pangolin-jags/Example-Gaussian-Gaussian.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "c340e51d",
   "metadata": {},
   "source": [
    "This is perhaps the simplest possible generative model\n",
    "\n",
    "$$ x \\sim \\mathcal{N}(0,σ\\ Ι)$$\n",
    "\n",
    "$$ y_i \\sim \\mathcal{N}(x, I), i \\in {1,\\cdots,N}$$\n",
    "\n",
    "We will observe $y_1, \\cdots, y_N$ and try to infer $x$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "22d652aa",
   "metadata": {},
   "outputs": [],
   "source": [
    "# Bayesian \"mean\" model\n",
    "\n",
    "from pangolin import d, t, Given, I, IID, vmap, recurse, scan, sample, E, P, var, std, cov, corr, jags_code, makerv\n",
    "from matplotlib import pyplot as plt\n",
    "import numpy as np\n",
    "\n",
    "def demo(ndata):\n",
    "    σ = 3\n",
    "    ndims = 2\n",
    "    \n",
    "    # manually generate data\n",
    "    x_tru = σ * np.random.randn(2)\n",
    "    y_obs = np.random.rand(ndata,ndims)+x_tru\n",
    "\n",
    "    # define model\n",
    "    x = d.mnorm_vcov(np.zeros(2),σ**2*np.eye(2))\n",
    "    y = [d.mnorm(x,np.eye(2)) for i in range(ndata)]\n",
    "    \n",
    "    # do inference\n",
    "    observations = [yi==yi_obs for (yi,yi_obs) in zip(y,y_obs)]\n",
    "    xs = sample(x,Given(*observations))\n",
    "\n",
    "    # plot\n",
    "    plt.figure(figsize=(10,6))\n",
    "    plt.plot(xs[:1000:10,0],xs[:1000:10,1],'rx',alpha=0.25,label='posterior samples ($x \\sim p(x|y)$)');\n",
    "    plt.plot(x_tru[0],x_tru[1],'kx',label='true x.',markersize=6)\n",
    "    plt.plot(y_obs[:,0],y_obs[:,1],'b.',label='observed y');\n",
    "    plt.legend()\n",
    "    plt.xlim([-3*σ,3*σ])\n",
    "    plt.ylim([-3*σ,3*σ]);\n",
    "    plt.title(str(ndata) + \" observation(s)\")\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "3481d298",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": "<Figure size 1000x600 with 1 Axes>",
      "image/png": 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\n"
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# with one observation the posterior is spread quite far out\n",
    "demo(ndata=1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "ead0bd46",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": "<Figure size 1000x600 with 1 Axes>",
      "image/png": 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\n"
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# with 3 observations it is smaller\n",
    "demo(ndata=3)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "5a0a152b",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": "<Figure size 1000x600 with 1 Axes>",
      "image/png": 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\n"
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# with 10 observations is much smaller\n",
    "\n",
    "demo(ndata=10)"
   ]
  },
  {
   "cell_type": "markdown",
   "source": [
    "Notice the uncertainty automatically shrinks in the right way so that it contains the true x."
   ],
   "metadata": {
    "collapsed": false
   }
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3 (ipykernel)",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.9.7"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}