{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# Import relevant modules\n",
    "import pymc\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# Some data\n",
    "n = 5 * np.ones(4, dtype=int)\n",
    "x = np.array([-.86, -.3, -.05, .73])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# Priors on unknown parameters\n",
    "alpha = pymc.Normal('alpha', mu=0, tau=.01)\n",
    "beta = pymc.Normal('beta', mu=0, tau=.01)\n",
    "\n",
    "# Arbitrary deterministic function of parameters\n",
    "@pymc.deterministic\n",
    "def theta(a=alpha, b=beta):\n",
    "    \"\"\"theta = logit^{-1}(a+b)\"\"\"\n",
    "    return pymc.invlogit(a + b * x)\n",
    "\n",
    "# Binomial likelihood for data\n",
    "d = pymc.Binomial('d', n=n, p=theta, value=np.array([0., 1., 3., 5.]),\n",
    "                  observed=True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "mymodel = pymc.Model([theta, d])\n",
    "S = pymc.MCMC(mymodel, db='pickle')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\r",
      " [-----------------100%-----------------] 10000 of 10000 complete in 0.3 sec"
     ]
    }
   ],
   "source": [
    "\n",
    "S.sample(iter=10000, burn=5000, thin=2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Plotting theta_0\n",
      "Plotting theta_1\n",
      "Plotting theta_2\n",
      "Plotting theta_3\n"
     ]
    }
   ],
   "source": [
    "pymc.Matplot.plot(S)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  }
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