{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# PyMC"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "PyMC is a python module that implements Bayesian statistical models and fitting algorithms, including Markov chain Monte Carlo. Its flexibility and extensibility make it applicable to a large suite of problems. Along with core sampling functionality, PyMC includes methods for summarizing output, plotting, goodness-of-fit and convergence diagnostics.\n",
    "\n",
    "Library documentation: <a>https://pymc-devs.github.io/pymc/</a>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "# objective is to model the number of coal mining disasters per year in the UK from 1851 to 1962 \n",
    "# start with some imports\n",
    "%matplotlib inline\n",
    "import numpy as np\n",
    "from pymc import *\n",
    "from pymc.Matplot import plot"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "# number of mining disasters per year\n",
    "disasters_array =  np.array([4, 5, 4, 0, 1, 4, 3, 4, 0, 6, 3, 3, 4, 0, 2, 6,\n",
    "                            3, 3, 5, 4, 5, 3, 1, 4, 4, 1, 5, 5, 3, 4, 2, 5,\n",
    "                            2, 2, 3, 4, 2, 1, 3, 2, 2, 1, 1, 1, 1, 3, 0, 0,\n",
    "                            1, 0, 1, 1, 0, 0, 3, 1, 0, 3, 2, 2, 0, 1, 1, 1,\n",
    "                            0, 1, 0, 1, 0, 0, 0, 2, 1, 0, 0, 0, 1, 1, 0, 2,\n",
    "                            3, 3, 1, 1, 2, 1, 1, 1, 1, 2, 4, 2, 0, 0, 1, 4,\n",
    "                            0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 1])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<pymc.distributions.DiscreteUniform 'switchpoint' at 0x7f69c67d4310>"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# variable representing the presumed \"switch point\" at which disasters became less frequent\n",
    "switchpoint = DiscreteUniform('switchpoint', lower=0, upper=110, doc='Switchpoint[year]')\n",
    "switchpoint"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(<pymc.distributions.Exponential 'early_mean' at 0x7f69c67d4490>,\n",
       " <pymc.distributions.Exponential 'late_mean' at 0x7f69c67d44d0>)"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# variables for the pre and post-switchpoint mean\n",
    "early_mean = Exponential('early_mean', beta=1.)\n",
    "late_mean = Exponential('late_mean', beta=1.)\n",
    "early_mean, late_mean"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "# deterministic rate parameter of the distribution of disasters\n",
    "@deterministic(plot=False)\n",
    "def rate(s=switchpoint, e=early_mean, l=late_mean):\n",
    "    ''' Concatenate Poisson means '''\n",
    "    out = np.empty(len(disasters_array))\n",
    "    out[:s] = e\n",
    "    out[s:] = l\n",
    "    return out"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<pymc.distributions.Poisson 'disasters' at 0x7f69c67d41d0>"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# actual distribution of disasters (observed)\n",
    "disasters = Poisson('disasters', mu=rate, value=disasters_array, observed=True)\n",
    "disasters"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "({'lower': 0, 'upper': 110},\n",
       " {'mu': <pymc.PyMCObjects.Deterministic 'rate' at 0x7f69c67d4a50>},\n",
       " {<pymc.distributions.Poisson 'disasters' at 0x7f69c67d41d0>})"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# take a look at the parents/children for these variables to see relationships\n",
    "switchpoint.parents, disasters.parents, rate.children"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "# create the model\n",
    "model = Model([switchpoint, early_mean, late_mean, disasters])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      " [-----------------100%-----------------] 10000 of 10000 complete in 3.7 sec"
     ]
    }
   ],
   "source": [
    "# Markov Chain Monte-Carlo sampling\n",
    "M = MCMC(model)\n",
    "M.sample(iter=10000, burn=1000, thin=10)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[91 46 46 46 46 46 46 46 46 46 46 46 46 46 46 46 46 46 46 46 46 46 46 46 46\n",
      " 46 46 46 46 46 46 46 46 46 46 46 46 46 46 46 46 46 46 46 46 46 46 46 46 46\n",
      " 46 46 46 46 46 46 46 46 46 46 46 46 46 46 46 46 46 46 46 46 46 46 46 46 46\n",
      " 46 46 46 46 46 46 46 46 46 46 46 46 46 46 46 46 46 46 46 46 46 46 46 46 46\n",
      " 46 46 46 46 46 46 46 46 46 46 46 46 46 46 46 37 37 37 37 37 37 37 37 37 37\n",
      " 37 37 37 37 37 37 37 37 37 37 37 37 37 37 37 37 37 37 37 37 37 37 37 37 37\n",
      " 37 37 37 37 37 37 37 37 37 37 37 37 37 37 37 37 37 37 37 37 37 37 37 37 37\n",
      " 37 37 37 37 37 37 37 37 37 37 37 37 37 37 37 37 37 37 37 37 37 37 37 37 37\n",
      " 37 37 37 37 48 40 40 40 40 40 40 40 40 40 40 40 40 45 45 46 43 43 43 37 43\n",
      " 43 43 37 41 41 41 41 41 41 41 41 41 41 41 41 36 37 41 41 41 41 41 41 41 41\n",
      " 41 40 40 40 40 40 40 40 43 38 38 36 38 38 38 39 39 46 38 43 43 39 41 39 39\n",
      " 39 39 39 39 39 39 39 37 38 38 36 36 39 39 39 39 39 40 40 37 37 44 39 39 44\n",
      " 44 37 37 37 38 37 37 37 37 46 40 40 40 36 46 39 39 39 45 43 46 47 39 39 46\n",
      " 36 40 39 44 39 39 39 39 39 39 41 41 46 42 43 43 44 39 39 39 39 39 39 41 40\n",
      " 40 40 40 40 40 40 40 46 46 41 41 41 41 41 39 41 41 41 41 41 41 36 36 41 41\n",
      " 41 41 41 41 41 41 41 41 36 46 37 37 41 41 41 41 41 41 41 39 39 39 39 44 39\n",
      " 39 39 39 39 37 43 43 39 39 39 40 40 37 41 41 41 41 41 41 41 41 41 37 44 37\n",
      " 37 38 38 37 37 39 39 44 44 39 39 39 41 41 46 39 39 39 39 39 39 39 39 39 39\n",
      " 39 39 39 44 39 39 36 41 36 39 39 39 39 39 39 39 40 40 37 39 39 39 39 37 36\n",
      " 36 46 37 41 41 43 39 39 39 44 39 39 39 37 40 40 40 47 36 39 39 42 42 42 42\n",
      " 42 40 40 40 40 40 40 40 39 36 40 40 40 40 40 39 39 41 41 41 41 41 37 41 36\n",
      " 36 41 37 37 40 40 40 38 41 46 41 38 42 36 39 39 39 43 40 40 40 40 40 39 36\n",
      " 42 43 42 41 40 36 39 39 40 40 40 39 39 40 40 40 40 40 43 41 41 41 42 41 41\n",
      " 36 42 38 42 38 38 41 41 40 40 40 40 40 39 35 36 40 42 40 40 40 40 40 38 38\n",
      " 41 41 41 41 41 36 36 46 40 43 39 39 39 39 44 37 37 41 42 35 36 40 40 39 39\n",
      " 39 39 39 39 44 42 40 40 36 40 40 36 36 40 42 37 37 40 40 40 36 44 42 36 41\n",
      " 41 41 38 36 36 37 40 40 40 44 40 36 36 49 39 36 46 41 41 37 41 41 40 40 36\n",
      " 40 40 40 40 40 40 40 40 41 44 43 41 41 41 41 38 40 36 40 41 42 37 39 37 41\n",
      " 39 39 40 39 39 41 41 46 40 40 41 37 39 42 40 36 43 39 36 40 42 37 41 43 37\n",
      " 40 42 40 36 35 36 41 41 37 41 41 42 40 41 41 41 41 41 46 37 40 46 39 44 41\n",
      " 42 41 37 36 40 46 40 40 38 39 39 39 41 41 41 41 41 41 46 40 36 40 42 42 36\n",
      " 40 40 39 39 43 37 39 38 39 39 39 39 41 36 39 36 40 40 40 42 35 35 41 41 45\n",
      " 39 41 41 41 39 46 38 40 36 39 43 32 34 36 40 40 41 41 38 41 40 39 40 37 41\n",
      " 44 42 40 38 39 40 42 37 40 36 40 42 43 36 39 39 37 37 39 42 39 39 39 37 37\n",
      " 42 42 36 41 36 42 40 41 37 40 37 39 41 41 39 41 43 41 37 36 41 36 39 41 39\n",
      " 40 40 40 32 39 39 40 42 40 39 39 39 39 39 40 40 37 42 46 41 41 43 38 44 41]\n"
     ]
    }
   ],
   "source": [
    "# examine a slice of the output\n",
    "print M.trace('switchpoint')[:]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Plotting switchpoint\n",
      "Plotting late_mean\n",
      "Plotting early_mean\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/home/john/anaconda/lib/python2.7/site-packages/numpy/core/fromnumeric.py:2499: VisibleDeprecationWarning: `rank` is deprecated; use the `ndim` attribute or function instead. To find the rank of a matrix see `numpy.linalg.matrix_rank`.\n",
      "  VisibleDeprecationWarning)\n"
     ]
    },
    {
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      ],
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f69c66f2dd0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
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      ],
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f69c650c690>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
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       "EbEX+COW2Z8yc0dE3E4rcDwC/If2rcJJUvR9fzvwQoDM3JqZd0bExojYQ+sW9BvH09Ra9Ow/8Drg\n",
       "iog4AvwLrRPRLDgN+FBEPIPWBYcPZ+b/jojLYea3fc++M7vbvUgCDLPtHSBUkiSpIiMZIFSSJGke\n",
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       "AABJRU5ErkJggg==\n"
      ],
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f69c6088a90>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# generate a composite figure for the model\n",
    "plot(M)"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 2",
   "language": "python",
   "name": "python2"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 2
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython2",
   "version": "2.7.9"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 0
}