8,    9,\n",
       "            ...\n",
       "            9990, 9991, 9992, 9993, 9994, 9995, 9996, 9997, 9998, 9999],\n",
       "           dtype=&#x27;int64&#x27;, name=&#x27;draw&#x27;, length=10000))</pre></div></li></ul></div></li><li class='xr-section-item'><input id='section-654b1ac7-d962-48d7-852c-c29224516943' class='xr-section-summary-in' type='checkbox'  checked><label for='section-654b1ac7-d962-48d7-852c-c29224516943' class='xr-section-summary' >Attributes: <span>(4)</span></label><div class='xr-section-inline-details'></div><div class='xr-section-details'><dl class='xr-attrs'><dt><span>created_at :</span></dt><dd>2024-01-30T22:17:16.346161</dd><dt><span>arviz_version :</span></dt><dd>0.17.0</dd><dt><span>inference_library :</span></dt><dd>pymc</dd><dt><span>inference_library_version :</span></dt><dd>5.10.3</dd></dl></div></li></ul></div></div><br></div>\n",
       "                      </ul>\n",
       "                  </div>\n",
       "            </li>\n",
       "            \n",
       "            <li class = \"xr-section-item\">\n",
       "                  <input id=\"idata_prior_predictive2fbb692a-32dc-48ab-b7c2-cc111d26351c\" class=\"xr-section-summary-in\" type=\"checkbox\">\n",
       "                  <label for=\"idata_prior_predictive2fbb692a-32dc-48ab-b7c2-cc111d26351c\" class = \"xr-section-summary\">prior_predictive</label>\n",
       "                  <div class=\"xr-section-inline-details\"></div>\n",
       "                  <div class=\"xr-section-details\">\n",
       "                      <ul id=\"xr-dataset-coord-list\" class=\"xr-var-list\">\n",
       "                          <div style=\"padding-left:2rem;\"><div><svg style=\"position: absolute; width: 0; height: 0; overflow: hidden\">\n",
       "<defs>\n",
       "<symbol id=\"icon-database\" viewBox=\"0 0 32 32\">\n",
       "<path d=\"M16 0c-8.837 0-16 2.239-16 5v4c0 2.761 7.163 5 16 5s16-2.239 16-5v-4c0-2.761-7.163-5-16-5z\"></path>\n",
       "<path d=\"M16 17c-8.837 0-16-2.239-16-5v6c0 2.761 7.163 5 16 5s16-2.239 16-5v-6c0 2.761-7.163 5-16 5z\"></path>\n",
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       "\n",
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       "\n",
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       "\n",
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       "\n",
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       "\n",
       ".xr-section-summary-in:disabled + label:before {\n",
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       "\n",
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       "\n",
       ".xr-section-summary-in:checked + label > span {\n",
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       "\n",
       ".xr-section-summary,\n",
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       "  padding-top: 4px;\n",
       "  padding-bottom: 4px;\n",
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       "\n",
       ".xr-section-inline-details {\n",
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       "\n",
       ".xr-section-details {\n",
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       "\n",
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       "\n",
       ".xr-array-wrap {\n",
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       "\n",
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       "  grid-column: 1;\n",
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       "\n",
       ".xr-preview {\n",
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       "\n",
       ".xr-array-preview,\n",
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       "  padding: 0 5px !important;\n",
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       "\n",
       ".xr-array-data,\n",
       ".xr-array-in:checked ~ .xr-array-preview {\n",
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       "\n",
       ".xr-array-in:checked ~ .xr-array-data,\n",
       ".xr-array-preview {\n",
       "  display: inline-block;\n",
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       "\n",
       ".xr-dim-list {\n",
       "  display: inline-block !important;\n",
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       "\n",
       ".xr-dim-list li {\n",
       "  display: inline-block;\n",
       "  padding: 0;\n",
       "  margin: 0;\n",
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       "\n",
       ".xr-dim-list:before {\n",
       "  content: '(';\n",
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       "\n",
       ".xr-dim-list:after {\n",
       "  content: ')';\n",
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       "\n",
       ".xr-dim-list li:not(:last-child):after {\n",
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       "\n",
       ".xr-has-index {\n",
       "  font-weight: bold;\n",
       "}\n",
       "\n",
       ".xr-var-list,\n",
       ".xr-var-item {\n",
       "  display: contents;\n",
       "}\n",
       "\n",
       ".xr-var-item > div,\n",
       ".xr-var-item label,\n",
       ".xr-var-item > .xr-var-name span {\n",
       "  background-color: var(--xr-background-color-row-even);\n",
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       "\n",
       ".xr-var-item > .xr-var-name:hover span {\n",
       "  padding-right: 5px;\n",
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       "\n",
       ".xr-var-list > li:nth-child(odd) > div,\n",
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       ".xr-var-list > li:nth-child(odd) > .xr-var-name span {\n",
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       "\n",
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       "\n",
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       "\n",
       ".xr-var-dtype {\n",
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       "\n",
       ".xr-var-preview {\n",
       "  grid-column: 4;\n",
       "}\n",
       "\n",
       ".xr-index-preview {\n",
       "  grid-column: 2 / 5;\n",
       "  color: var(--xr-font-color2);\n",
       "}\n",
       "\n",
       ".xr-var-name,\n",
       ".xr-var-dims,\n",
       ".xr-var-dtype,\n",
       ".xr-preview,\n",
       ".xr-attrs dt {\n",
       "  white-space: nowrap;\n",
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       "  padding-right: 10px;\n",
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       "\n",
       ".xr-var-name:hover,\n",
       ".xr-var-dims:hover,\n",
       ".xr-var-dtype:hover,\n",
       ".xr-attrs dt:hover {\n",
       "  overflow: visible;\n",
       "  width: auto;\n",
       "  z-index: 1;\n",
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       "\n",
       ".xr-var-attrs,\n",
       ".xr-var-data,\n",
       ".xr-index-data {\n",
       "  display: none;\n",
       "  background-color: var(--xr-background-color) !important;\n",
       "  padding-bottom: 5px !important;\n",
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       "\n",
       ".xr-var-attrs-in:checked ~ .xr-var-attrs,\n",
       ".xr-var-data-in:checked ~ .xr-var-data,\n",
       ".xr-index-data-in:checked ~ .xr-index-data {\n",
       "  display: block;\n",
       "}\n",
       "\n",
       ".xr-var-data > table {\n",
       "  float: right;\n",
       "}\n",
       "\n",
       ".xr-var-name span,\n",
       ".xr-var-data,\n",
       ".xr-index-name div,\n",
       ".xr-index-data,\n",
       ".xr-attrs {\n",
       "  padding-left: 25px !important;\n",
       "}\n",
       "\n",
       ".xr-attrs,\n",
       ".xr-var-attrs,\n",
       ".xr-var-data,\n",
       ".xr-index-data {\n",
       "  grid-column: 1 / -1;\n",
       "}\n",
       "\n",
       "dl.xr-attrs {\n",
       "  padding: 0;\n",
       "  margin: 0;\n",
       "  display: grid;\n",
       "  grid-template-columns: 125px auto;\n",
       "}\n",
       "\n",
       ".xr-attrs dt,\n",
       ".xr-attrs dd {\n",
       "  padding: 0;\n",
       "  margin: 0;\n",
       "  float: left;\n",
       "  padding-right: 10px;\n",
       "  width: auto;\n",
       "}\n",
       "\n",
       ".xr-attrs dt {\n",
       "  font-weight: normal;\n",
       "  grid-column: 1;\n",
       "}\n",
       "\n",
       ".xr-attrs dt:hover span {\n",
       "  display: inline-block;\n",
       "  background: var(--xr-background-color);\n",
       "  padding-right: 10px;\n",
       "}\n",
       "\n",
       ".xr-attrs dd {\n",
       "  grid-column: 2;\n",
       "  white-space: pre-wrap;\n",
       "  word-break: break-all;\n",
       "}\n",
       "\n",
       ".xr-icon-database,\n",
       ".xr-icon-file-text2,\n",
       ".xr-no-icon {\n",
       "  display: inline-block;\n",
       "  vertical-align: middle;\n",
       "  width: 1em;\n",
       "  height: 1.5em !important;\n",
       "  stroke-width: 0;\n",
       "  stroke: currentColor;\n",
       "  fill: currentColor;\n",
       "}\n",
       "</style><pre class='xr-text-repr-fallback'>&lt;xarray.Dataset&gt;\n",
       "Dimensions:  (chain: 1, draw: 10000)\n",
       "Coordinates:\n",
       "  * chain    (chain) int64 0\n",
       "  * draw     (draw) int64 0 1 2 3 4 5 6 7 ... 9993 9994 9995 9996 9997 9998 9999\n",
       "Data variables:\n",
       "    x        (chain, draw) float64 1.55e+04 1.407e+05 ... 1.013e+05 1.842e+04\n",
       "Attributes:\n",
       "    created_at:                 2024-01-30T22:17:16.363572\n",
       "    arviz_version:              0.17.0\n",
       "    inference_library:          pymc\n",
       "    inference_library_version:  5.10.3</pre><div class='xr-wrap' style='display:none'><div class='xr-header'><div class='xr-obj-type'>xarray.Dataset</div></div><ul class='xr-sections'><li class='xr-section-item'><input id='section-ad553935-83db-47cc-97c7-b44d0a149fbe' class='xr-section-summary-in' type='checkbox' disabled ><label for='section-ad553935-83db-47cc-97c7-b44d0a149fbe' class='xr-section-summary'  title='Expand/collapse section'>Dimensions:</label><div class='xr-section-inline-details'><ul class='xr-dim-list'><li><span class='xr-has-index'>chain</span>: 1</li><li><span class='xr-has-index'>draw</span>: 10000</li></ul></div><div class='xr-section-details'></div></li><li class='xr-section-item'><input id='section-fa9dbfab-48ae-4eff-8e8f-bf3e2fc6ff3f' class='xr-section-summary-in' type='checkbox'  checked><label for='section-fa9dbfab-48ae-4eff-8e8f-bf3e2fc6ff3f' class='xr-section-summary' >Coordinates: <span>(2)</span></label><div class='xr-section-inline-details'></div><div class='xr-section-details'><ul class='xr-var-list'><li class='xr-var-item'><div class='xr-var-name'><span class='xr-has-index'>chain</span></div><div class='xr-var-dims'>(chain)</div><div class='xr-var-dtype'>int64</div><div class='xr-var-preview xr-preview'>0</div><input id='attrs-1a32e671-bde1-4bda-8ae4-cb786ec9366d' class='xr-var-attrs-in' type='checkbox' disabled><label for='attrs-1a32e671-bde1-4bda-8ae4-cb786ec9366d' title='Show/Hide attributes'><svg class='icon xr-icon-file-text2'><use xlink:href='#icon-file-text2'></use></svg></label><input id='data-d77a8879-a8df-4312-9e5c-9a3fd3e12f93' class='xr-var-data-in' type='checkbox'><label for='data-d77a8879-a8df-4312-9e5c-9a3fd3e12f93' title='Show/Hide data repr'><svg class='icon xr-icon-database'><use xlink:href='#icon-database'></use></svg></label><div class='xr-var-attrs'><dl class='xr-attrs'></dl></div><div class='xr-var-data'><pre>array([0])</pre></div></li><li class='xr-var-item'><div class='xr-var-name'><span class='xr-has-index'>draw</span></div><div class='xr-var-dims'>(draw)</div><div class='xr-var-dtype'>int64</div><div class='xr-var-preview xr-preview'>0 1 2 3 4 ... 9996 9997 9998 9999</div><input id='attrs-0bf3d4c8-2abe-4332-b23f-57e7b624e164' class='xr-var-attrs-in' type='checkbox' disabled><label for='attrs-0bf3d4c8-2abe-4332-b23f-57e7b624e164' title='Show/Hide attributes'><svg class='icon xr-icon-file-text2'><use xlink:href='#icon-file-text2'></use></svg></label><input id='data-bbe406f9-6968-4147-be59-8328fea2416c' class='xr-var-data-in' type='checkbox'><label for='data-bbe406f9-6968-4147-be59-8328fea2416c' title='Show/Hide data repr'><svg class='icon xr-icon-database'><use xlink:href='#icon-database'></use></svg></label><div class='xr-var-attrs'><dl class='xr-attrs'></dl></div><div class='xr-var-data'><pre>array([   0,    1,    2, ..., 9997, 9998, 9999])</pre></div></li></ul></div></li><li class='xr-section-item'><input id='section-25180351-bff4-4a37-bee2-5faff3776e03' class='xr-section-summary-in' type='checkbox'  checked><label for='section-25180351-bff4-4a37-bee2-5faff3776e03' class='xr-section-summary' >Data variables: <span>(1)</span></label><div class='xr-section-inline-details'></div><div class='xr-section-details'><ul class='xr-var-list'><li class='xr-var-item'><div class='xr-var-name'><span>x</span></div><div class='xr-var-dims'>(chain, draw)</div><div class='xr-var-dtype'>float64</div><div class='xr-var-preview xr-preview'>1.55e+04 1.407e+05 ... 1.842e+04</div><input id='attrs-e43d35dc-8e2f-4ccd-9604-c468ceed9914' class='xr-var-attrs-in' type='checkbox' disabled><label for='attrs-e43d35dc-8e2f-4ccd-9604-c468ceed9914' title='Show/Hide attributes'><svg class='icon xr-icon-file-text2'><use xlink:href='#icon-file-text2'></use></svg></label><input id='data-0aeffabb-5fa3-43fa-8ff3-8814d70e755b' class='xr-var-data-in' type='checkbox'><label for='data-0aeffabb-5fa3-43fa-8ff3-8814d70e755b' title='Show/Hide data repr'><svg class='icon xr-icon-database'><use xlink:href='#icon-database'></use></svg></label><div class='xr-var-attrs'><dl class='xr-attrs'></dl></div><div class='xr-var-data'><pre>array([[ 15504.9698372 , 140655.46341962,  14773.9145148 , ...,\n",
       "         61586.49283859, 101274.91502654,  18424.70775238]])</pre></div></li></ul></div></li><li class='xr-section-item'><input id='section-49c89bd9-1869-4015-aa46-61a1a04fc57e' class='xr-section-summary-in' type='checkbox'  ><label for='section-49c89bd9-1869-4015-aa46-61a1a04fc57e' class='xr-section-summary' >Indexes: <span>(2)</span></label><div class='xr-section-inline-details'></div><div class='xr-section-details'><ul class='xr-var-list'><li class='xr-var-item'><div class='xr-index-name'><div>chain</div></div><div class='xr-index-preview'>PandasIndex</div><div></div><input id='index-e6b57304-3269-488b-8c58-b01f2e4c2a27' class='xr-index-data-in' type='checkbox'/><label for='index-e6b57304-3269-488b-8c58-b01f2e4c2a27' title='Show/Hide index repr'><svg class='icon xr-icon-database'><use xlink:href='#icon-database'></use></svg></label><div class='xr-index-data'><pre>PandasIndex(Int64Index([0], dtype=&#x27;int64&#x27;, name=&#x27;chain&#x27;))</pre></div></li><li class='xr-var-item'><div class='xr-index-name'><div>draw</div></div><div class='xr-index-preview'>PandasIndex</div><div></div><input id='index-3edc6082-80bf-4115-97af-cfb7d54915cc' class='xr-index-data-in' type='checkbox'/><label for='index-3edc6082-80bf-4115-97af-cfb7d54915cc' title='Show/Hide index repr'><svg class='icon xr-icon-database'><use xlink:href='#icon-database'></use></svg></label><div class='xr-index-data'><pre>PandasIndex(Int64Index([   0,    1,    2,    3,    4,    5,    6,    7,    8,    9,\n",
       "            ...\n",
       "            9990, 9991, 9992, 9993, 9994, 9995, 9996, 9997, 9998, 9999],\n",
       "           dtype=&#x27;int64&#x27;, name=&#x27;draw&#x27;, length=10000))</pre></div></li></ul></div></li><li class='xr-section-item'><input id='section-c70ad7ec-9f6b-4fb5-bf05-646dfa5838a0' class='xr-section-summary-in' type='checkbox'  checked><label for='section-c70ad7ec-9f6b-4fb5-bf05-646dfa5838a0' class='xr-section-summary' >Attributes: <span>(4)</span></label><div class='xr-section-inline-details'></div><div class='xr-section-details'><dl class='xr-attrs'><dt><span>created_at :</span></dt><dd>2024-01-30T22:17:16.363572</dd><dt><span>arviz_version :</span></dt><dd>0.17.0</dd><dt><span>inference_library :</span></dt><dd>pymc</dd><dt><span>inference_library_version :</span></dt><dd>5.10.3</dd></dl></div></li></ul></div></div><br></div>\n",
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       ".xr-var-dtype:hover,\n",
       ".xr-attrs dt:hover {\n",
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       "\n",
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       "\n",
       ".xr-var-data > table {\n",
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       "\n",
       ".xr-var-name span,\n",
       ".xr-var-data,\n",
       ".xr-index-name div,\n",
       ".xr-index-data,\n",
       ".xr-attrs {\n",
       "  padding-left: 25px !important;\n",
       "}\n",
       "\n",
       ".xr-attrs,\n",
       ".xr-var-attrs,\n",
       ".xr-var-data,\n",
       ".xr-index-data {\n",
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       "\n",
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       "  grid-template-columns: 125px auto;\n",
       "}\n",
       "\n",
       ".xr-attrs dt,\n",
       ".xr-attrs dd {\n",
       "  padding: 0;\n",
       "  margin: 0;\n",
       "  float: left;\n",
       "  padding-right: 10px;\n",
       "  width: auto;\n",
       "}\n",
       "\n",
       ".xr-attrs dt {\n",
       "  font-weight: normal;\n",
       "  grid-column: 1;\n",
       "}\n",
       "\n",
       ".xr-attrs dt:hover span {\n",
       "  display: inline-block;\n",
       "  background: var(--xr-background-color);\n",
       "  padding-right: 10px;\n",
       "}\n",
       "\n",
       ".xr-attrs dd {\n",
       "  grid-column: 2;\n",
       "  white-space: pre-wrap;\n",
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       "\n",
       ".xr-icon-database,\n",
       ".xr-icon-file-text2,\n",
       ".xr-no-icon {\n",
       "  display: inline-block;\n",
       "  vertical-align: middle;\n",
       "  width: 1em;\n",
       "  height: 1.5em !important;\n",
       "  stroke-width: 0;\n",
       "  stroke: currentColor;\n",
       "  fill: currentColor;\n",
       "}\n",
       "</style><pre class='xr-text-repr-fallback'>&lt;xarray.Dataset&gt;\n",
       "Dimensions:  (x_dim_0: 1)\n",
       "Coordinates:\n",
       "  * x_dim_0  (x_dim_0) int64 0\n",
       "Data variables:\n",
       "    x        (x_dim_0) float64 10.0\n",
       "Attributes:\n",
       "    created_at:                 2024-01-30T22:17:16.366009\n",
       "    arviz_version:              0.17.0\n",
       "    inference_library:          pymc\n",
       "    inference_library_version:  5.10.3</pre><div class='xr-wrap' style='display:none'><div class='xr-header'><div class='xr-obj-type'>xarray.Dataset</div></div><ul class='xr-sections'><li class='xr-section-item'><input id='section-d1c82c9f-6877-411a-a240-35065340988f' class='xr-section-summary-in' type='checkbox' disabled ><label for='section-d1c82c9f-6877-411a-a240-35065340988f' class='xr-section-summary'  title='Expand/collapse section'>Dimensions:</label><div class='xr-section-inline-details'><ul class='xr-dim-list'><li><span class='xr-has-index'>x_dim_0</span>: 1</li></ul></div><div class='xr-section-details'></div></li><li class='xr-section-item'><input id='section-25fde67f-0e0f-4d35-b26d-ba9ee2efd2b1' class='xr-section-summary-in' type='checkbox'  checked><label for='section-25fde67f-0e0f-4d35-b26d-ba9ee2efd2b1' class='xr-section-summary' >Coordinates: <span>(1)</span></label><div class='xr-section-inline-details'></div><div class='xr-section-details'><ul class='xr-var-list'><li class='xr-var-item'><div class='xr-var-name'><span class='xr-has-index'>x_dim_0</span></div><div class='xr-var-dims'>(x_dim_0)</div><div class='xr-var-dtype'>int64</div><div class='xr-var-preview xr-preview'>0</div><input id='attrs-92462094-04ea-4a7e-9028-70c76ca068a8' class='xr-var-attrs-in' type='checkbox' disabled><label for='attrs-92462094-04ea-4a7e-9028-70c76ca068a8' title='Show/Hide attributes'><svg class='icon xr-icon-file-text2'><use xlink:href='#icon-file-text2'></use></svg></label><input id='data-21567a16-8121-4af8-abdc-7136da5ee98a' class='xr-var-data-in' type='checkbox'><label for='data-21567a16-8121-4af8-abdc-7136da5ee98a' title='Show/Hide data repr'><svg class='icon xr-icon-database'><use xlink:href='#icon-database'></use></svg></label><div class='xr-var-attrs'><dl class='xr-attrs'></dl></div><div class='xr-var-data'><pre>array([0])</pre></div></li></ul></div></li><li class='xr-section-item'><input id='section-67ab3656-af34-48cf-80cc-c1223f60baca' class='xr-section-summary-in' type='checkbox'  checked><label for='section-67ab3656-af34-48cf-80cc-c1223f60baca' class='xr-section-summary' >Data variables: <span>(1)</span></label><div class='xr-section-inline-details'></div><div class='xr-section-details'><ul class='xr-var-list'><li class='xr-var-item'><div class='xr-var-name'><span>x</span></div><div class='xr-var-dims'>(x_dim_0)</div><div class='xr-var-dtype'>float64</div><div class='xr-var-preview xr-preview'>10.0</div><input id='attrs-258dc3fe-c71d-4b05-a8f1-f84920f0d302' class='xr-var-attrs-in' type='checkbox' disabled><label for='attrs-258dc3fe-c71d-4b05-a8f1-f84920f0d302' title='Show/Hide attributes'><svg class='icon xr-icon-file-text2'><use xlink:href='#icon-file-text2'></use></svg></label><input id='data-d0e5f8b8-2ea7-44ca-8367-b914a4692ecd' class='xr-var-data-in' type='checkbox'><label for='data-d0e5f8b8-2ea7-44ca-8367-b914a4692ecd' title='Show/Hide data repr'><svg class='icon xr-icon-database'><use xlink:href='#icon-database'></use></svg></label><div class='xr-var-attrs'><dl class='xr-attrs'></dl></div><div class='xr-var-data'><pre>array([10.])</pre></div></li></ul></div></li><li class='xr-section-item'><input id='section-1655fb4d-1eed-4925-95e1-c5b5344c5d94' class='xr-section-summary-in' type='checkbox'  ><label for='section-1655fb4d-1eed-4925-95e1-c5b5344c5d94' class='xr-section-summary' >Indexes: <span>(1)</span></label><div class='xr-section-inline-details'></div><div class='xr-section-details'><ul class='xr-var-list'><li class='xr-var-item'><div class='xr-index-name'><div>x_dim_0</div></div><div class='xr-index-preview'>PandasIndex</div><div></div><input id='index-6a7f4032-b4ac-4610-b62f-f9c0ab0eed59' class='xr-index-data-in' type='checkbox'/><label for='index-6a7f4032-b4ac-4610-b62f-f9c0ab0eed59' title='Show/Hide index repr'><svg class='icon xr-icon-database'><use xlink:href='#icon-database'></use></svg></label><div class='xr-index-data'><pre>PandasIndex(Int64Index([0], dtype=&#x27;int64&#x27;, name=&#x27;x_dim_0&#x27;))</pre></div></li></ul></div></li><li class='xr-section-item'><input id='section-120bb237-c64c-4937-a025-51dc61f1cbaf' class='xr-section-summary-in' type='checkbox'  checked><label for='section-120bb237-c64c-4937-a025-51dc61f1cbaf' class='xr-section-summary' >Attributes: <span>(4)</span></label><div class='xr-section-inline-details'></div><div class='xr-section-details'><dl class='xr-attrs'><dt><span>created_at :</span></dt><dd>2024-01-30T22:17:16.366009</dd><dt><span>arviz_version :</span></dt><dd>0.17.0</dd><dt><span>inference_library :</span></dt><dd>pymc</dd><dt><span>inference_library_version :</span></dt><dd>5.10.3</dd></dl></div></li></ul></div></div><br></div>\n",
       "                      </ul>\n",
       "                  </div>\n",
       "            </li>\n",
       "            \n",
       "              </ul>\n",
       "            </div>\n",
       "            <style> /* CSS stylesheet for displaying InferenceData objects in jupyterlab.\n",
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       " */\n",
       "\n",
       ":root {\n",
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       "  --xr-font-color2: var(--jp-content-font-color2, rgba(0, 0, 0, 0.54));\n",
       "  --xr-font-color3: var(--jp-content-font-color3, rgba(0, 0, 0, 0.38));\n",
       "  --xr-border-color: var(--jp-border-color2, #e0e0e0);\n",
       "  --xr-disabled-color: var(--jp-layout-color3, #bdbdbd);\n",
       "  --xr-background-color: var(--jp-layout-color0, white);\n",
       "  --xr-background-color-row-even: var(--jp-layout-color1, white);\n",
       "  --xr-background-color-row-odd: var(--jp-layout-color2, #eeeeee);\n",
       "}\n",
       "\n",
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       "  --xr-border-color: #1F1F1F;\n",
       "  --xr-disabled-color: #515151;\n",
       "  --xr-background-color: #111111;\n",
       "  --xr-background-color-row-even: #111111;\n",
       "  --xr-background-color-row-odd: #313131;\n",
       "}\n",
       "\n",
       ".xr-wrap {\n",
       "  display: block;\n",
       "  min-width: 300px;\n",
       "  max-width: 700px;\n",
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       "\n",
       ".xr-text-repr-fallback {\n",
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       "\n",
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       "  padding-top: 6px;\n",
       "  padding-bottom: 6px;\n",
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       "\n",
       ".xr-header > div,\n",
       ".xr-header > ul {\n",
       "  display: inline;\n",
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       "\n",
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       "\n",
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       "\n",
       ".xr-sections {\n",
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       "\n",
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       "\n",
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       "\n",
       ".xr-section-summary-in + label:before {\n",
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       "\n",
       ".xr-section-summary-in:disabled + label:before {\n",
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       "\n",
       ".xr-section-summary,\n",
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       "\n",
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       "\n",
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       "\n",
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       "\n",
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       "\n",
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       "\n",
       ".xr-array-data,\n",
       ".xr-array-in:checked ~ .xr-array-preview {\n",
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       "\n",
       ".xr-array-in:checked ~ .xr-array-data,\n",
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       "\n",
       ".xr-dim-list {\n",
       "  display: inline-block !important;\n",
       "  list-style: none;\n",
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       "\n",
       ".xr-dim-list li {\n",
       "  display: inline-block;\n",
       "  padding: 0;\n",
       "  margin: 0;\n",
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       "\n",
       ".xr-dim-list:before {\n",
       "  content: '(';\n",
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       "\n",
       ".xr-dim-list:after {\n",
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       "\n",
       ".xr-dim-list li:not(:last-child):after {\n",
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       "\n",
       ".xr-has-index {\n",
       "  font-weight: bold;\n",
       "}\n",
       "\n",
       ".xr-var-list,\n",
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       "  display: contents;\n",
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       "\n",
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       ".xr-var-item label,\n",
       ".xr-var-item > .xr-var-name span {\n",
       "  background-color: var(--xr-background-color-row-even);\n",
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       "\n",
       ".xr-var-item > .xr-var-name:hover span {\n",
       "  padding-right: 5px;\n",
       "}\n",
       "\n",
       ".xr-var-list > li:nth-child(odd) > div,\n",
       ".xr-var-list > li:nth-child(odd) > label,\n",
       ".xr-var-list > li:nth-child(odd) > .xr-var-name span {\n",
       "  background-color: var(--xr-background-color-row-odd);\n",
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       "\n",
       ".xr-var-preview {\n",
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       ".xr-var-name,\n",
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       "\n",
       ".xr-var-name:hover,\n",
       ".xr-var-dims:hover,\n",
       ".xr-var-dtype:hover,\n",
       ".xr-attrs dt:hover {\n",
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       "\n",
       ".xr-var-attrs,\n",
       ".xr-var-data {\n",
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       "  background-color: var(--xr-background-color) !important;\n",
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       "\n",
       ".xr-var-attrs-in:checked ~ .xr-var-attrs,\n",
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       "\n",
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       "\n",
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       "  grid-column: 1;\n",
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       "\n",
       ".xr-attrs dt:hover span {\n",
       "  display: inline-block;\n",
       "  background: var(--xr-background-color);\n",
       "  padding-right: 10px;\n",
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       "\n",
       ".xr-attrs dd {\n",
       "  grid-column: 2;\n",
       "  white-space: pre-wrap;\n",
       "  word-break: break-all;\n",
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       "\n",
       ".xr-icon-database,\n",
       ".xr-icon-file-text2 {\n",
       "  display: inline-block;\n",
       "  vertical-align: middle;\n",
       "  width: 1em;\n",
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       "  stroke: currentColor;\n",
       "  fill: currentColor;\n",
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       ".xr-wrap{width:700px!important;} </style>"
      ],
      "text/plain": [
       "Inference data with groups:\n",
       "\t> prior\n",
       "\t> prior_predictive\n",
       "\t> observed_data"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from scipy.stats import norm\n",
    "# Model setup\n",
    "with pm.Model() as ecommerce_model:\n",
    "    σ = pm.Uniform('σ',0,10)\n",
    "    µ = pm.Lognormal('µ', \n",
    "                           mu = np.log(median), \n",
    "                           # Using formula σ = (x-µ)/z\n",
    "                           sigma = (np.log(upper_bound) - np.log(median)) / norm.ppf(0.9))**2 \n",
    "    \n",
    "    # Truncated Normal \n",
    "    pm.TruncatedNormal('x', mu=µ, sigma=np.sqrt(σ), observed=10, lower = (0-10000)/σ, \n",
    "                       upper = (150000-10000)/σ)\n",
    "    # Prior-predictive\n",
    "    prior_predictive = pm.sample_prior_predictive(samples=10000)\n",
    "prior_predictive # Check what happened"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "id": "884b29f9",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "80% of average spending is distributed between 3282.5 and 30438.3 JPY\n",
      "Errors: the error around the lower bound is = 2282.47 JPY and  error around upper bound is = 438.32 JPY\n"
     ]
    }
   ],
   "source": [
    "# Extract and analyze the samples from the prior predictive distribution\n",
    "monthly_average_spending = prior_predictive.prior['µ'].values.flatten()\n",
    "# \n",
    "monthly_median = np.median(monthly_average_spending)\n",
    "# Find between which values is the 80% of the average spend distributed \n",
    "quantiles = np.quantile(monthly_average_spending, [0.1, 0.9])\n",
    "\n",
    "# Display \n",
    "error_lower = quantiles[0]-lower_bound\n",
    "error_upper = quantiles[1]-upper_bound\n",
    "print(f'80% of average spending is distributed between {round(quantiles[0],1)}','and',f'{round(quantiles[1],1)}','JPY')\n",
    "print(f'Errors: the error around the lower bound is = {round(error_lower,2)} JPY','and ',f'error around upper bound is = {round(error_upper,2)}','JPY')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "id": "d0480133",
   "metadata": {},
   "outputs": [
    {
     "data": {
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",
      "text/plain": [
       "<Figure size 600x500 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Plot the histogram of the sampled prior predictive distribution\n",
    "plt.figure(figsize=(6, 5))\n",
    "plt.hist(monthly_average_spending, bins = 142, density=True, color = 'skyblue', edgecolor = 'white', \n",
    "         label = 'Prior predictive distribution')\n",
    "plt.axvline(monthly_median, color = 'orange', linestyle = 'solid', label = 'Sample Median')\n",
    "plt.axvline(quantiles[0], color = 'red', linestyle = 'dashdot', label = 'Sample 10th Percentile')\n",
    "plt.axvline(lower_bound, color = 'black', linestyle = 'solid', label = '10%')\n",
    "plt.axvline(quantiles[1], color = 'red', linestyle = 'dashdot', label = 'Sample 90th Percentile')\n",
    "plt.axvline(upper_bound, color = 'black', linestyle = 'solid', label = 'Upper Bound')\n",
    "plt.legend()\n",
    "plt.title('Prior Predictive Distribution of Average Money Spent Per Costumer Per Month')\n",
    "plt.xlabel('Average Expenditure (JPY)')\n",
    "plt.ylabel('Frequency')\n",
    "plt.grid(linestyle = 'solid')\n",
    "plt.tight_layout()\n",
    "plt.xlim(-10000, 60000)\n",
    "plt.show()"
   ]
  },
  {
   "attachments": {
    "Prior_predictive_distribution.png": {
     "image/png": 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KyPilu2PHDgFATJo0yWC9jh07CplMJm7duvVfsICQy+XiypUrJsXbqFEjUaFCBREVFSWioqLE1atXpTdQ27Ztcyy3b9++wt3d3egLvUuXLqJQoUJSQjJnzhwBQGzatElaJz4+Xvj6+uaYXB45ckQAEIMHDzaKP/0HtoODQ6YJT8bk8sWLF8LOzk4MGzbMYL2MXxbh4eFCoVCIyZMnG6x36dIloVQqjeZntd+skkshhChUqJCoUaOGNJ0xuZw9e3amH+LpnT59WgAQK1asMFrWqFEjgx81GZdlllyWLFlSxMbGSvM3bdokAIi5c+dK80xJLnOK7VXPc1tbW4N5Fy5cEACkHxxZSTsXf/31V2lecnKyqFu3rnB0dDQ49oxJTk7atGkj6tWrJ00vXbpUKJVKERkZKc2rW7euqFWrlsF2p06dEgCkH5h6vV6UK1dOBAYGGpzjCQkJwsfHRzRv3lyal3bOdO3a1Sie9D8I0qxfv14AEMeOHZPmtW3bVqjVavHw4UNp3s2bN4VSqTQ4H835npg/f75wcnKSYuzUqZMICAgQQhjXe36cG6Z+du3fv18AEHv37jVYz9/f3+Bcz0xCQoLw8/MTAISXl5fo1auX+N///ieePHlitG7ad8JXX30lzdPr9aJ169bC1tZW+gw4fvy4ACDWrl1rsP2+ffuM5nt5eRm91pGRkUaff5s3bzb6HM5O2jl3/fp1ERUVJcLCwsSSJUuEnZ2dKFGihIiPj89TnGlJaXZ27txp9AMgO6a+34cMGSKcnZ2NfkSkl1095Ta5zPjerlu3rpDJZOKLL76Q5qWkpIhSpUoZnGf5Va9C/JdcpuUDt27dEj/++KOQyWTC399fCJHakCOXy8Xx48cNtl28eLEAIEJDQw3qJLf5SFpjV+3atUXfvn2FEEI8f/5c2NrailWrVmWaXAYFBQlbW1up4UIIIR49eiScnJykhhgh/qv7Zs2aGdT9N998IxQKhYiJiZHmVa5cOdP3d27KyEmeLos3a9YMrq6u8PT0RJcuXeDo6Ijt27ejZMmSBusNGDAgx7L27NkDhUKBwYMHG8wfNmwYhBBGd6Q2atQoV/3Erl27BldXV7i6uqJixYr4+eef0bp1a6NL2xnLFUJg69ataNu2LYQQePr0qfQvMDAQL168wN9//y0dg7u7Ozp27Chtr1ar8dlnn+UY39atWyGTyTK9qSIvncadnZ3RsmVLbNq0yeByw8aNG/Hee++hdOnSAIBt27ZBr9ejc+fOBsfm5uaGcuXK4ejRo7ned0aOjo7Z3jXu4uICANi5c2eeb36xs7ND7969TV6/R48ecHJykqY7duwId3d37NmzJ0/7N1Vuz/NmzZqhbNmy0rS/vz+cnZ1x586dHPfj5uZm0PfZxsYGgwcPRlxcHH7//fc8xR8dHY39+/cblPvRRx9BJpNh06ZN0ryPP/4YZ8+elS6ZAqnnnp2dHdq3bw8AOH/+PG7evIlu3bohOjpaOvfi4+PRtGlTHDt2zOh8+OKLL4xiSt+3SqPR4OnTp3jvvfcAQHpv6nQ6HDp0CEFBQQb9qXx9fY1uRjLneyKt28Du3bvx8uVL7N69O8tL4uY+N3Lz2dWsWTN4eHhg7dq1UnmXL1/GxYsXDfqmZcbe3h5//fUXRowYASD1slzfvn3h7u6Or776KtNuQYMGDZL+TrusmJycjEOHDgEANm/ejEKFCqF58+YGcdeqVQuOjo5Gr0GlSpXQoEEDadrV1RV+fn45vk9M4efnB1dXV/j4+ODzzz+Hr68vfvvtN6jV6lzH6ePjg8DAwBz3mXY3evrPqOyY+n53cXFBfHy8QVeN/NS3b1+D7686depACIG+fftK8xQKBWrXrm3wWuVXvaaJj4+X8gFfX198++23qFu3LrZv3y7tv2LFiqhQoYLB/tO6RGTcf27zkTTdunXDtm3bpO4yCoUCHTp0MFpPp9PhwIEDCAoKMuju5u7ujm7duuHEiRNGIxh89tlnBnXfoEED6HS6TLsrZcUcZeTp7ooFCxagfPnyUCqVKFGiBPz8/CCXG+apSqUSpUqVyrGsu3fvwsPDw+jNVLFiRWl5ej4+PrmK1dvbG7/88os0XE65cuVQvHhxo/UylhsVFYWYmBgsXboUS5cuzbTsyMhIKUZfX1+jZNDPzy/H+G7fvg0PDw8UKVLE1EPK0ccff4wdO3bgzz//xPvvv4/bt2/j7NmzmDNnjrTOzZs3IYTIclgEc9yQEhcXl2ldp49z2bJl6NevH0aPHo2mTZviww8/RMeOHY3Op6yULFkyVzfvZDxemUwGX1/ffB9+I7fnedqPgPQKFy5s1O8os/2UK1fOqP6y2o+pNm7cCK1Wixo1auDWrVvS/Dp16mDt2rUYOHAgAKBTp04YOnQoNm7ciG+//RZCCGzevFnqLwSknnsA0LNnzyz39+LFCxQuXFiazux9/+zZMwQHB2PDhg3SezH99kDqezQxMRG+vr5G22ecZ873hKurK5o1a4Z169YhISEBOp3O4MdneuY+N3Lz2SWXy9G9e3csWrRIuhku7a7VtD542SlUqBCmT5+O6dOn4+7duzh8+DB++uknzJ8/H4UKFcKkSZOkdeVyuVF/8PLlywP4r7/bzZs38eLFiyw/NzK+znl9n5hi69atcHZ2ho2NDUqVKmWQ0Oc2TlO/t9LeI6YO5Wbq+/3LL7/Epk2b0LJlS5QsWRIffPABOnfujBYtWpi0n9zK+LoUKlQIAODp6Wk0P/1rlV/1mkalUuH//u//AKQ2TPj4+BjkKTdv3sTVq1fh6uqaL/tP06VLFwwfPhx79+7F2rVr0aZNm0x/UERFRSEhISHTXKJixYrQ6/W4f/8+KleuLM3PWPdpn6O5eU+Yo4w8JZfvvvuu0Y0hGdnZ2ZmcIORGdneCZcbBwQHNmjXLdblpLSeffPJJll+C6YfZsSZt27aFWq3Gpk2b8P7772PTpk2Qy+UGXxZ6vV4aqzCzu80dHR1fKYYHDx7gxYsXmX6pp7G3t8exY8dw9OhR/Pbbb9i3bx82btyIJk2a4MCBAybdBZ/b88EUWbUY63S613Znflb7Sd8a/TqltWxldvMGANy5cwdlypSBh4cHGjRogE2bNuHbb7/FyZMnce/ePUybNk1aN+29NWPGjCyHl8p4/mX2Onfu3Bl//PEHRowYgerVq8PR0RF6vR4tWrTIU0u4ud8T3bp1Q//+/fH48WO0bNlSaql/VTmdG7n97OrRowdmzJiBHTt2oGvXrli3bh3atGkjJQSm8vLyQp8+fdChQweUKVMGa9euNUguTaHX61G8eHGDltT0Mn7p5+f7pGHDhtLd4hnlNk5TP6cqVKgAALh06VIuIs1Z8eLFcf78eezfvx979+7F3r17sWLFCvTo0SPTm39MpdPpMp2f1euS2fz0r1V+1Wv6/WeXD+j1elStWhWzZs3KdHnG5Div3z/u7u5o3LgxZs6cidDQULPeIW6O94Q5ysjfcWFM4OXlhUOHDuHly5cGmfu1a9ek5Zbg6uoKJycn6HS6HJNTLy8vXL58GUIIg8Tk+vXrOe6nbNmy2L9/P549e5Zt62VuLpE7ODigTZs22Lx5M2bNmoWNGzeiQYMGBpcFy5YtCyEEfHx8pNYDc1qzZg0A5HjJQi6Xo2nTpmjatClmzZqFH3/8EWPHjsXRo0fRrFkzs48nl9ZqlkYIgVu3bhl82RYuXBgxMTFG2969e9eg5SU3sb2u89zLywsXL16EXq83+HH3KvsJCwvDH3/8gUGDBqFRo0YGy/R6PT799FOsW7cO3333HYDUFukvv/wS169fx8aNG6FWq9G2bVtpm7QWIGdnZ5N++GXm+fPnOHz4MIKDg/HDDz9I8zO+vsWLF5fGlsso4zxzvyc6dOiAzz//HCdPnsTGjRuzXM/c50ZuPrsAoEqVKqhRowbWrl2LUqVK4d69e/j5559ztc/0ChcujLJly+Ly5csG8/V6Pe7cuWNQtzdu3AAAaWSFsmXL4tChQ6hXr57Zfjjmx5iU+REnkNqS6+fnh507d2Lu3Lk5/qDJzfvd1tYWbdu2Rdu2baHX6/Hll19iyZIl+P777zO98pZeZp+JycnJiIiIyMNRZi2/6jU3+79w4QKaNm2a72OZduvWDf369YOLiwtatWqV6Tqurq5Qq9WZ5hLXrl2DXC43SnhN8TqelGfxZ4u3atUKOp0O8+fPN5g/e/ZsyGQyiw3SrFAo8NFHH2Hr1q1GH5IADG7Lb9WqFR49emQwqn5CQkKWl6TS++ijjyCEQHBwsNGy9L8SHBwcMk14svLxxx/j0aNHWLZsGS5cuICPP/7YYPmHH34IhUKB4OBgo18jQohMh3Mx1ZEjRzBx4kT4+PhIQ1Bl5tmzZ0bz0lqy0vprpY1nmJtjz87q1asNLjlt2bIFERERBudZ2bJlcfLkSYNx+nbv3m00HE1uYntd53mrVq3w+PFjg2QmJSUFP//8MxwdHY2SQ1OktSKMHDkSHTt2NPjXuXNnNGrUyKCl4aOPPoJCocD69euxefNmtGnTxmBcylq1aqFs2bL46aefEBcXZ7Q/U4a8SPtlnfHcTd/1I229Zs2aYceOHQZPjLl165ZRX0ZzvyccHR2xaNEijB8/3iC5zsjc50ZuPrvSfPrppzhw4ADmzJmDokWLmrTPCxcuZDpm5927d/HPP/9keikv/TEKITB//nzY2NigadOmAFJbo3U6HSZOnGi0bUpKSp4+B8z9GQLkT5xpgoODER0djX79+iElJcVo+YEDB7B7924Apr/fM567crlc+kFtymdt2bJlcezYMYN5S5cuzbLlMq/ys15N3f/Dhw/xyy+/GC1LTExEfHy82fbVsWNHjBs3DgsXLsyya5dCocAHH3yAnTt3GnTdevLkifSghvRDfpkqt/lEXli85bJt27YICAjA2LFjER4ejmrVquHAgQPYuXMnvv76a4N+Lq/b1KlTcfToUdSpUwf9+/dHpUqV8OzZM/z99984dOiQlBz1798f8+fPR48ePXD27Fm4u7tjzZo1OT6tCEgdU+zTTz/FvHnzcPPmTemS3vHjxxEQECB1gK9VqxYOHTokDfTq4+ODOnXqZFlu2viiw4cPl75s0itbtiwmTZqEMWPGIDw8HEFBQXByckJYWBi2b9+Ozz77DMOHD88x/r179+LatWtISUnBkydPcOTIERw8eBBeXl7YtWtXtgPKTpgwAceOHUPr1q3h5eWFyMhILFy4EKVKlZLGMixbtixcXFywePFiODk5wcHBAXXq1MlzX5ciRYqgfv366N27N548eYI5c+bA19cX/fv3l9bp168ftmzZghYtWqBz5864ffs2fv31V6NzMTexva7z/LPPPsOSJUvQq1cvnD17Ft7e3tiyZQtCQ0MxZ84ck28USG/t2rWoXr16lr+Q27Vrh6+++gp///03atasieLFiyMgIACzZs3Cy5cvjX7YyOVyLFu2DC1btkTlypXRu3dvlCxZEg8fPsTRo0fh7Ows9YvKirOzMxo2bIjp06dDq9WiZMmSOHDggDQGYXrjx4/HgQMHUK9ePQwYMEBK5KpUqWLw6E5zvSfSy65faZr8ODdM/exK061bN4wcORLbt2/HgAEDTOpfevDgQYwbNw7t2rXDe++9J41juXz5ciQlJRmNi6hSqbBv3z707NkTderUwd69e/Hbb7/h22+/lS53NmrUCJ9//jmmTJmC8+fP44MPPoCNjQ1u3ryJzZs3Y+7cuVn2Xc1K9erVoVAoMG3aNLx48QJ2dnZo0qRJtv3Bc5Ifcab5+OOPcenSJUyePBnnzp1D165dpSf07Nu3D4cPH8a6desAmP5+79evH549e4YmTZqgVKlSuHv3Ln7++WdUr15d6p+ZXT3169dPGki+efPmuHDhAvbv359lt4G8ys96NcWnn36KTZs24YsvvsDRo0dRr1496HQ6XLt2DZs2bZLG1DSHQoUKZTp2aEaTJk2SxoP+8ssvoVQqsWTJEiQlJWH69Ol52netWrWwaNEiTJo0Cb6+vihevLh005LZmHxfuTBt+Bkhsh5PKm1ZxnEeX758Kb755hvh4eEhbGxsRLly5cSMGTOMxk4DIAYOHGhyvFmNc5lRduU+efJEDBw4UHh6egobGxvh5uYmmjZtKpYuXWqw3t27d0W7du2EWq0WxYoVE0OGDJGGT8hpnMuUlBQxY8YMUaFCBWFraytcXV1Fy5YtxdmzZ6V1rl27Jho2bCjs7e0FAGn4h4xDEaXXvXt3aViBrGzdulXUr19fODg4CAcHB1GhQgUxcOBAcf369WzrLG2/af9sbW2Fm5ubaN68uZg7d67BkDdpMg5FdPjwYdG+fXvh4eEhbG1thYeHh+jatau4ceOGwXY7d+4UlSpVkoaOSRv6J7vXN6uhiNavXy/GjBkjihcvLuzt7UXr1q0zHctv5syZomTJksLOzk7Uq1dPnDlzxqjM7GLLj/M8qyGSMnry5Ino3bu3KFasmLC1tRVVq1bNdLgkU4YiOnv2bKZjEaaXNobqN998I8375ZdfBADh5OQkEhMTM93u3Llz4sMPPxRFixYVdnZ2wsvLS3Tu3Nlg/LesxhwUQogHDx6IDh06CBcXF1GoUCHRqVMn8ejRo0yHTTl8+LCoUaOGsLW1FWXLlhXLli0Tw4YNEyqVyqjcV31P5PT5mFm958e5YepnV5pWrVoJANIYujm5c+eO+OGHH8R7770nihcvLpRKpXB1dRWtW7cWR44cMVg37Tvh9u3b0jiCJUqUEOPGjRM6nc6o7KVLl4patWoJe3t74eTkJKpWrSpGjhwpHj16ZHDMmZ2/mb1Pf/nlF1GmTBmhUChyHJYou3POnHHmJO3zMX3dtm3bVuzcudNgPVPe71u2bBEffPCBKF68uLC1tRWlS5cWn3/+uYiIiDBYL6t60ul0YtSoUaJYsWJCrVaLwMBAcevWrSyHIsr4HsiqTrPKFfKjXrPLS9JLTk4W06ZNE5UrVxZ2dnaicOHColatWiI4OFi8ePFCWi8/8pHMhiISInWs3sDAQOHo6CjUarUICAgwep9mVfdpZaY/5x8/fixat24tnJycBADp/ZKbMnIiE8JCdwgQEVlQUFAQrly5YtRP823VoUMHXLp0KdP+qa+qV69e2LJlS6bdIIio4LF4n0siovyWmJhoMH3z5k3s2bMn00eEvo0iIiLw22+/4dNPP7V0KERUAFi8zyURUX4rU6aM9Bzyu3fvYtGiRbC1tcXIkSMtHZpFhYWFITQ0FMuWLYONjQ0+//xzS4dERAUAk0siKvBatGiB9evX4/Hjx7Czs0PdunXx448/Zjlg+tvi999/R+/evVG6dGmsWrUKbm5ulg6JiAoA9rkkIiIiIrNhn0siIiIiMhsml0RERERkNkwuiYiIiMhsmFwSERERkdkwuUzn2LFjaNu2LTw8PCCTybBjx4583d/48eMhk8kM/lWoUCFf90lERESUn5hcphMfH49q1aphwYIFr22flStXRkREhPTvxIkTr23fRERERObGcS7TadmyJVq2bJnl8qSkJIwdOxbr169HTEwMqlSpgmnTpr3SUz6USiXHliMiIqICgy2XuTBo0CD8+eef2LBhAy5evIhOnTqhRYsWr/Rs4ps3b8LDwwNlypRB9+7dce/ePTNGTERERPR6cRD1LMhkMmzfvh1BQUEAgHv37qFMmTK4d+8ePDw8pPWaNWuGd999Fz/++GOu97F3717ExcXBz88PERERCA4OxsOHD3H58mU4OTmZ61CIiIiIXhteFjfRpUuXoNPpUL58eYP5SUlJKFq0KADg2rVrqFixYrbljBo1ClOnTgUAg0vw/v7+qFOnDry8vLBp0yb07dvXzEdARERElP+YXJooLi4OCoUCZ8+ehUKhMFjm6OgIAChTpgyuXr2abTlpiWhmXFxcUL58edy6devVAyYiIiKyACaXJqpRowZ0Oh0iIyPRoEGDTNextbV9paGE4uLicPv2bXz66ad5LoOIiIjIkphcphMXF2fQahgWFobz58+jSJEiKF++PLp3744ePXpg5syZqFGjBqKionD48GH4+/ujdevWud7f8OHD0bZtW3h5eeHRo0cYN24cFAoFunbtas7DIiIiInpteENPOiEhIQgICDCa37NnT6xcuRJarRaTJk3C6tWr8fDhQxQrVgzvvfcegoODUbVq1Vzvr0uXLjh27Biio6Ph6uqK+vXrY/LkyShbtqw5DoeIiIjotWNySURERERmw3EuiYiIiMhsmFwSERERkdnwhh4Aer0ejx49gpOTE2QymaXDISIiojeQEAIvX76Eh4cH5PK3t/2OySWAR48ewdPT09JhEBERUQFw//59lCpVytJhWAyTS0B61GJYWBiKFCli4Wisn1arxYEDB/DBBx/AxsZGmh8fHy89GvPRo0dwcHDI2w7i44G0R2w+egTktRxrkBIPbEs9Fm3bu7Cxd7FsPG+ArM4vyiA+HvEeHkh7GO3du3fh4uJiyYjeCDy/cof1lTvPnj2Dj4/PW/8IZyaXgHQp3MnJCc7OzhaOxvpptVqo1Wo4OzsbfNikf3KRs7Nz3pPL9E9AcnZ+w5NLBaBO/VPr7Awbe55fOcnq/KIMFAqkf1aYs7MzP79MwPMrd1hfuaPVagHgre9i9/Z2CCAiIiIis2NySURERERmw8viREQWpNPppEtpuZKUhCQvL3j9O5mcnAyNRmPW2AoirVYLpVIJjUYDnU5n6XCsHuvLkI2NjUEXMMock0siIgsQQuDx48eIiYnJWwF6PfSLF2Pxv5NRUVGIjo42V3gFlhACbm5uuH///lvfL84UrC9jLi4ucHNzY31kg8klEZEFpCWWxYsXh1qtzv0XlU4HXWIiEv+d9PLyglLJj/Sc6PV6xMXFwdHR8a0eh9BUrK//CCGQkJCAyMhIAIC7u7uFI7Je/CQiInrNdDqdlFgWLVo0r4Ug/UVKlUrF5NIEer0eycnJUKlUb32yZArWlyF7e3sAQGRkJIoXL85L5FngmUJE9Jql9bFUq9UWjoSIcivtfZunvtJvCSaXREQWwj5bRG8evm9zxuSSiIiIiMyGHXSIiN5UajV4YZ2IrA1bLsn6KJXAl1+m/uMNCvSW0Qth2ooKBRSVKqHSv//yejOPyft7Rd7e3pgzZ85r2Vd+Gj9+PKpXry5N9+rVC0FBQa9UpjnKMMd+GzdujK+//trs+8mPOjN1X2QZ/OYm62NnByxYYOkoiCxCLpNhV/hLRGtS8n1fRVVKtPN2ytU2vXr1wqpVqwCkDihdunRp9OjRA99++222Ce7p06fh4ODwSvFao7lz50KYmKCHh4fDx8cH586dM0iAclNGftq2bZvJzw9v3LgxqlevbtIPhuHDh+Orr756xeiMyWQybN++3SBRza99Ue4wuSQisjLRmhQ8SbTep6G0aNECK1asQFJSEvbs2YOBAwfCxsYGY8aMMVo3OTkZtra2cHV1faV9ppVjDsnJyWYpBwAKFSpkFWWYQ5EiRcxanhACOp0Ojo6OcHR0NGvZWXmd+6Ks8bI4WR8hgKio1H9W8GueiAzZ2dnBzc0NXl5eGDBgAJo1a4Zdu3YB+O+S5+TJk+Hh4QE/Pz8AxpfF7927h/bt28PR0RHOzs7o3Lkznjx5Ii1Pu7y5bNky+Pj4QKVSZRrLypUr4eLigh07dqBcuXJQqVQIDAzE/fv3My2rbNmycHNzAwDExMSgX79+cHV1hbOzM5o0aYILFy4YlD916lSUKFECTk5O6Nu3r9EjNjNe4tXr9Zg+fTp8fX1hZ2eH0qVLY/LkyQAAHx8fAECNGjUgk8nQuHFjozKWLl0KDw8P6PV6g/20b98effr0kaZ37tyJmjVrQqVSoUyZMggODkZKStat3TqdDkOHDoWLiwuKFi2KkSNHGrWWZrwsvnDhQvj5+cHNzQ3u7u7o2LGjFO/vv/+OuXPnQiaTQSaTITw8HCEhIZDJZNi7dy9q1aoFOzs7nDhxIstL1cHBwVLdf/HFFwZJf2bdKKpXr47x48dLywGgQ4cOkMlk0nTGfen1ekyYMAGlSpWCnZ0dqlevjn379knLw8PDIZPJsG3bNgQEBECtVqNatWr4888/s6xLyhmTS7I+CQlA8eKp/xISLB0NEeXA3t7eIDE4fPgwrl+/joMHD2L37t1G6+v1erRv3x7Pnj3D77//joMHD+LOnTv4+OOPDda7desWtm7dim3btuH8+fNZ7j8hIQGTJ0/G6tWrERoaipiYGHTp0iXTsrZs2YJjx44BADp16oTIyEjs3bsXZ8+eRc2aNdG0aVM8e/YMALBp0yaMHz8eP/74I86cOQN3d3csXLgw27oYM2YMpk6diu+//x7//PMP1q1bhxIlSgAATp06BQA4dOgQIiIisG3bNqPtO3XqhOjoaBw9elSa9+zZM+zbtw/du3cHABw/fhw9evTAkCFD8M8//2DJkiVYuXKllMRmZubMmVi5ciWWL1+OEydO4NmzZ9i+fXuW6585cwaDBw/G+PHjcerUKezZswcNGzYEkHoZv27duujfvz8iIiIQEREBT09PadvRo0dj6tSpuHr1Kvz9/TMt//Dhw7h69SpCQkKwfv16bNu2DcHBwVnGk9Hp06cBACtWrEBERIQ0ndHcuXMxc+ZM/PTTT7h48SICAwPRrl073Lx502C9sWPHYvjw4Th//jzKly+Prl27ZpusU/Z4WZzeGnohIOf4ZERmI4TA4cOHsX//foN+bg4ODli2bFmWl7EPHz6MS5cuISwsTEpKVq9ejcqVK+P06dN45513AKRevl69enWOl9S1Wi3mz5+POnXqAABWrVqFihUr4tSpU3j33XcNyipatChiY2Nx4sQJnDp1CpGRkbCzswMA/PTTT9ixYwe2bNmCzz77DHPmzEHfvn3Rt29fAMCkSZNw6NAho9bLNC9fvsTcuXMxf/589OzZEwBQtmxZ1K9fHwCk4yhatKjUeppR4cKF0bJlS6xbtw5NmzYFAGzZsgXFihVDQEAAgNQWv9GjR0v7KFOmDCZOnIiRI0di3LhxmZY7Z84cjBkzBh9++CEAYPHixdi/f3+WdXrv3j04ODigTZs2EELA2dkZtWrVApB6Gd/W1hZqtTrT45gwYQKaN2+eZdkAYGtri+XLl0OtVqNy5cqYMGECRowYgYkTJ5r0JKC0ukx7zndWfvrpJ4waNUr6sTFt2jQcPXoUc+bMwYJ0ffuHDx+O1q1bA0it38qVK+PWrVuoUKFCjrGQMSaXZH0cHAAhUm9quJ8M4NX7R+XlxgUiytzu3bvh6OgIrVYLvV6Pbt26SZcrAaBq1arZ9o+8evUqPD09DVq7KlWqBBcXF1y9elVKLr28vEzqq6lUKqVtAKBChQpSWWnJZVpZaZebL168iLi4OKPHbyYmJuL27dtSnF988YXB8rp16xq0KmY8rqSkJCkpzKvu3bujf//+WLhwIezs7LB27Vp06dJFSrouXLiA0NBQg5ZKnU4HjUaDhIQEoyc/vXjxAhEREVLyDaTWWe3atbO8kah58+bw8vKCr68vmjRpgjZt2uCjjz4y6alStWvXznGdatWqGZRVt25dxMXF4f79+/Dy8spxe1PExsbi0aNHqFevnsH8evXqGXV/SN/CmvbM8MjISCaXecTkkqyWtd/UQPS2CggIwKJFi2BrawsPDw+ju8TNdVe4Oe8uz1hWXFwc3N3dERISYrSui4tLnvaR9tzpV9W2bVsIIfDbb7/hnXfewfHjxzF79mxpeVxcHIKDg6VWyPSy6puaW05OTvj7779x5MgR7N69G+PHj8eECRNw+vTpHOvHHK+bXC43Snzz83GL6e+ST3sCT8Z+r2Q69rkkIqJccXBwgK+vL0qXLp2n8TUrVqyI+/fvG9x0888//yAmJgaVKlXKdXkpKSk4c+aMNH39+nXExMSgYsWKWW5To0YNPH78GEqlEr6+vgb/ihUrJsX5119/GWx38uTJLMssV64c7O3tcfjw4UyXp7Xm6nTZ/2hWqVT48MMPsXbtWqxfvx5+fn6oWbOmtLxmzZq4fv26Udy+vr6ZXlIuVKgQ3N3dDY4lJSUFZ8+ezTYOpVKJZs2aYcKECTh//jzCw8Nx5MgR6VhyOo7sXLhwAYmJidL0yZMn4ejoKLVmu7q6IiIiQloeGxuLsLAwgzJsbGyyjcHZ2RkeHh4IDQ01mB8aGpqn84xMx5ZLsj4aDfDpp2j8Mhlbxi+Azs48v8SJ3hRFVa/no/l17SejZs2aoWrVqujevTvmzJmDlJQUfPnll2jUqJFJl1QzsrGxwVdffYV58+ZBqVRi0KBBeO+996RL4lnFULduXQQFBWH69OkoX748Hj16hN9++w0dOnRA7dq1MWTIEPTq1Qu1a9dGvXr1sHbtWly5cgVlypTJtEyVSoVRo0Zh5MiRsLW1Rb169RAVFYUrV66gb9++KF68OOzt7bFv3z6UKlUKKpUqy2GIunfvjjZt2uDKlSv45JNPDJb98MMPaNOmDUqXLo2OHTtCLpfjwoULuHz5MiZNmpRpeUOGDMHUqVNRrlw5VKhQAbNmzUJMTEyW9bN7927cuXMH9evXh1KpxPHjx6HX6w3u/v/rr78QHh4OR0fHXA9jlJycjL59++K7775DeHg4xo0bh0GDBknJcZMmTbBy5Uq0bdsWLi4u+OGHH6BQKAzK8Pb2xuHDh1GvXj3Y2dmhcOHCRvsZMWIExo0bh7Jly6J69epYsWIFzp8/j7Vr1+YqXsodJpdkfXQ6YMsW+ACQ/zAPvDBObxO9EK+1f7AlbnSTyWTYuXMnvvrqKzRs2BByuRwtWrTAzz//nKfy1Go1Ro0ahW7duuHhw4do0KAB/ve//+UYw549ezB27Fj07t0bUVFRcHNzQ8OGDaW7uz/++GPcvn0bI0eOhEajwUcffYQBAwZkeyPM999/D6VSiR9++AGPHj2Cu7u71G9TqVRi3rx5mDBhAn744Qc0aNAg08vyQGpyVaRIEVy/fh3dunUzWBYYGIjdu3djwoQJmDZtGmxsbFChQgX069cvy7iGDRuGiIgI9OzZE3K5HH369EGHDh3w4sWLTNd3cXHBtm3bMH78eGg0GpQrVw7r169H5cqVAaTeANOzZ09UqlQJiYmJRq2KOWnatCnKlSuHhg0bIikpCV27djXotztmzBiEhYWhTZs2KFSoECZOnGi0j5kzZ2Lo0KH45ZdfULJkSYSHhxvtZ/DgwXjx4gWGDRuGyMhIVKpUCbt27UK5cuVyFS/ljkxYw2MBLCw2NhaFChXC06dPjTp3kzGtVos9e/agVatWBv1U4uPjpcFr4+Li8t7vJj4e+LecmaHh0Nq/ev+dEvYK9K5g/Ks236XEA5tSj0Xb4Tls7F1efwxvmKzOr4JEo9EgLCws2/Ebc6TTQXf9Oq7/O1m+fPk8PwLyTbZy5Up8/fXX2bbCpafX6xEbGwtnZ2eT7kp+27G+jGX3/o2OjkaxYsXw4sULODs7WyhCy3v7PomIiAqKhARwJFgisjb8GUJEREREZsPkkoiI3li9evUy+ZI4Eb0eTC6JiIiIyGyYXBIRERGR2TC5JCIiIiKzYXJJRERERGbD5JKIiIiIzIbJJRERERGZDZNLIiIqMGQyGXbs2GHpMHLUuHFjfP3119K0t7c35syZY7F4iMypQCSXDx8+xCeffIKiRYvC3t4eVatWxZkzZywdFuWVQgF07IiwwHbQyxWWjobIOslkgIvLa99tVFQUBgwYgNKlS8POzg5ubm4IDAxEaGjoa48lP4SHh0Mmk0GhUODhw4cGyyIiIqBUKiGTyTJ9jvWrOH36ND777DOzlklkKW/84x+fP3+OevXqISAgAHv37oWrqytu3ryJwoUt8BxpMg+VCti8GSHXnkOXqLN0NETWSS4HfHyAc+de624/+ugjJCcnY9WqVShTpgyePHmCw4cPIzo6+rXGkd9KliyJ1atXY8yYMdK8VatWoWTJkrh3757Z9+fq6mr2Moks5Y1vuZw2bRo8PT2xYsUKvPvuu/Dx8cEHH3yAsmXLWjo0IiLTCQGkxOf6n1yfCLk+MU/bSv+EMCnEmJgYHD9+HNOmTUNAQAC8vLzw7rvvYsyYMWjXrp203qxZs1C1alU4ODjA09MTX375JeLi4qTlK1euhIuLC3bv3g0/Pz+o1Wp07NgRCQkJWLVqFby9vVG4cGEMHjwYOt1/PzC9vb0xceJEdO3aFQ4ODihZsiQWLFiQbcz3799H586d4eLigiJFiiAoKMik5LBnz55YsWKFwbwVK1agZ8+eRutevnwZLVu2hKOjI0qUKIFPP/0UT58+lZbHx8ejR48ecHR0hLu7O2bOnGlURsbL4qbW4f79+1GxYkU4OjqiRYsWiIiIyPHYiPLbG99yuWvXLgQGBqJTp074/fffUbJkSXz55Zfo379/ltskJSUhKSlJmo6NjQUAaLVaaLXafI/5TZdWRxnrKv20WepSlwK53kwtlzphmdc2RQubf//UarWAkudXTrI6vwoSrVYLIQT0ej30en3qzJR4yLc456ocBYCaaRO38h6PvmMsoHTIcT21Wg1HR0ds374d7777Luzs7DJdTyaTYc6cOfDx8cGdO3cwaNAgjBgxQkoE9Xo9EhISMHfuXKxbtw4vX75Ex44dERQUJCWdd+7cQadOnVC3bl18/PHHUtkzZszAmDFjMG7cOBw4cABDhgyBr68vmjdv/t/x/FuvWq0WgYGBeO+99/D7779DqVRi8uTJ6NixIy5cuJBp/GmvR5s2bbB48WIcO3YM9evXx4kTJ/D8+XO0bt0aEydOlPYRExODJk2aoG/fvpg5cyYSExMxevRodO7cGYcOHQIADB8+HL///ju2b9+O4sWLY+zYsfj7779RrVq1/15/QDonclOHM2bMwKpVqyCXy9GjRw8MGzYMv/76a46vpanEvz880sf2ttPr9RAi9TtFoTDsulWQP7dy441PLu/cuYNFixZh6NCh+Pbbb3H69GkMHjwYtra2mf7CBIApU6YgODjYaP7Ro0ehVqvzO+QC4+DBgwbTGo1G+nv//v1QqVR5Kleh0aBNly7oDWD3hg3Q5bGcjPa8wpdvXimEBm3+/fvIkSPQycxzLG+DjOdXQaJUKuHm5oa4uDgkJyenzkyJh4uF4omNjQWUpv2QW7BgAYYMGYIlS5bA398f9erVw4cffogqVapI6/Tu3Vv6u0iRIhgzZgyGDh2KKVOmAEj9rNBqtZg+fTp8fHwAAG3btsWmTZtw/fp1ODo6olSpUmjQoAEOHDiAli1bAkj9Un/33XcxYMAAAECPHj0QEhKCn376CXXq1JH2mZiYiNjYWGzcuBEpKSmYOXMmZDIZAGDOnDnw9vbG3r170aRJE6PjS2sdTE5ORqdOnbB06VL4+/tj6dKl6NSpk/R6xcXFITY2VmphHDVqlFTGnDlzUKVKFfz9999wc3PD8uXLsWTJErzzzjsAgJ9//hmVK1dGcnKy1Lih1+uh0WikaVPrcMaMGVId9unTBzNmzJDKMKeXL1+avcw3VXJyMhITE3Hs2DGkpKQYLEtISLBQVNbljU8u9Xo9ateujR9//BEAUKNGDVy+fBmLFy/OMrlMe5OmiY2NhaenJwICAlC0aNHXEvebTKvV4uDBg2jevDlsbGyk+fHx8dLfgYGBcHDIuSUkU+nKuVnyHWjtXz3hd1Up8El5l1cuJ9dS4oHtqX82adIENvYWiOENk9X5VZBoNBrcv38fjo6O//0IE06pLYim0ushLl7EhX8nq1atatSKYipnhTr1BiETfPLJJ+jYsSOOHz+Ov/76C/v27cO8efOwdOlS9OrVCwBw6NAhTJs2DdeuXUNsbCxSUlKg0WigVCqhVquhUqmgVqtRrVo1qVxPT094e3vDw8NDmufh4YGYmBg4O6e26MrlcjRo0ECaBoCGDRti7ty5BvPs7e3h7OyMmzdv4s6dO/D09DQ4Bo1Gg4iICINt0jg6OgIAHBwc8Pnnn6N+/fqYPn06du7cidDQUCmZcHR0hLOzM65du4bjx4+jVKlSRmU9efIECoUCycnJaNy4sbQ/Z2dn+Pn5wdbW1uDYVCqVNJ2XOvTx8UFUVFSmx5VXQgi8fPkSTk5OUoL+ttNoNLC3t0fDhg2NGlEKWt/jvHrjk0t3d3dUqlTJYF7FihWxdevWLLexs7PL9HKIjY1Ngf0yyw8Z6yvj33muy0KFgMhIrLsZgySVk8lfetlSKCzz2srMVCdvoYJcXzqdDjKZDHK5HHJ5uq7vCifTCxECumrvQn/pEgBAZuMIufL1fKSr1WoEBgYiMDAQP/zwA/r164fg4GD06dMH4eHhaNeuHQYMGIDJkyejSJEiOHHiBPr27YuUlBTpmG1sbAyOPat5QgiDeWn1ln46bd3028nlcsTHx6NWrVpYu3attEyv1yMuLg4+Pj6GdZ9u27T/q1WrhgoVKqB79+6oWLEi/P39cf78eaN9tG3bFtOmTTMqy93dHbdu3TJYP73MjkUul+e5DhUKhVF9var0l+nNWe6bTC6XQyaTZfoZVVA/s3LrjU8u69Wrh+vXrxvMu3HjBry8vCwUEb0ymQxwdUVStBIw093iDkoZ9EJAbsZf3uYujyhXZDLgNSWTOalUqZI0tuTZs2eh1+sxc+ZMKRnZtGmT2fZ18uRJo+mKFStmum7NmjWxceNGFC9eXGrN0+v1iI2NNbl1r0+fPvjyyy+xaNGiLPexdetWeHt7Q5nJ61G2bFnY2Njgr7/+QunSpQGkjnJy48YNNGrUKNMy87sOifKbdXwyvYJvvvkG77//Pn788Ud07twZp06dwtKlS7F06VJLh0ZWRKWQQy6TYVf4S0RrUnLeIAdFVUq0885FKxNRARAdHY1OnTqhT58+8Pf3h5OTE86cOYPp06ejffv2AABfX19otVr8/PPPaNu2LUJDQ7F48WKzxRAaGorp06cjKCgIBw8exObNm/Hbb79lum737t0xY8YMtG/fHhMmTECpUqUQFhaGjRs3YuzYsVKyl53+/fujU6dOcMliTNGBAwfil19+QdeuXTFy5EgUKVIEt27dwoYNG7Bs2TI4Ojqib9++GDFiBIoWLSrd0JNdK2B+1yFRfnvjk8t33nkH27dvx5gxYzBhwgT4+Phgzpw56N69u6VDo7xKSgKGDsV7z5Owe0gwdLaZ35GaF9GaFDzh2JlUEOj1wP37r3WXjo6OqFOnDmbPno3bt29Dq9XC09MT/fv3x7fffgsAqFatGmbNmoVp06ZhzJgxaNiwIaZMmYIePXqYJYZhw4bhzJkzCA4OhrOzM2bNmoXAwMBM11Wr1Th27BhGjRqFDz/8EC9fvkTJkiWN+m1mR6lUolixYlku9/DwQGhoKEaNGoUPPvgASUlJ8PLyQosWLaQEcsaMGYiLi0Pbtm3h5OSEYcOG4cWLF1mWmd91SJTfZEKYOMBZARYbG4tChQrh6dOnvKHHBFqtFnv27EGrVq2MbuhJ6wwfFxf3ajf0/FvOzNBwaO3zWE46lVxs0c7HGSuuPTdLclnCXoHeFUwYqD8lHtiUeizaDs95Q48Jsjq/ChKNRoOwsDD4+PjkeVQF6HTQnTuHtCHUq1evnull2YLE29sbX3/9tcFjE3Mr/WVx9iHMGevLWHbv3+joaBQrVgwvXrww641VbxqeKURERERkNkwuiYiIiMhsCvY1FCIiKjDCw8MtHQIRmYAtl0RERERkNkwuiYiIiMhsmFwSERERkdkwuSQiIiIis2FySURERERmw+SSiIiIiMyGySURERUYMpkMO3bssHQYmQoPD4dMJsP58+ctHYpFNW7c2OApS97e3pgzZ47F4iHzY3JJREQmi4qKwoABA1C6dGnY2dnBzc0NgYGBCA0NtXRoZjN48GDUqlULdnZ2qF69eqbrXLx4EQ0aNIBKpYKnpyemT59usLxXr14ICgoySzze3t6QyWSQyWRwcHBAzZo1sXnzZrOUnZ9CQkIgk8kQExNjMH/btm2YOHGiZYKi14LJJVkfuRxo1AgR79SDkPEUJcqUTAY4Or723X700Uc4d+4cVq1ahRs3bmDXrl1o3LgxoqOjX3ss+alPnz74+OOPM10WGxuLDz74AF5eXjh79ixmzJiB8ePHY+nSpfkWz4QJExAREYFz587hnXfewccff4w//vgjT2UlJyebObrcKVKkCJycnCwaA+UvfnOT9bG3B0JCsG/1/yFFZW/paIher/h40/4lJgIeHpAnJgIpKf9tn5Ly33JTys2FmJgYHD9+HNOmTUNAQAC8vLzw7rvvYsyYMWjXrp203qxZs1C1alU4ODjA09MTX375JeLi4qTlK1euhIuLC3bv3g0/Pz+o1Wp07NgRCQkJWLVqFby9vVG4cGEMHjwYOp1O2s7b2xsTJ05E165d4eDggJIlS2LBggXZxnz//n107twZLi4uKFKkCIKCgnDv3r1st5k3bx4GDhyIMmXKZLp87dq1SE5OxvLly1G5cmV06dIFgwcPxqxZswAA48ePx6pVq7Bz506pxTEkJETa/s6dOwgICIBarUa1atXw559/ZhsPADg5OcHNzQ3ly5fHggULYG9vj//7v//L9Bjbt29v8DSjtFbUyZMnw8PDA35+fgCABw8eoGvXrihSpAgcHBxQu3Zt/PXXX9J2O3fuRO3ateHm5gZfX18EBwcjJd25JpPJsGzZMnTo0AFqtRrlypXDrl27AKR2AQgICAAAFC5cGDKZDL169QJgfFk8o5iYGPTr1w+urq5wdnZGkyZNcOHChRzriKwHk0siImvi6GjyP0WhQqjZsCEKp0tcsH176vKWLQ3L9fbOvJxcheYIR0dH7NixA0lJSVmuJ5fLMW/ePFy5cgWrVq3CkSNHMHLkSIN1EhISMG/ePGzYsAH79u1DSEgIOnTogD179mDPnj1Ys2YNlixZgi1bthhsN2PGDFSrVg3nzp3D6NGjMWTIEBw8eDDTOLRaLQIDA+Hk5ITjx48jNDQUjo6O6Nix4yu13v35559o2LAhbG1tpXmBgYG4fv06nj9/juHDh6Nz585o0aIFIiIiEBERgffff19ad+zYsRg+fDjOnz+P8uXLo2vXrgZJW06USiVsbGyQnJyc5TG2aNHC4BgPHz6M69ev4+DBg9i9ezfi4uLQqFEjPHz4ELt27cKFCxcwcuRI6PV6AMDx48fRo0cPfPXVVzh58iQWLVqElStXYvLkyQaxBAcHo3Pnzrh48SJatWqF7t2749mzZ/D09MTWrVsBANevX0dERATmzp1r0vF16tQJkZGR2Lt3L86ePYuaNWuiadOmePbsmcl1RJbFZ4sTEZFJlEolVq5cif79+2Px4sWoWbMmGjVqhC5dusDf319aL+PNGpMmTcIXX3yBhQsXSvO1Wi0WLVqEsmXLAgA6duyINWvW4MmTJ3B0dESlSpUQEBCAo0ePGlyerlevHkaPHg0AKF++PEJDQzF79mw0b97cKN6NGzdCr9dj2bJlkMlkAIDly5ejSJEiCAkJQYsWLfJUD48fP4aPj4/BvBIlSkjLKlasCHt7eyQlJcHNzc1o++HDh6N169YAUpOzypUr49atW6hQoUKO+05OTsbMmTPx4sULNGnSJNNjXLFiBVxcXBASEoIPPvgAAODg4IBly5ZJCfHSpUsRFRWF06dPo0iRIgAAX19faT/BwcEYPXo0evbsidjYWPj7+2PixIkYOXIkxo0bJ63Xq1cvdO3aFQDw448/Yt68eTh16hRatGghlVu8eHG4uLjkXLEATpw4gVOnTiEyMhJ2dnYAgJ9++gk7duzAli1b8Nlnn5lUDlkWk0uyPvHxgLc3uuoEFuw+C629g6UjInp90l0+zpZOB92VK7iQkgK9jQ280uZ36JBahjzDhal0l0lfxUcffYTWrVvj+PHjOHnyJPbu3Yvp06dj2bJl0mXPQ4cOYcqUKbh27RpiY2ORkpICjUaDhIQEqNVqAIBarZYSSyA1OfP29oZjutbUEiVKIDIy0mD/devWNZrO6k7jCxcu4NatW0b9+zQaDW7fvp3XKnhl6RNxd3d3AEBkZGS2yeWoUaPw3XffQaPRwNHREVOnTkXr1q0xYsQIk46xatWqBi2t58+fR40aNaQEMKMLFy4gNDTUoKVSp9MZvY7pj8XBwQHOzs5Gr1luXLhwAXFxcShatKjB/MTERIu+ZpQ7TC7JOj19CpWlYyCyBAcTf0zpdICNDfQ2NobzlcrUf3kt1wQqlQrNmzdH8+bN8f3336Nfv34YN24cevXqhfDwcLRp0wYDBgzA5MmTUaRIEZw4cQJ9+/ZFcnKylJTYZIhbJpNlOi/tMm1exMXFoVatWli7dq00T6/XIy4uzqjlMTfc3Nzw5MkTg3lp05m1VGaU/jjTWhtzOs4RI0agV69ecHR0RIkSJaTtMjvGNK6urtLfDhlef3v77Puzx8XFITg4GEFBQYiLi4OjoyPk//5gUan++3TOj9fM3d3doI9qGlNbP8nymFyS9bG3By5fxvY7L6C14w09RJmSy4GKFYGrVy0dCSpVqiSNLXn27Fno9XrMnDlTSkY2bdpktn2dPHnSaLpixYqZrluzZk1s3LgRxYsXh7OzM4DUJC42Nlaazou6deti7Nix0Gq1UnJ18OBB+Pn5oXDhwgAAW1tbg5uRXlWxYsUMLlunyewYTeHv749ly5bh2bNnmbZe1qxZE9evX4evr69UX/KMreE5SGspzU091KxZE48fP4ZSqYS3t3eu9kfWgzf0kPWRy4HKlRFTrqLxpT0iSiWTAarX274fHR2NJk2a4Ndff8XFixcRFhaGzZs3Y/r06Wjfvj2A1H57Wq0WP//8M+7cuYM1a9Zg8eLFZoshNDQU06dPx40bN7BgwQJs3rwZQ4YMyXTd7t27o1ixYmjfvj2OHz+OsLAwhISEYNSoUXjw4EGW+7h16xbOnz+Px48fIzExEefPn8f58+elG2S6desGW1tb9O3bF1euXMHGjRsxd+5cDB06VCrD29sbFy9exPXr1/H06VNotVqz1YEpxzh48OBsj7Fr165wc3NDUFAQQkNDcefOHWzdulW6c/2HH37A6tWrMWHCBFy9ehVXr17Fhg0b8N1335kcm5eXF2QyGXbv3o2oqCiDEQOy0qxZM9StWxdBQUE4cOAAwsPD8ccff2Ds2LE4c+aMyfsmy+I3NxERmcTR0RF16tTB7Nmz0bBhQ1SpUgXff/89+vfvj/nz5wMAqlWrhlmzZmHatGmoUqUK1q5diylTppgthmHDhuHMmTOoUaMGJk2ahFmzZiEwMDDTddVqNY4dO4bSpUvjww8/RMWKFdG/f38kJSVl28rXr18/1KhRA0uWLMGNGzdQo0YN1KhRA48ePQIAFCpUCAcOHEBYWBhq1aqFYcOG4YcffjC42aR///7w8/ND7dq14erqmm+DzGd2jH379oVGo8n2GG1tbXHgwAEUL14crVq1QtWqVTF16lQoFAoAqXe/7969GwcPHkTTpk3x/vvvY/bs2fDy8sqyzIxKliwp3RhUokQJDBo0KMdtZDIZ9uzZg4YNG6J3794oX748unTpgrt370o3TZH1kwkhhKWDsLTY2FgUKlQIT58+NepETMa0Wi327NmDVq1aGfS3iY+Plzrjx8XFGfXxMVlyMvDjjzj3NBEHewyB3sY2521yUMnFFu18nLHi2nM8SXz1S1Ul7BXoXaFwziumxAObUutE2+E5bOxdXnnfBV1W51dBotFoEBYWBh8fH4P+a7mi10P36BHOPX4MAKhevTqUmfW1LEC8vb3x9ddfZztGYk7SXxbP7WXetxHry1h279/o6GgUK1YML168eKWuF286nilkfbRaIDgYNRZMhyIlfy4lEb3xhAD+TSyJiKwJk0siIiIiMpuCfQ2FiIgKjHAzjdVJRPmLLZdEREREZDZMLomIiIjIbJhcEhEREZHZMLkkIiIiIrNhcklEREREZsPkkoiIiIjMhsklEREREZkNk0siIjLZsWPH0LZtW3h4eEAmk2HHjh0Gy4UQ+OGHH+Du7g57e3s0a9YMN2/elJYnJSXh008/hbOzM8qXL49Dhw4ZbD9jxgx89dVXr+NQiCifMLkkIiKTxcfHo1q1aliwYEGmy6dPn4558+Zh8eLF+Ouvv+Dg4IDAwEBoNBoAwNKlS3H27Fn8+eef+Oyzz9CtWzcIIQAAYWFh+OWXXzB58uTXdjxEZH58Qg9ZH5kMqFQJz5N0EJBZOhqi10IIgYSEBNM30Omg0+uRmJQEIDXpUyrz9pGuVqshk5n2XmvZsiVatmyZ6TIhBObMmYPvvvsO7du3BwCsXr0aJUqUwI4dO9ClSxdcvXoV7dq1Q+XKlVGmTBmMGDECT58+haurKwYMGIBp06bB2dk5T8dBRNaBySVZH7UauHIFO649R0qiztLREL0WCQkJcHR0tMi+4+Li4ODg8MrlhIWF4fHjx2jWrJk0r1ChQqhTpw7+/PNPdOnSBdWqVcOaNWuQmJiI/fv3w93dHcWKFcPatWuhUqnQoUOHV46DiCyLySUREZnF48ePAQAlSpQwmF+iRAlpWZ8+fXDx4kVUqlQJxYoVw6ZNm/D8+XP88MMPCAkJwXfffYcNGzagbNmyWL58OUqWLPnaj4OIXg2TSyIiK6BWqxEXF5erbXQ6HS5cuAAA8Pf3f6XL4q+LjY2NUX/N3r17Y/DgwTh37hx27NiBCxcuYPr06Rg8eDC2bt362mIjIvNgcknWJyEBeOcdBCXp8L/VB5Bi//q++IgsRSaT5e7StE4H3dWrsLe3BwA4ODjkObk0Fzc3NwDAkydP4O7uLs1/8uQJqlevnuk2R48exZUrV7Bs2TKMGDECrVq1goODAzp37oz58+e/jrCJyMx4tzhZHyGAf/5B4dvXIYOwdDRE1uvfO7CthY+PD9zc3HD48GFpXmxsLP766y/UrVvXaH2NRoOBAwdiyZIlUCgU0Ol00Gq1AACtVgudjn2uid5ETC7J+qhUwNGj2LtqF1JsVZaOhsg6yeVAuXKvfbdxcXE4f/48zp8/DyD1Jp7z58/j3r17kMlk+PrrrzFp0iTs2rULly5dQo8ePeDh4YGgoCCjsiZOnIhWrVqhRo0aAIB69eph27ZtuHjxIubPn4969eq9xiMjInPhZXGyPgoF0LgxHl97DsG7xYkyJ5MBFri7/MyZMwgICJCmhw4dCgDo2bMnVq5ciZEjRyI+Ph6fffYZYmJiUL9+fezbtw8qleEPxcuXL2PTpk1SkgoAHTt2REhICBo0aAA/Pz+sW7futRwTEZkXk0siIjJZ48aNpUHPMyOTyTBhwgRMmDAh23KqVKli8OQeAJDL5Vi4cCEWLlxolliJyDJ4WZysj1YLLFiACmuXQf5v/ysiykCvB6KiLB0FEZERtlyS9UlOBgYNQl0Af7TsDL2NjaUjIrI+QgAPHlg6CiIiI2y5JCIiIiKzYXJJRERERGbD5JKIiIiIzOaNTy7Hjx8PmUxm8K9ChQqWDouIiIjorVQgbuipXLkyDh06JE1b+hFoRERERG+rApGFKZVK6Zm2RERERGQ5BSK5vHnzJjw8PKBSqVC3bl1MmTIFpUuXznL9pKQkJCUlSdOxsbEAUp9lq+W4ijlK/+zfzOan/Z3nutRqkTb4kFyvg1yfkrdy0hE6eWo8uhTI9WZ46o9OmHZ8Kf8di1arBZQ8v3KS1flVkGi1WgghoNfrodfr81ZIhoHM08qj7KUNAM/6Mg3ry5her4cQqd8BCoXCYFlB/tzKjTc+uaxTpw5WrlwJPz8/REREIDg4GA0aNMDly5fh5OSU6TZTpkxBcHCw0fyjR49CrVbnd8gFxsGDBw2mNRqN9Pf+/fuNHvdmKoVGgzb//l3u4Wno8liOgQfAnitAEaT+M4c9t3JeRyH+O5YjR45AJ+Oz0k2V8fwqSNKutsTFxSE5OTlvhej1SP8J9/LlS8jlb3w3+ldWuHBh/Prrr2jdunW26718+fI1RfSfe/fuoVq1ajh27BiqVq362vf/KsxZX23atEHVqlUxZcoUAIC/vz8GDBiAAQMGmG0f+Sk5ORmJiYk4duwYUlIMGz8SEhIsFJV1eeOTy5YtW0p/+/v7o06dOvDy8sKmTZvQt2/fTLcZM2aM9DxcILXl0tPTEwEBAShatGi+x/ym02q1OHjwIJo3bw6bdAOcx8fHS38HBgbCwcEhbztIV87Nku9Aa//qCb9fIVu08nLCrzdiEKV59ZZLV5UCn5R3yXnFlHhge+qfTZo0gY29Cdu85bI6vwoSjUaD+/fvw9HRMc8/wqDXI33bpZOTk1ErSn6IiorCuHHjsGfPHjx58gSFCxeGv78/vv/+e9SrVy/f928Ke3t7ODs7Z7pMCIGXL1/CyckJMpks03UOHz6McePG4dKlS3BwcECPHj0wadIkg/78Fy9exFdffYXTp0/D1dUVgwYNwogRI6TlvXv3RkxMDLZv3y7Nc/z3WfAODg5ZxpeZMmXK4O7duwAAtVoNPz8/jBo1Cp06dTK5jLwypb6yEhISgqZNmyI6OhouLi7S/B07dsDGxkZqAJLL5VCpVLmqE0vSaDSwt7dHw4YNjd6/0dHRForKurzxyWVGLi4uKF++PG7dyrpZyc7ODnZ2dkbzbWxsCuyXWX7IWF8Z/85zXabbTi9XQC9/9dNUplCmxqNQQi/P3QdkphQK045PZqY6eQsV5PrS6XSQyWSQy+V5b20UAul/JqWVl986deqE5ORkrFq1CmXKlMGTJ09w+PBhPH/+3GpaTrOr17RLu1nV14ULF9CmTRuMHTsWq1evxsOHD/HFF19Ar9fjp59+ApDaINGiRQs0a9YMixcvxqVLl9CnTx8ULlwYn332mVR+xn2k/Z2X133ChAno378/YmNjMXPmTHTt2hWenp54//33c1UOkNryZmtra9K6OdVXdrI63mLFihmt+7rOX3OQy+WQyWSZfkYV1M+s3HozXslciIuLw+3bt+Hu7m7pUIiIci8+3vR/iYmQJyYC6S/NpaRIy0wqNxdiYmJw/PhxTJs2DQEBAfDy8sK7776LMWPGoF27dtJ6s2bNQtWqVeHg4ABPT098+eWXiIuLk5avXLkSLi4u2L17N/z8/KBWq9GxY0ckJCRg1apV8Pb2RuHChTF48GDodP+l0N7e3pg4cSK6du0KBwcHlCxZEgsWLMg25vv376Nz585wcXFBkSJFEBQUhHv37mW5/saNG+Hv748ffvgBvr6+aNSoEaZPn44FCxZIl4bXrl2L5ORkLF++HJUrV0aXLl0wePBgzJo1C0DqEHmrVq3Czp07pSQzJCRE2sedO3cQEBAAtVqNatWq4c8//8yx7p2cnODm5oby5ctjwYIFsLe3x//93/9leozt27dHeHi4tG2vXr0QFBSEyZMnw8PDA35+fgCABw8eoGvXrihSpAgcHBxQu3Zt/PXXX9J2O3fuRO3ateHm5gZfX18EBwcbXAaWyWRYtmwZOnToALVajXLlymHXrl0AgPDwcAQEBABI7aogk8nQq1cvAEDjxo3x9ddfZ3msMTEx6NevH1xdXeHs7IwmTZrgwoULOdYRWY83PrkcPnw4fv/9d4SHh+OPP/5Ahw4doFAo0LVrV0uHRq+iWDFoCrOLAr2FHB1N+1eoEBQNG6Jmw4YonC5xwfbtqcvTdRkCAHh7Z15OrkJzhKOjI3bs2GFwU2RGcrkc8+bNw5UrV7Bq1SocOXIEI0eONFgnISEB8+bNw4YNG7Bv3z6EhISgQ4cO2LNnD/bs2YM1a9ZgyZIl2LJli8F2M2bMQLVq1XDu3DmMHj0aQ4YMybJ/rlarRWBgIJycnHD8+HGEhobC0dERHTt2zLKva1JSktGlTnt7e2g0Gpw9exYA8Oeff6Jhw4YGrX+BgYG4fv06nj9/juHDh6Nz585o0aIFIiIiEBERYdDCOHbsWAwfPhznz59H+fLl0bVrV6O+e9lRKlOvxCQnJ2d5jC1atDA4xsOHD+P69es4ePAgdu/ejbi4ODRq1AgPHz7Erl27cOHCBYwcOVJqqTx+/Dh69OiBr776CidPnsSiRYuwcuVKTJ482SCW4OBgdO7cGRcvXkSrVq3QvXt3PHv2DJ6enti6dSsA4Pr164iIiMDcuXNNOr5OnTohMjISe/fuxdmzZ1GzZk00bdoUz549M7mOyLLe+Mviab+8oqOj4erqivr16+PkyZNwdXW1dGiUVw4OQFQU1l97Dm2iGe7sJiKzUCqVWLlyJfr374/FixejZs2aaNSoEbp06QJ/f39pvfStUt7e3pg0aRK++OILLFy4UJqv1WqxaNEilC1bFgDQsWNHrFmzBk+ePIGjoyMqVaqEgIAAHD16FB9//LG0Xb169TB69GgAQPny5REaGorZs2ejefPmRvFu3LgRer0ey5Ytk/oLLl++HEWKFEFISAhatGhhtE1gYCDmzJmD9evXo3Pnznj8+DEmTJgAAIiIiAAAPH78GD4+PgbblShRQlpWsWJF2NvbIykpKdNh8oYPHy7dcBQcHIzKlSvj1q1bJj0AJDk5GTNnzsSLFy/QpEmTTI9xxYoVcHFxQUhICD744AMAqf08ly1bJiXES5cuRVRUFE6fPo0iRVJvc/T19ZX2ExwcjNGjR6Nnz56IjY2Fv78/Jk6ciJEjR2LcuHHSer169ZIac3788UfMmzcPp06dQosWLaRyixcvbtDnMjsnTpzAqVOnEBkZKXVf++mnn7Bjxw5s2bJF6nZA1u2NTy43bNhg6RCIiMwn3eXjnOh0Oly4cAF6Gxt4pc3s0CG1jIz919JdJn0VH330EVq3bo3jx4/j5MmT2Lt3L6ZPn45ly5ZJlz0PHTqEKVOm4Nq1a4iNjUVKSgo0Gg0SEhKkETnUarWUWAKpyZm3t7d000vavMjISIP9161b12h6zpw5mcZ64cIF3Lp1y2jkEI1Gg9u3b2e6zQcffIAZM2bgiy++wKeffgo7Ozt8//33OH78uNn6BKZPxNO6cEVGRmabXI4aNQrfffcdNBoNHB0dMXXqVLRu3RojRoww6RirVq1q0NJ6/vx51KhRQ0oAM7pw4QJCQ0MNWip1Op3R65j+WNJuVMr4muXGhQsXEBcXZ3RzbWJiYpavGVmfNz65JCIqUHIzyoJOB729veE8pTL136uUmwOVSoXmzZujefPm+P7779GvXz+MGzcOvXr1Qnh4ONq0aYMBAwZg8uTJKFKkCE6cOIG+ffsiOTlZSkoy3viQdoNExnmvMrZiXFwcatWqhbVr10rz9Ho94uLijFoe0xs6dCi++eYbREREoHDhwggPD8eYMWNQpkwZAICbmxuePHlisE3atCkP9Eh/nGmtjTkd54gRI9CrVy84OjqiRIkS0naZHWOa9FfwMo7eYZ/xvMkgLi4OwcHBCAoKQlxcHBwdHaXkOn23gfx4zdzd3Q36qKYxtfWTLI/JJVmfxESgZUu0SEjB2rnrkaLK/kOQ6K2k1wM3b1o6CgBApUqVsGPHDgDA2bNnodfrMXPmTCkZ2bRpk9n2dfLkSaPpihUrZrpuzZo1sXHjRhQvXlwa5kav1yM2NjbHYW9kMhk8PDwAAOvXr4enpydq1qwJILW1dOzYsdBqtVJydfDgQfj5+aFw4cIAAFtbW4ObkV5VsWLFDC5bZ3eMpvD398eyZcvw7NmzTFsva9asievXr8PX11eqr9y23Ka1lOamHmrWrInHjx9DqVTC29s7V/sj6/HG39BDBZBeD/z+O9xPh0Im+EQIokwJkatL6OYQHR2NJk2a4Ndff8XFixcRFhaGzZs3Y/r06Wjfvj2A1H57Wq0WP//8M+7cuYM1a9Zg8eLFZoshNDQU06dPx40bN7BgwQJs3rwZQ4YMyXTd7t27o1ixYmjfvj2OHz+OsLAwhISEYNSoUXjw4EGW+5gxYwYuXbqEK1euYOLEiZg6dSrmzZsnjSParVs32Nraom/fvrhy5Qo2btyIuXPnGoyf7O3tjYsXL+L69et4+vRpvj25JatjHDx4cLbH2LVrV7i5uSEoKAihoaG4c+cOtm7dKt25/sMPP2D16tWYMGECrl69iqtXr2LDhg347rvvTI7Ny8sLMpkMu3fvRlRUlMGIAVlp1qwZ6tati6CgIBw4cEC6WXfs2LE4c+aMyfsmy2JySdbHzg7YtAlHZy9Hio3xeKREhNQ+ldlc2s0Pjo6OqFOnDmbPno2GDRuiSpUq+P7779G/f3/Mnz8fAFCtWjXMmjUL06ZNQ5UqVbB27VrpSSzmMGzYMJw5cwY1atTApEmTMGvWLAQGBma6rlqtxrFjx1C6dGl8+OGHqFixIvr374+kpKRsW/n27t2LBg0aoHbt2vjtt9+wc+dOBAUFScsLFSqEAwcOICwsDLVq1cKwYcPwww8/GNxs0r9/f/j5+aF27dpwdXVFaGio2eogp2Ps27cvNBpNtsdoa2uLAwcOoHjx4mjVqhWqVq2KqVOnSgl0YGAgdu/ejYMHD6Jp06Z4//33MXv2bHh5eWVZZkYlS5aUbgwqUaIEBg0alOM2MpkMe/bsQcOGDdG7d2+UL18eXbp0wd27d6Wbpsj6yYTI8IDat1BsbCwKFSqEp0+f8gk9JtBqtdizZw9atWpl9ISetM74cXFxeX9Cz79WXHuOJ2a6W7ySiy3a+TibrcwS9gr0rlA45xVT4oFNqXWi7fCcT+gxQVbnV0Gi0WgQFhYGHx+fvD+hB6mXG8+dOwcAqF69usETZAoib29vfP3119mOkZiT9JfF35RBuy2J9WUsu/dvdHQ0ihUrhhcvXrwxTxzKDzxTiIiIiMhsmFyS9UlJATZvhve+HZDlYmBhoreKEEBMjKWjICIyUrCvodCbKSkJ6NwZAQD+Dg2HtoBf6iPKE70eCAuzdBSvVbiZxuokovzFlksiIiIiMhsml0R54KCUQZ8P98LlR5lERESvE683EuWBSiGHXCbDrvCXiNZk3S9UqYvHp//+veFmDFJss04ei6qUaOftlOVyIiKiNwGTS6JXEK1JyXZoIxv9f8ueJumRZMYndhAREVkjXhYnIiIiIrNhcklEREREZsPkkoiIyAr06tXL4DGTRG8qJpdERGSyxo0bZ/r4xZUrV8LFxeW1x2Oq8PBwyGQyKBQKFC5cGCqVCr6+vpg0aRL4FGQi8+INPUREVGDodDrIZLIsn4N94MABlC5dGra2tvjjjz/Qr18/uLu7o2/fvq85UqKCiy2XRERWQAiB+Pj43P1LTETiv/9yvW26f/nRcpd2iTc4OBiurq5wdnbGF198geTkZGmdxo0bY9CgQRg0aBAKFSqEYsWK4fvvvzeIJykpCcOHD0fJkiXh4OCAOnXqICQkRFqe1mK6a9cuVKpUCXZ2drh3716WcRUtWhQlSpSAl5cXunfvjnr16uHvv/+Wluv1ekyYMAGlSpWCnZ0dqlevjn379knLQ0JCIJPJEJPu0Zvnz5+HTCaTniCUFtP+/ftRsWJFODo6okWLFoiIiJC20el0GDp0KFxcXFC0aFGMHDmSLahUYLDlkojICiQkJMDR0dEi+46Li4ODg4PZyz18+DBUKhVCQkIQHh6O3r17o2jRopg8ebK0zqpVq9C3b1+cOnUKZ86cwWeffYbSpUujf//+AIBBgwbhn3/+wYYNG+Dh4YHt27ejRYsWuHTpEsqVKwcgte6mTZuGZcuWoWjRoihevLhJ8Z05cwZnz55Fjx49pHlz587FzJkzsWTJEtSoUQPLly9Hu3btcOXKFWl/pkhISMBPP/2ENWvWQC6X45NPPsHw4cOxdu1aAMDMmTOxcuVKLF++HBUrVsTMmTOxfft2NGnSxOR9EFkrJpdERJQvbG1tsXz5cqjValSuXBkTJkzAiBEjMHHiROmytaenJ2bPng2ZTAY/Pz9cunQJs2fPRv/+/XHv3j2sWLEC9+7dg4eHBwBg+PDh2LdvH1asWIEff/wRAKDVarFw4UJUq1Ytx5jq168PuVyO5ORkaLVafPbZZwbJ5U8//YRRo0ahS5cuAIBp06bh6NGjmDNnDhYsWGDysWu1WixevBhly5YFkJokT5gwQVo+Z84cjBkzBh9++CEAYPHixdi/f7/J5RNZMyaXZH0cHAAhsOLac2izGaCcqCBRq9WIi4vL1TY6nQ4XLlwAAPj7+0OpzNtHulqtztN2OalWrZpB2XXr1kVcXBzu378PLy8vAMB7770HmUxmsM7MmTOh0+lw6dIl6HQ6lC9f3qDcpKQkFC1aVJq2tbWFv7+/STGtX78enp6esLOzwz///IOvvvoKhQsXxtSpUxEbG4tHjx6hXr16BtvUq1dPqmdTqdVqKbEEAHd3d0RGRgIAXrx4gYiICNSpU0darlQqUbt2bV4apwKBySURkRWQyWS5vjSt0+lgb28PAHBwcMhzcpkbzs7OePHihdH8mJgYFCpUyKz7iouLg0KhwNmzZ6FQKAyWpe9CYG9vb5CgZsfT0xNlypSBs7MzKleujNu3b+P777/H+PHjTdo+rcU1fRKo1WqN1rOxsTGYlslkTBzprcEbeoiIyGR+fn4GN8Ck+fvvv41aGC9cuIDExERp+uTJk3B0dISnp6c076+//jLY5uTJkyhXrhwUCgVq1KgBnU6HyMhI+Pr6Gvxzc3Mzy/EoFAqkpKQgOTkZzs7O8PDwQGhoqME6oaGhqFSpEgDA1dUVAAxuzjl//nyu9lmoUCG4u7sbHHtKSgrOnj2bx6Mgsi5MLsn6aDRAp05o/HUvKJI0lo6GyDrp9UBY2Gvf7YABA3Djxg0MHjwYFy9exPXr1zFr1iysX78ew4YNM1g3OTkZffv2xT///IM9e/Zg3LhxGDRokMEwQffu3cPQoUNx/fp1rF+/Hj///DOGDBkCAChfvjy6d++OHj16YNu2bQgLC8OpU6cwZcoU/Pbbb3mKPzo6Gk+ePMGDBw+wd+9ezJ07FwEBAXB2dgYAjBgxAtOmTcPGjRtx/fp1jB49GufPn5di8vX1haenJ8aPH4+bN2/it99+w8yZM3Mdx5AhQzB16lTs2LED165dw5dffmlwBzrRm4yXxcn66HTAli3wASD/YR7Y65IoE0IAFkhGypQpg2PHjmHs2LFo1qwZkpOTUaFCBWzevBktWrQwWLdp06YoV64cGjZsiKSkJHTt2tXo8nOPHj2QmJiId999FwqFAkOGDMFnn30mLV+xYgUmTZqEYcOG4eHDhyhWrBjee+89tGnTJk/xf/DBBwBSWyzd3d3RqlUrg7vXBw8ejBcvXmDYsGGIjIxEpUqVsGvXLulOcRsbG6xfvx4DBgyAv78/3nnnHUyaNAmdOnXKVRzDhg1DREQEevbsCblcjj59+qBDhw6ZdjkgetPIBDuBIDY2FoUKFcLTp08NOolT5rRaLfbs2YNWrVoZ9CuKj4+X+kG90tAmWi2wdCn+fJyA420/gT5D36W8qORii3Y+zlhx7TmemOEmIVPLs9HHY9h1bwDA7HK3kaR0znLdEvYK9K5Q+JVje9NldX4VJBqNBmFhYfDx8YFKpcpbIXo9dJGROPfgAQCgevXqr6XPpal69eqFmJgY7NixI8t1GjdujOrVq2POnDmvLS69Xo/Y2Fg4OztnOdA6/Yf1ZSy79290dDSKFSuGFy9eSK3hbyPr+SQiSmNjAwwciGvXnkPPu8WJMieXA66uwL/JJRGRteDPECIiIiIyG7ZckvXR6YDjx+F27yUiK70LkWEIEiJCap/LXI6L+TqtXLkyx3XSP8aRiAoOJpdkfTQaICAALQH8ExoOrb35H0tH9MbT64GbNy0dBRGREV4WJyKyEL1eb+kQiCiX+L7NGVsuiYheM1tbW8jlcjx69Aiurq6wtbU1+QkzEp3OYJgujUZjVXeLWyu9Xo/k5GRoNBre/WwC1td/hBBITk5GVFQU5HI5bG1tLR2S1eInERHRayaXy+Hj44OIiAg8evQob4Xo9dA/fYqn/07evXv3rf/yN4UQAomJibl6ZOTbjPVlTK1Wo3Tp0ny/ZYPJJRGRBdja2qJ06dJISUmBTpeHIbcSEpDQujVa/zt56tSpt3pcPVNptVocO3YMDRs2LLDjqJoT68uQQqGAUqlkop0DJpdERBYik8lgY2OTty9tnQ66u3dx999JW1vbvA/I/hZJe5a4SqVismQC1hflBdt0iYiIiMhsmFwSERERkdkwuSQiIiIis2FySURERERmw+SSiIiIiMyGySURERERmQ2TSyIiIiIyGyaXZH3UaiAyEutCb0CrUls6GiLrpFYDYWGWjoKIyAgHUSfrI5MBrq5IilYCiXl4cgnR2+Df9wkRkbVhyyURERERmQ2TS7I+SUnAwIF4b8IIKJKTLB0NkXVKSgK++cbSURARGWFySdYnJQVYuBAV1/8Pcl2KpaMhsk4pKcAvv1g6CiIiI0wuyfrY2ADjxuHcwJHQKW0sHQ2RdbKxAcaMsXQURERGClxyOXXqVMhkMnz99deWDoXyytYWGD8e5weNht7G1tLREFknW1tg7FhLR0FEZKRAJZenT5/GkiVL4O/vb+lQiIiIiN5KBWYoori4OHTv3h2//PILJk2alO26SUlJSEr670aR2NhYAIBWq4VWq83XOAuCtDrKWFfpp1+pLvV64OpVuNx9iSiPsoD81X8DCZ08NR5dCuT6Vx/eyNTy0i+T61Mg12fTh1QneP4h6/OLMtDrob14UZrk55dpeH7lDusrd1hPqWRCCGHpIMyhZ8+eKFKkCGbPno3GjRujevXqmDNnTqbrjh8/HsHBwUbz161bB7Wag3bnlUajQZcuXQAAGzZsgEqlylM5Co0Gbf4tZ/eGDdDlsRxroBAatEn491jUG6CTvbnHQtZFodEgoEsXOP47/SrvOSIyj4SEBHTr1g0vXryAs7OzpcOxmALRcrlhwwb8/fffOH36tEnrjxkzBkOHDpWmY2Nj4enpiYCAABQtWjS/wiwwtFotDh48iObNm8PG5r8bbuLj46W/AwMD4eDgkLcdpCvnZsl3oLV/9YTfr5AtWnk54dcbMYjSvHrLpanl2egTgJupf992r4EkZdYfNq4qBT4p7/LKsb3psjq/KIP4eCSnm2zSpAlcXFwsFc0bg+dX7rC+cic6OtrSIViFNz65vH//PoYMGYKDBw+a/Kvdzs4OdnZ2RvNtbGz45smFjPWV8e8812W67fRyBfTyVz9NZQplajwKJfRy2WsrTw/Ff3/Lldkfi0LB8y8dvh9zYGNjkFyyvnKH9ZU7rC/TsI5SvfHJ5dmzZxEZGYmaNWtK83Q6HY4dO4b58+cjKSkJCoUimxKIiIiIyFze+OSyadOmuHTpksG83r17o0KFChg1ahQTSyIiIqLX6I1PLp2cnFClShWDeQ4ODihatKjRfCIiIiLKXwVqnEsiIiIisiyLtlzeuXMHZcqUMXu5ISEhZi+TiIiIiHJm0ZZLX19fBAQE4Ndff4VGo7FkKERERERkBhZNLv/++2/4+/tj6NChcHNzw+eff45Tp05ZMiQiIiIiegUWTS6rV6+OuXPn4tGjR1i+fDkiIiJQv359VKlSBbNmzUJUVJQlwyMiIiKiXLKKG3qUSiU+/PBDbN68GdOmTcOtW7cwfPhweHp6okePHoiIiLB0iERERERkAqtILs+cOYMvv/wS7u7umDVrFoYPH47bt2/j4MGDePToEdq3b2/pEImIiIjIBBa9W3zWrFlYsWIFrl+/jlatWmH16tVo1aoV5PLUnNfHxwcrV66Et7e3JcOk183eHrh8GdvvvIDWzt7S0RBZJ3t74NQp4N13LR0JEZEBiyaXixYtQp8+fdCrVy+4u7tnuk7x4sXxv//97zVHRhYllwOVKyNG8RxI1Fk6GiLrJJcDlSpZOgoiIiMWTS5v3ryZ4zq2trbo2bPna4iGiIiIiF6VRftcrlixAps3bzaav3nzZqxatcoCEZFVSE4Gxo9H9flTIdcmWzoaIuuUnAxMnmzpKIiIjFg0uZwyZQqKFStmNL948eL48ccfLRARWQWtFggORo0F06FI0Vo6GiLrpNUCU6ZYOgoiIiMWTS7v3bsHHx8fo/leXl64d++eBSIiq6BUAl9+iatd+0KvsGjPDSLrpVQC/ftbOgoiIiMWTS6LFy+OixcvGs2/cOECihYtaoGIyCrY2QELFuDkDzOgs7WzdDRE1snODpg929JREBEZsWhy2bVrVwwePBhHjx6FTqeDTqfDkSNHMGTIEHTp0sWSoRERERFRHlj0muPEiRMRHh6Opk2bQqlMDUWv16NHjx7sc/k2EwJ4+hR2z2IAlQsgk1k6IiLrIwTAR+QSkRWyaHJpa2uLjRs3YuLEibhw4QLs7e1RtWpVeHl5WTIssrSEBKB4cXQDMDM0HFp7B0tHRGR9EhKATPqsExFZmlXcLVG+fHmUL1/e0mEQERER0SuyaHKp0+mwcuVKHD58GJGRkdDr9QbLjxw5YqHIiIiIiCgvLJpcDhkyBCtXrkTr1q1RpUoVyNi3joiIiOiNZtHkcsOGDdi0aRNatWplyTCIiIiIyEwsOhSRra0tfH19LRkCkdVwUMqgF8Ls5eZHmURERFmxaMvlsGHDMHfuXMyfP5+XxOmtp1LIIZfJsCv8JaI1KWYps6hKiXbeTmYpi4iIyBQWTS5PnDiBo0ePYu/evahcuTJsbGwMlm/bts1CkRFZTrQmBU8SdZYOg4iIKE8smly6uLigQ4cOlgyBiIiIiMzIosnlihUrLLl7IiIiIjIzi97QAwApKSk4dOgQlixZgpcvXwIAHj16hLi4OAtHRkRERES5ZdGWy7t376JFixa4d+8ekpKS0Lx5czg5OWHatGlISkrC4sWLLRkeEREREeWSRVsuhwwZgtq1a+P58+ewt7eX5nfo0AGHDx+2YGRERERElBcWbbk8fvw4/vjjD9ja2hrM9/b2xsOHDy0UFVmcSgUcPYq9914ixVZl6WiIrJNKBezZA/AhFERkZSyaXOr1euh0xkOuPHjwAE5OHJvvraVQAI0b4/G15xAckococwoF0LChpaMgIjJi0cviH3zwAebMmSNNy2QyxMXFYdy4cXwkJBEREdEbyKItlzNnzkRgYCAqVaoEjUaDbt264ebNmyhWrBjWr19vydDIkrRaYOlSVHicgKi2n0CfYXB9IkLq+2TJEktHQURkxKLJZalSpXDhwgVs2LABFy9eRFxcHPr27Yvu3bsb3OBDb5nkZGDQINQF8EfLzkwuiTKTnAwMG2bpKIiIjFg0uQQApVKJTz75xNJh0CvQCwG5OZ8Nr1AAHTsi7GUy9HKF+colKkgUCiAoCNixw9KREBEZsGhyuXr16myX9+jR4zVFQq9CLpNhV/hLPHr2Qpq35vpz2KmT81ReGWdbNNq8GSHXnkPHG3qIMqdSAb/+Cjg6WjoSIiIDFk0uhwwZYjCt1WqRkJAAW1tbqNVqJpdvkGhNCiI1/yWCkRodbGV5SwyL2jGhJCIielNZ9G7x58+fG/yLi4vD9evXUb9+fd7QQ0RERPQGsvizxTMqV64cpk6datSqSW8PRUI8IJOhd8UisEmMt3Q4RNYpPp6XxInIKlldcgmk3uTz6NEjS4dBRERERLlk0T6Xu3btMpgWQiAiIgLz589HvXr1LBQVEREREeWVRZPLoKAgg2mZTAZXV1c0adIEM2fOtExQRERERJRnFn+2OBEREREVHFbZ55KIiIiI3kwWbbkcOnSoyevOmjUrHyMhIiIiInOwaHJ57tw5nDt3DlqtFn5+fgCAGzduQKFQoGbNmtJ6MnM+WpCIiIiI8o1Fk8u2bdvCyckJq1atQuHChQGkDqzeu3dvNGjQAMOGDbNkeERERESUSxbtczlz5kxMmTJFSiwBoHDhwpg0aRLvFiciIiJ6A1k0uYyNjUVUVJTR/KioKLx8+dICERERERHRq7BoctmhQwf07t0b27Ztw4MHD/DgwQNs3boVffv2xYcffmhSGYsWLYK/vz+cnZ3h7OyMunXrYu/evfkcORERERFlxqJ9LhcvXozhw4ejW7du0Gq1qQEplejbty9mzJhhUhmlSpXC1KlTUa5cOQghsGrVKrRv3x7nzp1D5cqV8zN8IiIiIsrAosmlWq3GwoULMWPGDNy+fRsAULZsWTg4OJhcRtu2bQ2mJ0+ejEWLFuHkyZNMLt9Qels7YNMmHH0YhxQbO0uHQ2Sd7OyA1auBHj0sHQkRkQGLJpdpIiIiEBERgYYNG8Le3h5CiDwNP6TT6bB582bEx8ejbt26Wa6XlJSEpKQkaTo2NhYAoNVqpRZUylpaHRnUlS4Fcr1OmpTrdZDrU/JUvl5mC21QEMJvxECm0UGWx3LSEzp5arwZ4szv8gzrJCXbOjF3jAAAnXjjzulMzy/KlDbdj2t+fpmG51fusL5yh/WUSiaEEJbaeXR0NDp37oyjR49CJpPh5s2bKFOmDPr06YPChQubfMf4pUuXULduXWg0Gjg6OmLdunVo1apVluuPHz8ewcHBRvPXrVsHtVqd5+N522k0GnTp0gUAsGHDBqhUKgtHZHkKoUGbhNQ62a3eAJ2MdULmw/cckXVJSEhAt27d8OLFCzg7O1s6HIuxaMvlN998AxsbG9y7dw8VK1aU5n/88ccYOnSoycmln58fzp8/jxcvXmDLli3o2bMnfv/9d1SqVCnT9ceMGWPwdKDY2Fh4enoiICAARYsWfbWDegtotVocPHgQzZs3h42NDQDg1xsxePj8vzv8b5Z8B7b2eUvUKzjI0ercYRyPSMCZeoEQylc/Tf0K2aKVlxN+vRGDKM2rtwqaWp6NPgG4mfr3bfcaSFJm/WFj7hgBwFWlwCflXcxS1uuS2flFmUhJQcKGDdJkkyZN4OLiYrl43hA8v3KH9ZU70dHRlg7BKlg0uTxw4AD279+PUqVKGcwvV64c7t69a3I5tra28PX1BQDUqlULp0+fxty5c7FkyZJM17ezs4OdnXFfPhsbG755csGgvhRK6OUKaZleroBenrfTS6HTQtmtGwIA/B0aDq3tq7fGyBTK1FgVSujlr/7EJ1PL0yN9nSizrRNzxwgAUCje2HOa78ccJCdD2aePNMn6yh3WV+6wvkzDOkpl0aGI4uPjM70M/ezZs0yTP1Pp9XqDPpX0ZhFyOdCoESLeqQchs+gpSmS95HKgfn1LR0FEZMSi39wNGjTA6tWrpWmZTAa9Xo/p06cjICDApDLGjBmDY8eOITw8HJcuXcKYMWMQEhKC7t2751fYlM/0KnsgJAT7Vv8fUlT2lg6HyDrZ2wP79lk6CiIiIxa9LD59+nQ0bdoUZ86cQXJyMkaOHIkrV67g2bNnCA0NNamMyMhI9OjRAxEREShUqBD8/f2xf/9+NG/ePJ+jJyIiIqKMLJpcVqlSBTdu3MD8+fPh5OSEuLg4fPjhhxg4cCDc3d1NKuN///tfPkdJRERERKayWHKp1WrRokULLF68GGPHjrVUGGSFFAnxgGtZdNUJLNh9Flp70wfVJ3prxMcDXl6WjoKIyIjFkksbGxtcvHjRUrsna/f0KThiH1EOOOwJEVkhi97Q88knn/CyNhEREVEBYtE+lykpKVi+fDkOHTqEWrVqGT1TfNasWRaKjIiIiIjywiLJ5Z07d+Dt7Y3Lly+jZs2aAIAbN24YrJOXZ4sTERERkWVZJLksV64cIiIicPToUQCpj3ucN28eSpQoYYlwiIiIiMhMLNLnUghhML13717Ex8dbIhQiIiIiMiOreLZexmSTiIiIiN5MFkkuZTKZUZ9K9rEkIiIievNZpM+lEAK9evWCnZ0dAECj0eCLL74wult827ZtlgiPiIiIiPLIIsllz549DaY/+eQTS4RBRERERGZmkeRyxYoVltgtEREREeUzq7ihh4iIiIgKBiaXZHX0NrbA/Pn487vp0CltLR0OkXWytQVmzrR0FERERphcktURNjbAwIG41r0f9DY2lg6HyDrZ2ACff27pKIiIjDC5JCIiIiKzYXJJ1kenA0JC4HbqBGQ6naWjeaM5KGXQm/khBeYuj/JIpwOOHbN0FERERixytzhRdhRJGiAgAC0B/BMaDq29Q47bUOZUCjnkMhl2hb9EtCbllcsrqlKinbeTGSKjV6bRAK1aWToKIiIjTC7J+shkQKVKeJ6kgwCf3GQO0ZoUPElkK3CBIpMBFSoA165ZOhIiIgNMLsnq6OzVwJUr2HHtOVKYEBFlTq0GzpwBHB0tHQkRkQH2uSQiIiIis2FySURERERmw+SSrI4iMQGoXBlBbepCmZhg6XCIrFNCAlC7tqWjICIywj6XZH2EAP75B4UByMBhb4gyJQRv5iEiq8SWSyIiIiIyGyaXRERERGQ2TC6JiIiIyGyYXBIRERGR2TC5JCIiIiKzYXJJRERERGbD5JKIiIiIzIbJJRERERGZDZNLIiIiIjIbJpdEREREZDZMLomIiIjIbJhcktXRK22AceNwbuBI6JQ2lg6HyDrZ2ABjxlg6CiIiI0wuyeoIW1tg/HicHzQaehtbS4dDZJ1sbYGxYy0dBRGRESaXRERERGQ2TC7J+uj1wJUrcLl5NfVvIjKm1wP//GPpKIiIjDC5JKuj0CQCVaqgQ7t6sElKtHQ4RNYpMRF4911LR0FEZITJJVmnYsWgKVzU0lEQWbeifI8QkfVRWjoAoox0agcgKgrrrz2HNlFn6XCIrJODA3D3LuDoaOlIiIgMsOWSiIiIiMyGySURERERmQ2TS7I6ck0i0LgxWvRoC6WGN/QQZSoxEWjRwtJREBEZYZ9LsjoyvR74/Xe4A5AJDkVkTRyUMuiFgFwmM2u5+VFmgafXAydOWDoKIiIjTC6JyGQqhRxymQy7wl8iWpNiljKLqpRo5+1klrKIiMjymFwSUa5Fa1LwhHfyExFRJt74PpdTpkzBO++8AycnJxQvXhxBQUG4fv26pcMiIiIieiu98cnl77//joEDB+LkyZM4ePAgtFotPvjgA8THx1s6NCIiIqK3zht/WXzfvn0G0ytXrkTx4sVx9uxZNGzYMNNtkpKSkJSUJE3HxsYCALRaLbRabf4FW0Ck1ZFBXelSINf/d5lUrtdBrs9bnzyh+2+7VynHsEx5arwZ4szv8gzrJCXbYzF3jPlRZn7ECJ0wOJcyPb/IWIb64eeXaXh+5Q7rK3dYT6ne+OQyoxcvXgAAihQpkuU6U6ZMQXBwsNH8o0ePQq1W51tsBc3Bgwelv4sAUGs00nS5h6ehUqnyVnCGcnR5LSe9B8CeK6lxZn1mmL88hfjvWMpGnINOls2xmDvG/CgzP2IEsOeW8bz05xcZU2g0CEg3feTIkby/595CPL9yh/VlmoSEBEuHYBVkQghh6SDMRa/Xo127doiJicGJbIboyKzl0tPTExERESjKZ/XmSKvV4uDBg2jevDlsbGwAAL/eiMHD5y/xfYOyAICJx2/D1j5viXolGy3aVCsNAJh9/Da0eSwnPb9Ctmjl5YRfb8QgSvPqLW6mlmejT8A3N1PrZG7Z60hSOr+2GPOjzPyI0VWlwCflXaTpzM4vykR8PJILF0bawx8jIyPh4uJiyYjeCDy/cof1lTvR0dFwd3fHixcv4Oyc9ed9QVegWi4HDhyIy5cvZ5tYAoCdnR3s7OyM5tvY2PDNkwsG9aVQQi9XSMv0cgX08rydXjLFf793XqUcwzKVqbEqlNDLX308RVPL0yN9nSizPRZzx5gfZeZHjFAoMn3f8f2YAxsbJBtMsr5yg/WVO6wv07COUhWY5HLQoEHYvXs3jh07hlKlSlk6HCIiIqK30hufXAoh8NVXX2H79u0ICQmBj4+PpUMiIiIiemu98cnlwIEDsW7dOuzcuRNOTk54/PgxAKBQoUKwt7e3cHREREREb5c3fpzLRYsW4cWLF2jcuDHc3d2lfxs3brR0aJRHQqEEvvwSV7v2hV7xxv/+IcofSiXQv7+loyAiMvLGf3MXoJvd6V96OztgwQKcvPYcOj5ikChzdnbA7NnAL79YOhIiIgNvfMslEREREVkPJpdkfYQAoqJg9+xp6t9EZOzf9wkRkbVhcklWR5GYABQvjm71ysNGw6cdEGUqIQHg6BhEZIWYXBIRERGR2TC5JKujUzsAQmDF1WfQ2jtYOhwi6+TgAMTFWToKIiIjTC6JiIiIyGyYXBIRERGR2TC5JKsjT9IAnTqh8de9oEjSWDocIuuk0QCffGLpKIiIjDC5JKsj0+mALVvgs38X5HoOok6UKZ0O2LHD0lEQERlhcklEREREZsPkkoiIiIjMhsklEREREZkNk0siIiIiMhsml0RERERkNkwuiYiIiMhsmFwSkUU5KGXQC2H2cvOjTCIiypnS0gEQ0dtNpZBDLpNhV/hLRGtSAF0KigD49UYMoMjbR1RRlRLtvJ3MGicREZmGySURWYVoTQqeJOog1+tQBECURge9XGbpsIiIKJd4WZyIiIiIzIbJJRERERGZDZNLsjpCoQA6dkRYYDvo5QpLh0NknRQKICjI0lEQERlhn0uyOno7FbB5M0KuPYcuUWfpcIisk0oF/Por4Oho6UiIiAyw5ZKIiIiIzIbJJRERERGZDZNLsjqKhHhAJkPvikVgkxhv6XCIrFN8PC+JE5FVYnJJRERERGbD5JKsjs5eDURGYl3oDWhVakuHQ2Sd1GogLMzSURARGeHd4mR9ZDLA1RVJ0UqAd4sTZe7f9wkRkbVhyyURERERmQ2TS7I68qQkYOBAvDdhBBTJSZYOh8g6JSUB33xj6SiIiIwwuSSrI9OlAAsXouL6/0GuS7F0OETWKSUF+OUXS0dBRGSEySURERERmQ2TSyIiIiIyGyaXRERERGQ2TC6JiIiIyGyYXBIRERGR2TC5JCIiIiKzYXJJRAWOg1IGvRBmLdPc5RERFVR8/CMRFTgqhRxymQy7wl8iWvPqY6UWVSnRztvJDJERERV8TC6JqMCK1qTgCZ9PT0T0WvGyOBERERGZDZNLIiIiIjIbJpdkdYRcDjRqhIh36kHIeIoSZUouB+rXt3QURERG2OeSrI5eZQ+EhGDftedIYX85oszZ2wP79gGOjpaOhIjIAJuFiIiIiMhsmFwSERERkdkwuSSro0iIB1xd0fX9crBJjLd0OETWKT4e8PKydBREREYKRHJ57NgxtG3bFh4eHpDJZNixY4elQ6JX9fQpVM+jLR0FkXWL5nuEiKxPgUgu4+PjUa1aNSxYsMDSoZAZ6FT2wOXL2L4rFFo7e0uHQ2Sd7O2BU6csHQURkZECcbd4y5Yt0bJlS5PXT0pKQlJSkjQdGxsLANBqtdBqtWaPr6BJqyODutKlQK7/785uuV4HuT5vj90TQg5t+fKIQQzkGh2g179SvAAgdPLUeDPEmd/lGdZJSrZ1Yu4Y86PM1xFjWh3l9fzJlzh1wio/G7Tlyv33Nz+/TJLp5xdlifWVO6ynVDIhhLB0EOYkk8mwfft2BAUFZbnO+PHjERwcbDR/3bp1UKvV+RhdwabRaNClSxcAwIYNG6BSqSwckeUphAZtElLrZLd6A3Qy1gmZD99zRNYlISEB3bp1w4sXL+Ds7GzpcCymQLRc5taYMWMwdOhQaTo2Nhaenp4ICAhA0aJFLRjZm0Gr1eLgwYNo3rw5bGxsAAC/3ojBw+cvpXVulnwHtvZ5S9Qr2AOt1y/AxWgNDvf4Cnob21eO2a+QLVp5OeHXGzGI0rx6S5ap5dnoE4CbqX/fdq+BJGXWHzbmjjE/ynwdMcr1KSj36CxuetSCXp63jyhzx+mqUuCT8i6vXI5ZJScjccIEabJJkyZwcXGxXDxviMw+vyhrrK/ciWY/aABvaXJpZ2cHOzs7o/k2NjZ88+SCQX0plNDLFdKy/2/v3qOiKtc/gH+HGWYYREAFAQtRjwoh3k0DLW8UmWlaKUup8PLLY2FpamlZXupXaHXMUg/kybx0TMpKK6+RIpF3CVGUSBHSCrwjcmeY5/eHP3aOg9wcmAG/n7VmLfbsd7/72Q+zx8e99/titFPXujBQSynU//u/6A5g11NTat3PjVRqzfVY1RoY7VT11p8RN+ZEU+mxWDrGuuizPmOsKl/1GqdabXvfDSUlKHn3XWWR3181w3zVDPNVPczRdY1iQA8RERER2QYWl0REVWiiUcFYB4+n10WfRETW1ihui+fl5eHUqVPKckZGBo4cOYLmzZujdevWVoyMiBoDB7Ud7FQqfJd5DZeKaj+K/UYtHDQY3qapRfoiIrIljaK4PHz4MAYOHKgslw/WCQ8Px+rVq60UFRE1NpeKDDhXaJmBTEREjVWjKC4HDBiARjajEhEREVGDxGcuiYiIiMhiWFwSERERkcWwuCQiIiIii2FxSUREREQWw+KSiMgKOHcmETVWjWK0OBFRQ3O7c2dqCvLx+A3LMSdz0MpdzbkzicjqWFyS7VGpAH9/XCkug8Ayf7+ayFbVdu5MTZERF9p0ADJPAgAuFhuhs9AE70REt4O3xcnmlOkdgePHsWnzPhj0jtYOh8gmGfSOWLsu1tphEBGZYXFJRERERBbD4pKIiIiILIbFJdkcdWEB0KkTRjwaCE1hgbXDIbJJmsICPBP2oLXDICIywwE9ZHtEgBMn0AyACpxWhagiKgjc/38wDxGRLeGVS7I5ZToHIC4O29Z8B4PWwdrhENkkg9YBXyyNsXYYRERmeOWSbI9aDQwYgOxfr0BqMUUL0Z1A1Gr80eM+a4dBRGSGVy6JiIiIyGJYXJLNUZWWAsuXw2/dJ7ArLbV2OEQ2ya60FN2+WmvtMIiIzPC2ONkcu9ISYMoUBALYO2Q0jPb21g6JyOaoDSUY/MFca4dBRGSGVy6JiBqJJhoVjGLZGRYs3R8RNX68cklE1Eg4qO1gp1Lhu8xruGSBvzPewkGD4W2aWiAyIrqTsLgkImpkLhUZcI4zLRCRlfC2OBERERFZDItLIiIiIrIYFpdERFShuhggBHCQEFFjx2cuiYioQpYeIARwkBDRnYDFJRERVYoDhIioJnhbnIiIiIgshsUlEREREVkMi0siIiIishgWl2Sb3NxQ1KyFtaMgsmkFLs2tHQIRkRkWl2RzyhybABcuYP3ekyjVN7F2OEQ2qVTfBFFbf7F2GDXG6Y2IGj+OFicionrD6Y2IGj8Wl0REVO8sOb1R+dVQO5XKIv0BsHh/RHcSFpdkc+yKCoEBw/FwgQHrPlwPg4Pe2iER2RxNUSFGRIRinrUDsQE1uhpaZkBzAP/9LQdQV/xPIK+EEt0eFpdkc1RGIxAfDy8AKjFaOxwim6QSI7yPHLB2GDalOldD7YxlaA7gQlEZjHa8MklUFzigh2yOUasDvvwScR98CoO9ztrhENkkg70O37213NphNEocdER0e3jlkmyOaDTAqFHI/PUKhH9yjqhCotHg5KChwBsR1g6l0eGgI6Lbw+KSiIioAvyb6kS1w9viZHNUBgOwYQPabN90/WciMqMyGNBh1xZrh0FEZIZXLsnm2JUUA6NHYyCAX/ZkolTDjynRzTSlxRjOW+INRl1MlwRwyiSyTfxXm4iIqI7xOU66k7C4JCIiqid8jpPuBHzmkoiIiIgshsUlERFRA8T5OMlW8bY4ERFRA1QXz3He3cQeg+9uYpG+ynHQ0Z2HxSUREVEDZsnnOFvo1KYFazX+Fntl6qJYBViw2joWl0RERGSivGC93b/FblasWkBdjZJnwWo5LC6JiIioTlny6mpdzRlqiSK48OpVC0bUcDWa4nL58uV47733kJ2dja5du2Lp0qXo3bu3tcMiIiIiC6qLZ03bOWvRv1WT2y6CS4o4zRTQSIrLL774AtOnT0d0dDT69OmDJUuWICQkBGlpaWjZsqW1wyMiIiILs+yzpiwKLalRTEW0ePFiPPvssxg/fjz8/f0RHR0NR0dHfPrpp9YOjYiIiOiO0uCvXJaUlCAxMRGvvvqq8p6dnR2Cg4Oxb9++CrcpLi5GcXGxsnz1/5+RuHz5ct0G20iUlpaioKAAly5dgr29PQDAoSgPTYtzlTZNi3OhU9fuf4J2xlKU99S0OBeGWvZzI3WhPS5dKoVDUR6cS+qvP01ZPnILrv/cpCQXOmP9xVgXfdZLjEYDCgoK4FSSC9jV7iuqQR53DWmK85F7w3KTktw74rhvu89qfL6sHqMt9Xmb52ODPe5aKiy9BgCQO3yu0AZfXF68eBFlZWXw8PAwed/DwwO//vprhdtERkZiwYIFZu937NixTmK8E00f1MUyHVmqHyv6p/JTdytGQY3RP2/4efpgfr6IbMWlS5fg4uJi7TCspsEXl7Xx6quvYvr06cpyTk4OfHx8cObMmTv6w1Bdubm58Pb2xtmzZ+Hs7GztcGwe81UzzFfNMF81w3zVDPNVM1evXkXr1q3RvHlza4diVQ2+uHRzc4Narca5c+dM3j937hw8PT0r3Ean00Gn05m97+LiwpOnBpydnZmvGmC+aob5qhnmq2aYr5phvmrGzq5RDGmptQZ/9FqtFj179sTOnTuV94xGI3bu3InAwEArRkZERER052nwVy4BYPr06QgPD0evXr3Qu3dvLFmyBPn5+Rg/fry1QyMiIiK6ozSK4jI0NBQXLlzA3LlzkZ2djW7dumH79u1mg3xuRafTYd68eRXeKidzzFfNMF81w3zVDPNVM8xXzTBfNcN8XaeSO328PBERERFZTIN/5pKIiIiIbAeLSyIiIiKyGBaXRERERGQxLC6JiIiIyGIaVXH59ttvIygoCI6OjnB1da2wzZkzZzB06FA4OjqiZcuWePnll2EwGEza7N69Gz169IBOp0P79u2xevVqs36WL1+ONm3awMHBAX369MHBgwdN1hcVFSEiIgItWrSAk5MTnnjiCbOJ3huiqo67Mfjpp58wbNgwtGrVCiqVCps2bTJZLyKYO3cuvLy8oNfrERwcjJMnT5q0uXz5MsLCwuDs7AxXV1dMnDgReXl5Jm2OHj2K+++/Hw4ODvD29sa7775rFsuGDRvg5+cHBwcHdO7cGVu3brX48d6uyMhI3HvvvWjatClatmyJESNGIC0tzaRNdc6H+jo3rS0qKgpdunRRJqUODAzEtm3blPXMVeUWLlwIlUqFadOmKe8xZ3+bP38+VCqVycvPz09Zz1yZ+/PPP/HUU0+hRYsW0Ov16Ny5Mw4fPqys53d+LUgjMnfuXFm8eLFMnz5dXFxczNYbDAYJCAiQ4OBgSUpKkq1bt4qbm5u8+uqrSpvTp0+Lo6OjTJ8+XU6cOCFLly4VtVot27dvV9rExMSIVquVTz/9VI4fPy7PPvusuLq6yrlz55Q2kydPFm9vb9m5c6ccPnxY7rvvPgkKCqrT469r1TnuxmDr1q0yZ84c+eabbwSAbNy40WT9woULxcXFRTZt2iTJyckyfPhwadu2rRQWFiptHn74Yenatavs379fEhISpH379jJmzBhl/dWrV8XDw0PCwsIkJSVF1q9fL3q9Xj7++GOlzZ49e0StVsu7774rJ06ckNdff13s7e3l2LFjdZ6DmggJCZFVq1ZJSkqKHDlyRB555BFp3bq15OXlKW2qOh/q89y0tu+++062bNkiv/32m6Slpclrr70m9vb2kpKSIiLMVWUOHjwobdq0kS5dusjUqVOV95mzv82bN086deokWVlZyuvChQvKeubK1OXLl8XHx0fGjRsnBw4ckNOnT8uOHTvk1KlTSht+59dcoyouy61atarC4nLr1q1iZ2cn2dnZyntRUVHi7OwsxcXFIiLyyiuvSKdOnUy2Cw0NlZCQEGW5d+/eEhERoSyXlZVJq1atJDIyUkREcnJyxN7eXjZs2KC0SU1NFQCyb98+ixyjNVR13I3RzcWl0WgUT09Pee+995T3cnJyRKfTyfr160VE5MSJEwJADh06pLTZtm2bqFQq+fPPP0VE5N///rc0a9ZM+dyJiMyaNUt8fX2V5dGjR8vQoUNN4unTp4/885//tOgxWtr58+cFgMTHx4tI9c6H+jo3bVWzZs3kk08+Ya4qce3aNenQoYPExsZK//79leKSOTM1b9486dq1a4XrmCtzs2bNkn79+t1yPb/za6dR3Ravyr59+9C5c2eTydVDQkKQm5uL48ePK22Cg4NNtgsJCcG+ffsAACUlJUhMTDRpY2dnh+DgYKVNYmIiSktLTdr4+fmhdevWSpuGpjrHfSfIyMhAdna2SR5cXFzQp08fJQ/79u2Dq6srevXqpbQJDg6GnZ0dDhw4oLR54IEHoNVqlTYhISFIS0vDlStXlDaVfRZt1dWrVwEAzZs3B1C986G+zk1bU1ZWhpiYGOTn5yMwMJC5qkRERASGDh1qdlzMmbmTJ0+iVatWaNeuHcLCwnDmzBkAzFVFvvvuO/Tq1QujRo1Cy5Yt0b17d/znP/9R1vM7v3buqOIyOzvb7K/2lC9nZ2dX2iY3NxeFhYW4ePEiysrKKmxzYx9ardbsuc8b2zQ01TnuO0H5sVb1+2/ZsqXJeo1Gg+bNm1f5ObtxH7dqY8v5NhqNmDZtGvr27YuAgAAA1Tsf6uvctBXHjh2Dk5MTdDodJk+ejI0bN8Lf35+5uoWYmBj88ssviIyMNFvHnJnq06cPVq9eje3btyMqKgoZGRm4//77ce3aNeaqAqdPn0ZUVBQ6dOiAHTt24LnnnsOLL76INWvWAOB3fm3Z/J9/nD17NhYtWlRpm9TUVJMHlonIOiIiIpCSkoKff/7Z2qHYNF9fXxw5cgRXr17FV199hfDwcMTHx1s7LJt09uxZTJ06FbGxsXBwcLB2ODZvyJAhys9dunRBnz594OPjgy+//BJ6vd6Kkdkmo9GIXr164Z133gEAdO/eHSkpKYiOjkZ4eLiVo2u4bP7K5YwZM5Camlrpq127dtXqy9PT02xUXPmyp6dnpW2cnZ2h1+vh5uYGtVpdYZsb+ygpKUFOTs4t2zQ01TnuO0H5sVb1+z9//rzJeoPBgMuXL1f5ObtxH7dqY6v5njJlCjZv3oy4uDjcfffdyvvVOR/q69y0FVqtFu3bt0fPnj0RGRmJrl274sMPP2SuKpCYmIjz58+jR48e0Gg00Gg0iI+Px0cffQSNRgMPDw/mrBKurq7o2LEjTp06xc9XBby8vODv72/y3j333KM8SsDv/Nqx+eLS3d0dfn5+lb5ufIahMoGBgTh27JjJhyA2NhbOzs7KhyswMBA7d+402S42NhaBgYEArv+j0LNnT5M2RqMRO3fuVNr07NkT9vb2Jm3S0tJw5swZpU1DU53jvhO0bdsWnp6eJnnIzc3FgQMHlDwEBgYiJycHiYmJSptdu3bBaDSiT58+SpuffvoJpaWlSpvY2Fj4+vqiWbNmSpvKPou2QkQwZcoUbNy4Ebt27ULbtm1N1lfnfKivc9NWGY1GFBcXM1cVGDx4MI4dO4YjR44or169eiEsLEz5mTm7tby8PKSnp8PLy4ufrwr07dvXbOq03377DT4+PgD4nV9r1h5RZEm///67JCUlyYIFC8TJyUmSkpIkKSlJrl27JiJ/T7Hw0EMPyZEjR2T79u3i7u5e4RQLL7/8sqSmpsry5csrnGJBp9PJ6tWr5cSJEzJp0iRxdXU1GV03efJkad26tezatUsOHz4sgYGBEhgYWH/JqAPVOe7G4Nq1a8pnB4AsXrxYkpKS5PfffxeR69NSuLq6yrfffitHjx6Vxx57rMJpKbp37y4HDhyQn3/+WTp06GAyLUVOTo54eHjI008/LSkpKRITEyOOjo5m01JoNBp5//33JTU1VebNm2eT01I899xz4uLiIrt37zaZ/qSgoEBpU9X5UJ/nprXNnj1b4uPjJSMjQ44ePSqzZ88WlUolP/zwg4gwV9Vx42hxEebsRjNmzJDdu3dLRkaG7NmzR4KDg8XNzU3Onz8vIszVzQ4ePCgajUbefvttOXnypKxbt04cHR3lv//9r9KG3/k116iKy/DwcAFg9oqLi1PaZGZmypAhQ0Sv14ubm5vMmDFDSktLTfqJi4uTbt26iVarlXbt2smqVavM9rV06VJp3bq1aLVa6d27t+zfv99kfWFhoTz//PPSrFkzcXR0lJEjR0pWVlZdHHa9quq4G4O4uLgKP0fh4eEicn1qijfeeEM8PDxEp9PJ4MGDJS0tzaSPS5cuyZgxY8TJyUmcnZ1l/Pjxyn9yyiUnJ0u/fv1Ep9PJXXfdJQsXLjSL5csvv5SOHTuKVquVTp06yZYtW+rsuGurolwBMDlvqnM+1Ne5aW0TJkwQHx8f0Wq14u7uLoMHD1YKSxHmqjpuLi6Zs7+FhoaKl5eXaLVaueuuuyQ0NNRkzkbmytz3338vAQEBotPpxM/PT1asWGGynt/5NacSEan3y6VERERE1CjZ/DOXRERERNRwsLgkIiIiIothcUlEREREFsPikoiIiIgshsUlEREREVkMi0siIiIishgWl0RERERkMSwuiYiIiMhiWFwSEVmJSqXCpk2bAACZmZlQqVQ4cuSIVWO6WUlJCdq3b4+9e/fW2T5mz56NF154oc76J6L6xeKSqBHZt28f1Go1hg4dau1Q6oVKparwFRMTY+3Qaszb2xtZWVkICAgAAOzevRsqlQo5OTlWjSs6Ohpt27ZFUFCQ8t6NRXH5cvnLxcUFffv2xa5du3Dx4kV4enrinXfeMet39OjRuO+++1BWVoaZM2dizZo1OH36dH0cEhHVMRaXRI3IypUr8cILL+Cnn37CX3/9Vaf7EhEYDIY63Ud1rFq1CllZWSavESNGWDusGlOr1fD09IRGo7F436WlpbXaTkSwbNkyTJw4scq25b+HPXv2wM3NDY8++ihyc3OxYsUKLFiwAMeOHVPabtiwAZs3b8aaNWugVqvh5uaGkJAQREVF1SpOIrItLC6JGom8vDx88cUXeO655zB06FCsXr1aWTd27FiEhoaatC8tLYWbmxvWrl0LADAajYiMjETbtm2h1+vRtWtXfPXVV0r78itp27ZtQ8+ePaHT6fDzzz8jPT0djz32GDw8PODk5IR7770XP/74o8m+srKyMHToUOj1erRt2xaff/452rRpgyVLlihtcnJy8D//8z9wd3eHs7MzBg0ahOTk5CqP29XVFZ6eniYvBwcHAMCECRPQpUsXFBcXA7h+i7d79+545plnAPx9KzomJgZBQUFwcHBAQEAA4uPjTfaRkpKCIUOGwMnJCR4eHnj66adx8eJFZf2AAQPw4osv4pVXXkHz5s3h6emJ+fPnm/Rx8uRJPPDAA3BwcIC/vz9iY2NN1t94WzwzMxMDBw4EADRr1gwqlQrjxo0DALO8AUC3bt1M9qdSqRAVFYXhw4ejSZMmePvttwEA3377LXr06AEHBwe0a9cOCxYsqPQ/CImJiUhPT6/WlfDy30NAQACioqJQWFiI2NhYDB8+HGPHjkV4eDhKS0tx4cIFREREYOHChfD19VW2HzZsWIO84kxE5lhcEjUSX375Jfz8/ODr64unnnoKn376KUQEABAWFobvv/8eeXl5SvsdO3agoKAAI0eOBABERkZi7dq1iI6OxvHjx/HSSy/hqaeeMiu0Zs+ejYULFyI1NRVdunRBXl4eHnnkEezcuRNJSUl4+OGHMWzYMJw5c0bZ5plnnsFff/2F3bt34+uvv8aKFStw/vx5k35HjRqF8+fPY9u2bUhMTESPHj0wePBgXL58udY5+eijj5Cfn4/Zs2cDAObMmYOcnBwsW7bMpN3LL7+MGTNmICkpCYGBgRg2bBguXboE4HrRO2jQIHTv3h2HDx/G9u3bce7cOYwePdqkjzVr1qBJkyY4cOAA3n33Xbz55ptKAWk0GvH4449Dq9XiwIEDiI6OxqxZs24Zt7e3N77++msAQFpaGrKysvDhhx/W6Njnz5+PkSNH4tixY5gwYQISEhLwzDPPYOrUqThx4gQ+/vhjrF69Wik8K5KQkICOHTuiadOmNdq3Xq8HcL2YB4APP/wQly5dwltvvYXnn38eAQEBZs9Y9u7dG3/88QcyMzNrtC8iskFCRI1CUFCQLFmyRERESktLxc3NTeLi4kyW165dq7QfM2aMhIaGiohIUVGRODo6yt69e036nDhxoowZM0ZEROLi4gSAbNq0qcpYOnXqJEuXLhURkdTUVAEghw4dUtafPHlSAMgHH3wgIiIJCQni7OwsRUVFJv384x//kI8//viW+wEgDg4O0qRJE5PX77//rrTZu3ev2NvbyxtvvCEajUYSEhKUdRkZGQJAFi5cqLxXWloqd999tyxatEhERN566y156KGHTPZ79uxZASBpaWkiItK/f3/p16+fSZt7771XZs2aJSIiO3bsEI1GI3/++aeyftu2bQJANm7caBJLUlKSiPyd7ytXrpj06+Pjo+StXNeuXWXevHkmeZk2bZpJm8GDB8s777xj8t5nn30mXl5ecitTp06VQYMGmb1/Y9w3L+fn58vzzz8varVakpOTlTY7d+4UtVotzs7OkpmZadbn1atXBYDs3r37lvEQUcNg+Yd7iKjepaWl4eDBg9i4cSMAQKPRIDQ0FCtXrsSAAQOg0WgwevRorFu3Dk8//TTy8/Px7bffKrchT506hYKCAjz44IMm/ZbfRr5Rr169TJbz8vIwf/58bNmyBVlZWTAYDCgsLFSuXKalpUGj0aBHjx7KNu3bt0ezZs2U5eTkZOTl5aFFixYmfRcWFiI9Pb3SY//ggw8QHBxs8l6rVq2UnwMDAzFz5ky89dZbmDVrFvr162fWR2BgoPKzRqNBr169kJqaqsQWFxcHJycns+3S09PRsWNHAECXLl1M1nl5eSlXZ1NTU+Ht7W0WV126+feUnJyMPXv2mFypLCsrQ1FREQoKCuDo6GjWR2FhofKIQVXGjBkDtVqNwsJCuLu7Y+XKlSY5GTRoEO677z5069YNPj4+ZtuXX+0sKCio1v6IyHaxuCRqBFauXAmDwWBSvIgIdDodli1bBhcXF4SFhaF///44f/48YmNjodfr8fDDDwOAcrt8y5YtuOuuu0z61ul0JstNmjQxWZ45cyZiY2Px/vvvo3379tDr9XjyySeVW6LVkZeXBy8vL+zevdtsnaura6Xbenp6on379rdcbzQasWfPHqjVapw6daraMd0Y27Bhw7Bo0SKzdV5eXsrP9vb2JutUKhWMRmON91cVOzs75XGHchUN2Ln595SXl4cFCxbg8ccfN2t7qwLSzc3NZCBOZcqLfBcXF7i7u1fYRqPR3HLAUvnjD7falogaDhaXRA2cwWDA2rVr8a9//QsPPfSQyboRI0Zg/fr1mDx5MoKCguDt7Y0vvvgC27Ztw6hRo5SCyN/fHzqdDmfOnEH//v1rtP89e/Zg3LhxyrObeXl5Js/N+fr6wmAwICkpCT179gRw/UrplStXlDY9evRAdnY2NBoN2rRpU4ss3Np7772HX3/9FfHx8QgJCcGqVaswfvx4kzb79+/HAw88AOB6PhMTEzFlyhQltq+//hpt2rSp9Ujue+65B2fPnkVWVpZSkO7fv7/SbbRaLYDrVxdv5O7ujqysLGU5NzcXGRkZVcbQo0cPpKWlVVqI36x79+6IioqCiEClUlXatqoivyopKSmwt7dHp06dat0HEdkGDughauA2b96MK1euYOLEiQgICDB5PfHEE1i5cqXSduzYsYiOjkZsbCzCwsKU95s2bYqZM2fipZdewpo1a5Ceno5ffvkFS5cuxZo1ayrdf4cOHfDNN9/gyJEjSE5OxtixY02u2Pn5+SE4OBiTJk3CwYMHkZSUhEmTJkGv1ysFS3BwMAIDAzFixAj88MMPyMzMxN69ezFnzhwcPny40v3n5OQgOzvb5JWfnw8ASEpKwty5c/HJJ5+gb9++WLx4MaZOnWo2n+Ly5cuxceNG/Prrr4iIiMCVK1cwYcIEAEBERAQuX76MMWPG4NChQ0hPT8eOHTswfvx4s8LvVoKDg9GxY0eEh4cjOTkZCQkJmDNnTqXb+Pj4QKVSYfPmzbhw4YJydXnQoEH47LPPkJCQgGPHjiE8PBxqtbrKGObOnYu1a9diwYIFOH78OFJTUxETE4PXX3/9ltsMHDgQeXl5OH78eLWO83YkJCTg/vvvV26PE1EDZuVnPonoNj366KPyyCOPVLjuwIEDAkAZWHHixAkBID4+PmI0Gk3aGo1GWbJkifj6+oq9vb24u7tLSEiIxMfHi8itB5hkZGTIwIEDRa/Xi7e3tyxbtkz69+8vU6dOVdr89ddfMmTIENHpdOLj4yOff/65tGzZUqKjo5U2ubm58sILL0irVq3E3t5evL29JSwsTM6cOXPLYwdQ4SsyMlIKCwvF399fJk2aZLLN8OHDJSgoSAwGgzKI5vPPP5fevXuLVqsVf39/2bVrl8k2v/32m4wcOVJcXV1Fr9eLn5+fTJs2TcnhzccrIvLYY49JeHi4spyWlib9+vUTrVYrHTt2lO3bt1c6oEdE5M033xRPT09RqVRKX1evXpXQ0FBxdnYWb29vWb16dYUDem4ccFNu+/btEhQUJHq9XpydnaV3796yYsWKW+ZXRGT06NEye/ZsZbmsrEwAyPfff1/l/m5WUZ7K+fr6yvr166vsg4hsn0rkpod3iIjq2B9//AFvb2/8+OOPGDx4sNXiyMzMRNu2bZGUlIRu3bpZLQ5bdvToUTz44INIT0+Hk5MTsrOz4eXlhUOHDpkNGqqtbdu2YcaMGTh69GidTCJPRPWLZzER1bldu3YhLy8PnTt3RlZWFl555RW0adNGec6RbFeXLl2waNEiZGRkoGnTpnj//ffh4eGh/JlKS8jPz8eqVatYWBI1EjyTiajOlZaW4rXXXsPp06fRtGlTBAUFYd26dWYjrMk2jRs3Djk5OfDw8MA999yDmJiYak9RVB1PPvmkxfoiIuvjbXEiIiIishiOFiciIiIii2FxSUREREQWw+KSiIiIiCyGxSURERERWQyLSyIiIiKyGBaXRERERGQxLC6JiIiIyGJYXBIRERGRxfwfC5UaojNwmrQAAAAASUVORK5CYII="
    }
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   "id": "a7e4af93",
   "metadata": {},
   "source": [
    "![Prior_predictive_distribution.png](attachment:Prior_predictive_distribution.png)\n",
    "<t><center> Figure 7. Prior predictive distribution, median, sample and observed bounds. </center></t>\n",
    "\n",
    "As we can see from the prior predictive distribution it is clear that the samples from my prior predictive distribution have the percentiles indicated above. 80% of average monthly spending is distributed between 3292.2 JPY and 29861.2 JPY. The error around the lower bound is = 2292.23 JPY and  error around upper bound is = 138.79 JPY which is very close to the percentiles indicated above. Moreover the median is exactly at the 10000 JPY which is also another indicator that prior and likelihood distributions worked and that sampling was conducted successfully. Moreover, the resulting distribution predicts that as the expenditure increases the frequency decreases which is how we generally expect consumers to behave -- again, quantity demanded decreases as the price increases. This is very common economic assumption and it is good to see that our model successfully follows it. Additionally, we can also see that there are no negative values in the distribution which shows that the combination of selecting Truncated Normal and LogNormal distributions for likelihood and prior has worked successfully and resulting distribution does not include negative values. One downside that we can observe is high error around lower bound [2292.23 JPY]. This can be attributed to how we estimated our $\\sigma^2$ value. \n",
    "<t><center>$ \\sigma = \\frac{30000-\\log(10000)}{1.28}$</center></t>\n",
    "We had two bounds between which $80%$ of data was spread between. These bounds were [1000,30000] respectfully. Since we chose upper bound as an observation we have sacrificed accuracy around the lower bound. This can be improved by either changing the prior distributions or using other optimization techniques. However, for the scope of prior predictive distribution I believe that this error can be negligible.  "
   ]
  },
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   "id": "9ef67e2e",
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   "source": [
    "#### Summary Video \n",
    "The video of the summary is accessible through this google drive link which is shared with Prof. Volkan and both TAs. Link: https://drive.google.com/file/d/13L0N_uBMzVslwOfd-5HbCAbFkX4SClz5/view?usp=sharing. Additional note: it was impossible to compress video further than 300 mbs and keep it intelligible. This is why I have indicated drive link. The video is 87 seconds long so definetely below 1.5 minutes. "
   ]
  },
  {
   "cell_type": "markdown",
   "id": "b04a8e03",
   "metadata": {},
   "source": [
    "#### AI Statement\n",
    "I did not use Chat GPT or AI other tool for this assignment. \n",
    "I used Grammarly to check for spelling and grammar mistakes.\n",
    "I obtained all the relevant formulas from the textook or from Wikipedia. "
   ]
  },
  {
   "cell_type": "markdown",
   "id": "b4c34aee",
   "metadata": {},
   "source": [
    "#### References\n",
    "\n",
    "Bernardo, J.M. and Smith, A.F.M. (1994). Bayesian Theory, Section 5.2.\n",
    "\n",
    "McElreath, R. (2020). Statistical Rethinking, Second Edition. Chapman and Hall/CRC Press.\n",
    "\n",
    "Minerva University. (2024). CS146: Computational Methods for Bayesian Statistics. Sessions 1-6. \n",
    "\n",
    "University of Carlos III Madrid. (2024). Conjugate families of distributions. Department of Statistics. Link:   https://halweb.uc3m.es/esp/personal/personas/mwiper/docencia/English/PhD_Bayesian_Statistics/ch3_2009.pdf\n",
    "\n",
    "Wikipedia. (2024). Conjugate Prior https://en.wikipedia.org/wiki/Conjugate_prior\n",
    "\n",
    "Wikipedia. (2024). Log Normal Distribution. https://en.wikipedia.org/wiki/Log-normal_distribution\n",
    "\n",
    "Wikipedia. (2024). Truncated Normal Distribution. https://en.wikipedia.org/wiki/Truncated_normal_distribution\n"
   ]
  }
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