PyMC Disaster Model.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<a href=\"https://pymc-devs.github.io/pymc/tutorial.html\">PyMC Tutorial</a>\n",
    "<h3>The Model:</h3>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "from pymc import DiscreteUniform, Exponential, deterministic, Poisson, Uniform\n",
    "import numpy as np\n",
    "\n",
    "disasters_array = \\\n",
    "        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])\n",
    "\n",
    "# switchpoint, all values equally likely a priori\n",
    "switchpoint = DiscreteUniform('switchpoint', lower=0, upper=110, doc='Switchpoint[year]')\n",
    "\n",
    "early_mean = Exponential('early_mean', beta=1.)\n",
    "late_mean = Exponential('late_mean', beta=1.)\n",
    "\n",
    "\"\"\"In PyMC terminology, the parameter rate is 'deterministic', meaning it's determined explicitly\n",
    "by observations of its parents. (It's still a random variable)\"\"\"\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)) # array of size 1 x len(disasters_array) with uninitialized values\n",
    "    out[:s] = e\n",
    "    out[s:] = l\n",
    "    return out                           # looks like [e, e, ..., e, l, l,...,l]\n",
    "\n",
    "\"\"\"Finally, we model the observed random variable, disasters. We have to assign it a probability distribution\n",
    "because we want to use Bayes' Theorem\"\"\"\n",
    "disasters = Poisson('disasters', mu=rate, value=disasters_array, observed=True) # note the declaration of observed"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "{'lower': 0, 'upper': 110}"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "import disaster_model\n",
    "disaster_model.switchpoint.parents"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "{'mu': <pymc.PyMCObjects.Deterministic 'rate' at 0x1061a1950>}"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "disaster_model.disasters.parents"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "{<pymc.distributions.Poisson 'disasters' at 0x1061a1990>}"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "disaster_model.rate.children"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Notice that parents are dictionaries while children are sets"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([4, 5, 4, 0, 1, 4, 3, 4, 0, 6, 3, 3, 4, 0, 2, 6, 3, 3, 5, 4, 5, 3, 1,\n",
       "       4, 4, 1, 5, 5, 3, 4, 2, 5, 2, 2, 3, 4, 2, 1, 3, 2, 2, 1, 1, 1, 1, 3,\n",
       "       0, 0, 1, 0, 1, 1, 0, 0, 3, 1, 0, 3, 2, 2, 0, 1, 1, 1, 0, 1, 0, 1, 0,\n",
       "       0, 0, 2, 1, 0, 0, 0, 1, 1, 0, 2, 3, 3, 1, 1, 2, 1, 1, 1, 1, 2, 4, 2,\n",
       "       0, 0, 1, 4, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 1])"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "disaster_model.disasters.value # we set this value"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array(81)"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "disaster_model.switchpoint.value # the following values were randomly assigned"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array(0.05980528931627297)"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "disaster_model.early_mean.value "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array(2.202582358708252)"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "disaster_model.late_mean.value"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 0.05980529,  0.05980529,  0.05980529,  0.05980529,  0.05980529,\n",
       "        0.05980529,  0.05980529,  0.05980529,  0.05980529,  0.05980529,\n",
       "        0.05980529,  0.05980529,  0.05980529,  0.05980529,  0.05980529,\n",
       "        0.05980529,  0.05980529,  0.05980529,  0.05980529,  0.05980529,\n",
       "        0.05980529,  0.05980529,  0.05980529,  0.05980529,  0.05980529,\n",
       "        0.05980529,  0.05980529,  0.05980529,  0.05980529,  0.05980529,\n",
       "        0.05980529,  0.05980529,  0.05980529,  0.05980529,  0.05980529,\n",
       "        0.05980529,  0.05980529,  0.05980529,  0.05980529,  0.05980529,\n",
       "        0.05980529,  0.05980529,  0.05980529,  0.05980529,  0.05980529,\n",
       "        0.05980529,  0.05980529,  0.05980529,  0.05980529,  0.05980529,\n",
       "        0.05980529,  0.05980529,  0.05980529,  0.05980529,  0.05980529,\n",
       "        0.05980529,  0.05980529,  0.05980529,  0.05980529,  0.05980529,\n",
       "        0.05980529,  0.05980529,  0.05980529,  0.05980529,  0.05980529,\n",
       "        0.05980529,  0.05980529,  0.05980529,  0.05980529,  0.05980529,\n",
       "        0.05980529,  0.05980529,  0.05980529,  0.05980529,  0.05980529,\n",
       "        0.05980529,  0.05980529,  0.05980529,  0.05980529,  0.05980529,\n",
       "        0.05980529,  2.20258236,  2.20258236,  2.20258236,  2.20258236,\n",
       "        2.20258236,  2.20258236,  2.20258236,  2.20258236,  2.20258236,\n",
       "        2.20258236,  2.20258236,  2.20258236,  2.20258236,  2.20258236,\n",
       "        2.20258236,  2.20258236,  2.20258236,  2.20258236,  2.20258236,\n",
       "        2.20258236,  2.20258236,  2.20258236,  2.20258236,  2.20258236,\n",
       "        2.20258236,  2.20258236,  2.20258236,  2.20258236,  2.20258236,\n",
       "        2.20258236])"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "disaster_model.rate.value"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<p><tt>logp</tt> returns the log of the probability density of a stochastic variable at their current values given the values\n",
    "of their parents. We can think of the -log probability as a scale of rarity, the larger the more rare.</p>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "-4.709530201312334"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "disaster_model.switchpoint.logp # log of uniform probability evaluated at switchpoint.value"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "-622.7366089468533"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "disaster_model.disasters.logp # sum of logs of joint density for each element of disasters \n",
    "                              # given parents' (the parameters') values"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "-0.05980528931627297"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "disaster_model.early_mean.logp # e~exp(1) so log(1*exp(-1*e)) = -e"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "-2.202582358708252"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "disaster_model.late_mean.logp"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.00900900900900901"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from math import exp\n",
    "\n",
    "exp(disaster_model.switchpoint.logp) # because this came from a uniform(0,110) distribution it is == 1/111"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "-622.73660894685349"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "\"\"\"What logp is really doing for vector valued objects\"\"\"\n",
    "from scipy import stats\n",
    "\n",
    "\n",
    "arr = np.array([np.log(stats.poisson.pmf(disaster_model.disasters.value[i], mu=disaster_model.rate.value[i])) \n",
    "                for i in range(disaster_model.disasters.value.shape[0])])\n",
    "np.sum(arr)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "{'e': array(0.05980528931627297),\n",
       " 'l': array(2.202582358708252),\n",
       " 's': array(81)}"
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "disaster_model.rate.parents.value # although these values are stochastic, "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      " [-----------------100%-----------------] 12000 of 12000 complete in 1.6 sec"
     ]
    }
   ],
   "source": [
    "from pymc import MCMC\n",
    "\n",
    "#Markov Chain Monte Carlo Sampling\n",
    "M = MCMC(disaster_model)\n",
    "\n",
    "M.sample(iter=12000, burn=3000, thin=10)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<p>M.sample creates a series of retained samples of (<tt>s, e, l</tt>) from the posterior distribution of the model. <br>\n",
    "The MCMC joint distribution for <strong>P</strong>(<tt>s, e, l|D)</tt> converges to the true distribution, so we <tt>burn</tt> the <br>\n",
    "first 1000 values. Because the values are generated by a autoregressive stochastic process close by values <br>\n",
    "of the samples will be strongly autocorrelated so we take only every 10 values (<tt>thin=10</tt>)</p>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {
    "collapsed": false,
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([43, 40, 40, 36, 41, 42, 37, 42, 37, 41, 42, 40, 39, 41, 40, 36, 40,\n",
       "       39, 37, 46, 40, 36, 37, 42, 40, 41, 40, 36, 39, 40, 40, 43, 44, 43,\n",
       "       39, 41, 36, 40, 38, 42, 37, 42, 40, 37, 46, 39, 42, 39, 37, 37, 36,\n",
       "       41, 41, 41, 41, 36, 43, 39, 37, 39, 40, 41, 39, 42, 40, 41, 46, 43,\n",
       "       40, 41, 41, 43, 42, 41, 41, 39, 40, 37, 40, 40, 40, 36, 37, 41, 41,\n",
       "       41, 41, 40, 39, 39, 41, 40, 39, 35, 39, 41, 44, 39, 41, 41, 37, 40,\n",
       "       36, 38, 37, 37, 41, 38, 46, 41, 36, 41, 45, 41, 40, 41, 40, 46, 40,\n",
       "       47, 40, 36, 42, 41, 42, 41, 40, 36, 41, 39, 39, 42, 36, 43, 42, 41,\n",
       "       39, 41, 42, 36, 39, 37, 41, 40, 36, 41, 40, 43, 40, 43, 43, 37, 36,\n",
       "       40, 40, 40, 40, 36, 39, 37, 39, 46, 37, 42, 39, 41, 41, 41, 37, 43,\n",
       "       40, 42, 39, 43, 41, 41, 42, 43, 42, 36, 40, 40, 36, 41, 39, 38, 46,\n",
       "       40, 41, 41, 41, 46, 40, 41, 37, 40, 38, 39, 40, 42, 39, 39, 39, 42,\n",
       "       42, 41, 40, 39, 43, 40, 41, 41, 37, 41, 40, 40, 42, 41, 36, 41, 39,\n",
       "       40, 42, 41, 42, 39, 41, 46, 41, 42, 39, 44, 40, 39, 42, 45, 40, 39,\n",
       "       40, 39, 41, 37, 38, 41, 41, 39, 41, 43, 40, 39, 40, 39, 39, 41, 36,\n",
       "       41, 41, 41, 42, 40, 39, 43, 40, 43, 41, 44, 36, 39, 38, 41, 40, 41,\n",
       "       46, 36, 45, 40, 41, 40, 42, 40, 42, 39, 41, 40, 41, 41, 39, 40, 39,\n",
       "       42, 37, 37, 41, 40, 38, 40, 41, 39, 42, 39, 39, 42, 40, 44, 40, 45,\n",
       "       46, 39, 39, 42, 42, 40, 39, 39, 42, 41, 41, 41, 37, 37, 40, 40, 37,\n",
       "       37, 40, 41, 41, 38, 43, 41, 39, 38, 40, 41, 43, 43, 36, 36, 41, 40,\n",
       "       40, 43, 38, 39, 43, 41, 39, 40, 39, 36, 41, 39, 42, 42, 41, 41, 37,\n",
       "       40, 37, 46, 41, 40, 40, 37, 38, 39, 41, 39, 42, 44, 41, 41, 36, 40,\n",
       "       46, 43, 40, 41, 41, 39, 36, 41, 41, 42, 42, 41, 41, 41, 42, 41, 39,\n",
       "       37, 40, 42, 44, 40, 41, 39, 37, 39, 41, 39, 40, 40, 43, 39, 37, 41,\n",
       "       42, 40, 42, 40, 39, 41, 41, 42, 40, 41, 41, 42, 43, 37, 42, 40, 40,\n",
       "       41, 38, 39, 37, 40, 39, 40, 41, 43, 41, 41, 38, 40, 41, 40, 38, 41,\n",
       "       40, 44, 46, 37, 43, 41, 37, 42, 37, 40, 47, 41, 46, 41, 44, 36, 41,\n",
       "       42, 41, 39, 41, 41, 40, 38, 36, 37, 41, 43, 36, 41, 41, 38, 41, 41,\n",
       "       40, 40, 39, 37, 37, 39, 41, 41, 46, 42, 41, 39, 39, 35, 39, 40, 42,\n",
       "       44, 39, 40, 39, 42, 43, 40, 40, 40, 38, 39, 39, 43, 47, 40, 37, 40,\n",
       "       35, 40, 46, 40, 41, 43, 43, 41, 40, 36, 41, 41, 42, 39, 41, 38, 43,\n",
       "       41, 40, 40, 40, 41, 41, 41, 41, 43, 37, 41, 37, 41, 43, 41, 41, 41,\n",
       "       40, 36, 40, 36, 41, 46, 40, 37, 43, 42, 43, 39, 42, 39, 46, 41, 42,\n",
       "       40, 39, 35, 41, 39, 40, 37, 41, 41, 43, 39, 43, 42, 37, 36, 40, 40,\n",
       "       46, 38, 39, 43, 39, 37, 39, 39, 41, 42, 40, 40, 41, 37, 41, 41, 41,\n",
       "       37, 42, 41, 45, 41, 42, 40, 41, 41, 39, 46, 46, 40, 41, 40, 42, 41,\n",
       "       39, 37, 42, 40, 42, 46, 40, 45, 38, 37, 39, 39, 41, 42, 42, 36, 37,\n",
       "       43, 41, 41, 34, 36, 39, 37, 39, 36, 36, 36, 39, 39, 39, 37, 40, 43,\n",
       "       38, 36, 41, 39, 41, 41, 39, 36, 46, 41, 42, 41, 40, 41, 45, 41, 40,\n",
       "       41, 37, 43, 36, 40, 37, 39, 40, 37, 37, 41, 40, 42, 42, 41, 40, 46,\n",
       "       34, 39, 41, 41, 39, 40, 41, 45, 42, 41, 39, 38, 40, 40, 42, 37, 40,\n",
       "       46, 40, 41, 42, 41, 43, 40, 41, 42, 37, 39, 46, 42, 36, 37, 39, 40,\n",
       "       46, 37, 41, 42, 40, 40, 41, 41, 41, 41, 39, 42, 42, 46, 39, 39, 40,\n",
       "       42, 41, 39, 37, 41, 40, 37, 41, 38, 46, 40, 41, 41, 38, 36, 39, 40,\n",
       "       41, 41, 40, 41, 39, 40, 40, 38, 36, 36, 37, 42, 40, 40, 39, 41, 41,\n",
       "       36, 37, 41, 37, 46, 35, 40, 40, 41, 36, 40, 36, 42, 41, 42, 36, 42,\n",
       "       38, 44, 38, 41, 46, 42, 41, 41, 39, 46, 40, 41, 36, 36, 42, 41, 40,\n",
       "       39, 36, 36, 41, 40, 40, 42, 39, 41, 41, 40, 41, 39, 40, 42, 42, 38,\n",
       "       42, 39, 39, 41, 36, 37, 39, 48, 46, 42, 39, 41, 47, 42, 40, 40, 41,\n",
       "       40, 42, 37, 36, 37, 41, 41, 39, 35, 37, 41, 41, 42, 42, 37, 37, 46,\n",
       "       41, 42, 34, 41, 39, 39, 40, 43, 41, 36, 37, 40, 40, 39, 42, 38, 41,\n",
       "       39, 39, 40, 36, 41, 39, 39, 41, 37, 46, 45, 36, 38, 42, 41, 37, 41,\n",
       "       41, 44, 39, 41, 43, 38, 36, 41, 39, 41, 36, 41, 40, 42, 41, 41])"
      ]
     },
     "execution_count": 33,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "M.trace('switchpoint')[:] # output of the model for switchpoint, there are (12000-3000) / 10 = 900 retained values"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAXkAAAEACAYAAABWLgY0AAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10b8b0450>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "from pylab import hist, show\n",
    "\n",
    "hist(M.trace(late_mean)[:]) # histogram of marginal posterior probability P(l|D)\n",
    "show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Plotting early_mean\n",
      "Plotting late_mean\n",
      "Plotting switchpoint\n"
     ]
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAlYAAAFwCAYAAAB6uDWpAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10e742ed0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAlYAAAFwCAYAAAB6uDWpAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nsBIREREJ5H8BD34p4/2tujMAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10e742f90>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAlQAAAFwCAYAAAB+TeWUAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\ngg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10b8b9810>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "from pymc.Matplot import plot\n",
    "plot(M)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "{'early_mean': {'95% HPD interval': array([ 2.51484891,  3.5987009 ]),\n",
       "  'mc error': 0.010124377241700405,\n",
       "  'mean': 3.0500212783909157,\n",
       "  'n': 900,\n",
       "  'quantiles': {2.5: 2.5380485710235021,\n",
       "   25: 2.8627066469130957,\n",
       "   50: 3.0344447825217329,\n",
       "   75: 3.2344755204367597,\n",
       "   97.5: 3.6432076661218611},\n",
       "  'standard deviation': 0.2748233401210417},\n",
       " 'late_mean': {'95% HPD interval': array([ 0.72486174,  1.18466654]),\n",
       "  'mc error': 0.0037733961556360371,\n",
       "  'mean': 0.93747474375775941,\n",
       "  'n': 900,\n",
       "  'quantiles': {2.5: 0.72501071384110327,\n",
       "   25: 0.85542630781293683,\n",
       "   50: 0.9361906145376816,\n",
       "   75: 1.0145064455749853,\n",
       "   97.5: 1.186620172644258},\n",
       "  'standard deviation': 0.1169296188692924},\n",
       " 'rate': {'95% HPD interval': array([[ 2.51484891,  2.51484891,  2.51484891,  2.51484891,  2.51484891,\n",
       "           2.51484891,  2.51484891,  2.51484891,  2.51484891,  2.51484891,\n",
       "           2.51484891,  2.51484891,  2.51484891,  2.51484891,  2.51484891,\n",
       "           2.51484891,  2.51484891,  2.51484891,  2.51484891,  2.51484891,\n",
       "           2.51484891,  2.51484891,  2.51484891,  2.51484891,  2.51484891,\n",
       "           2.51484891,  2.51484891,  2.51484891,  2.51484891,  2.51484891,\n",
       "           2.51484891,  2.51484891,  2.51484891,  2.51484891,  2.50756989,\n",
       "           2.52805643,  0.89214227,  0.84153704,  0.78557271,  0.78557271,\n",
       "           0.75085529,  0.69873942,  0.66507632,  0.64183898,  0.62534378,\n",
       "           0.66507632,  0.72486174,  0.72486174,  0.72486174,  0.72486174,\n",
       "           0.72486174,  0.72486174,  0.72486174,  0.72486174,  0.72486174,\n",
       "           0.72486174,  0.72486174,  0.72486174,  0.72486174,  0.72486174,\n",
       "           0.72486174,  0.72486174,  0.72486174,  0.72486174,  0.72486174,\n",
       "           0.72486174,  0.72486174,  0.72486174,  0.72486174,  0.72486174,\n",
       "           0.72486174,  0.72486174,  0.72486174,  0.72486174,  0.72486174,\n",
       "           0.72486174,  0.72486174,  0.72486174,  0.72486174,  0.72486174,\n",
       "           0.72486174,  0.72486174,  0.72486174,  0.72486174,  0.72486174,\n",
       "           0.72486174,  0.72486174,  0.72486174,  0.72486174,  0.72486174,\n",
       "           0.72486174,  0.72486174,  0.72486174,  0.72486174,  0.72486174,\n",
       "           0.72486174,  0.72486174,  0.72486174,  0.72486174,  0.72486174,\n",
       "           0.72486174,  0.72486174,  0.72486174,  0.72486174,  0.72486174,\n",
       "           0.72486174,  0.72486174,  0.72486174,  0.72486174,  0.72486174,\n",
       "           0.72486174],\n",
       "         [ 3.5987009 ,  3.5987009 ,  3.5987009 ,  3.5987009 ,  3.5987009 ,\n",
       "           3.5987009 ,  3.5987009 ,  3.5987009 ,  3.5987009 ,  3.5987009 ,\n",
       "           3.5987009 ,  3.5987009 ,  3.5987009 ,  3.5987009 ,  3.5987009 ,\n",
       "           3.5987009 ,  3.5987009 ,  3.5987009 ,  3.5987009 ,  3.5987009 ,\n",
       "           3.5987009 ,  3.5987009 ,  3.5987009 ,  3.5987009 ,  3.5987009 ,\n",
       "           3.5987009 ,  3.5987009 ,  3.5987009 ,  3.5987009 ,  3.5987009 ,\n",
       "           3.5987009 ,  3.5987009 ,  3.5987009 ,  3.5987009 ,  3.61431123,\n",
       "           3.66952666,  3.53083311,  3.5170244 ,  3.4417898 ,  3.42727977,\n",
       "           3.38443579,  3.18481698,  2.9324096 ,  2.7611281 ,  2.50756989,\n",
       "           1.30928264,  1.19309883,  1.18662017,  1.18466654,  1.18466654,\n",
       "           1.18466654,  1.18466654,  1.18466654,  1.18466654,  1.18466654,\n",
       "           1.18466654,  1.18466654,  1.18466654,  1.18466654,  1.18466654,\n",
       "           1.18466654,  1.18466654,  1.18466654,  1.18466654,  1.18466654,\n",
       "           1.18466654,  1.18466654,  1.18466654,  1.18466654,  1.18466654,\n",
       "           1.18466654,  1.18466654,  1.18466654,  1.18466654,  1.18466654,\n",
       "           1.18466654,  1.18466654,  1.18466654,  1.18466654,  1.18466654,\n",
       "           1.18466654,  1.18466654,  1.18466654,  1.18466654,  1.18466654,\n",
       "           1.18466654,  1.18466654,  1.18466654,  1.18466654,  1.18466654,\n",
       "           1.18466654,  1.18466654,  1.18466654,  1.18466654,  1.18466654,\n",
       "           1.18466654,  1.18466654,  1.18466654,  1.18466654,  1.18466654,\n",
       "           1.18466654,  1.18466654,  1.18466654,  1.18466654,  1.18466654,\n",
       "           1.18466654,  1.18466654,  1.18466654,  1.18466654,  1.18466654,\n",
       "           1.18466654]]),\n",
       "  'mc error': array([ 0.01012438,  0.01012438,  0.01012438,  0.01012438,  0.01012438,\n",
       "          0.01012438,  0.01012438,  0.01012438,  0.01012438,  0.01012438,\n",
       "          0.01012438,  0.01012438,  0.01012438,  0.01012438,  0.01012438,\n",
       "          0.01012438,  0.01012438,  0.01012438,  0.01012438,  0.01012438,\n",
       "          0.01012438,  0.01012438,  0.01012438,  0.01012438,  0.01012438,\n",
       "          0.01012438,  0.01012438,  0.01012438,  0.01012438,  0.01012438,\n",
       "          0.01012438,  0.01012438,  0.01012438,  0.01012438,  0.01032113,\n",
       "          0.01152806,  0.01923702,  0.02573224,  0.02676634,  0.029873  ,\n",
       "          0.03257279,  0.02727596,  0.02112021,  0.01697763,  0.01489331,\n",
       "          0.01337829,  0.00652259,  0.00438171,  0.0037734 ,  0.0037734 ,\n",
       "          0.0037734 ,  0.0037734 ,  0.0037734 ,  0.0037734 ,  0.0037734 ,\n",
       "          0.0037734 ,  0.0037734 ,  0.0037734 ,  0.0037734 ,  0.0037734 ,\n",
       "          0.0037734 ,  0.0037734 ,  0.0037734 ,  0.0037734 ,  0.0037734 ,\n",
       "          0.0037734 ,  0.0037734 ,  0.0037734 ,  0.0037734 ,  0.0037734 ,\n",
       "          0.0037734 ,  0.0037734 ,  0.0037734 ,  0.0037734 ,  0.0037734 ,\n",
       "          0.0037734 ,  0.0037734 ,  0.0037734 ,  0.0037734 ,  0.0037734 ,\n",
       "          0.0037734 ,  0.0037734 ,  0.0037734 ,  0.0037734 ,  0.0037734 ,\n",
       "          0.0037734 ,  0.0037734 ,  0.0037734 ,  0.0037734 ,  0.0037734 ,\n",
       "          0.0037734 ,  0.0037734 ,  0.0037734 ,  0.0037734 ,  0.0037734 ,\n",
       "          0.0037734 ,  0.0037734 ,  0.0037734 ,  0.0037734 ,  0.0037734 ,\n",
       "          0.0037734 ,  0.0037734 ,  0.0037734 ,  0.0037734 ,  0.0037734 ,\n",
       "          0.0037734 ,  0.0037734 ,  0.0037734 ,  0.0037734 ,  0.0037734 ,\n",
       "          0.0037734 ]),\n",
       "  'mean': array([ 3.05002128,  3.05002128,  3.05002128,  3.05002128,  3.05002128,\n",
       "          3.05002128,  3.05002128,  3.05002128,  3.05002128,  3.05002128,\n",
       "          3.05002128,  3.05002128,  3.05002128,  3.05002128,  3.05002128,\n",
       "          3.05002128,  3.05002128,  3.05002128,  3.05002128,  3.05002128,\n",
       "          3.05002128,  3.05002128,  3.05002128,  3.05002128,  3.05002128,\n",
       "          3.05002128,  3.05002128,  3.05002128,  3.05002128,  3.05002128,\n",
       "          3.05002128,  3.05002128,  3.05002128,  3.05002128,  3.04265077,\n",
       "          3.02916226,  2.88501434,  2.6969292 ,  2.62246421,  2.31225118,\n",
       "          1.92728616,  1.40279122,  1.17748019,  1.07537709,  1.04800782,\n",
       "          1.02825732,  0.94776163,  0.93954976,  0.93747474,  0.93747474,\n",
       "          0.93747474,  0.93747474,  0.93747474,  0.93747474,  0.93747474,\n",
       "          0.93747474,  0.93747474,  0.93747474,  0.93747474,  0.93747474,\n",
       "          0.93747474,  0.93747474,  0.93747474,  0.93747474,  0.93747474,\n",
       "          0.93747474,  0.93747474,  0.93747474,  0.93747474,  0.93747474,\n",
       "          0.93747474,  0.93747474,  0.93747474,  0.93747474,  0.93747474,\n",
       "          0.93747474,  0.93747474,  0.93747474,  0.93747474,  0.93747474,\n",
       "          0.93747474,  0.93747474,  0.93747474,  0.93747474,  0.93747474,\n",
       "          0.93747474,  0.93747474,  0.93747474,  0.93747474,  0.93747474,\n",
       "          0.93747474,  0.93747474,  0.93747474,  0.93747474,  0.93747474,\n",
       "          0.93747474,  0.93747474,  0.93747474,  0.93747474,  0.93747474,\n",
       "          0.93747474,  0.93747474,  0.93747474,  0.93747474,  0.93747474,\n",
       "          0.93747474,  0.93747474,  0.93747474,  0.93747474,  0.93747474,\n",
       "          0.93747474]),\n",
       "  'n': 900,\n",
       "  'quantiles': {2.5: array([ 2.53804857,  2.53804857,  2.53804857,  2.53804857,  2.53804857,\n",
       "           2.53804857,  2.53804857,  2.53804857,  2.53804857,  2.53804857,\n",
       "           2.53804857,  2.53804857,  2.53804857,  2.53804857,  2.53804857,\n",
       "           2.53804857,  2.53804857,  2.53804857,  2.53804857,  2.53804857,\n",
       "           2.53804857,  2.53804857,  2.53804857,  2.53804857,  2.53804857,\n",
       "           2.53804857,  2.53804857,  2.53804857,  2.53804857,  2.53804857,\n",
       "           2.53804857,  2.53804857,  2.53804857,  2.53804857,  2.52025339,\n",
       "           2.46480743,  0.95529933,  0.86497913,  0.85372307,  0.80381778,\n",
       "           0.77834813,  0.75085529,  0.74778221,  0.73949221,  0.73949221,\n",
       "           0.73949221,  0.72960171,  0.72501071,  0.72501071,  0.72501071,\n",
       "           0.72501071,  0.72501071,  0.72501071,  0.72501071,  0.72501071,\n",
       "           0.72501071,  0.72501071,  0.72501071,  0.72501071,  0.72501071,\n",
       "           0.72501071,  0.72501071,  0.72501071,  0.72501071,  0.72501071,\n",
       "           0.72501071,  0.72501071,  0.72501071,  0.72501071,  0.72501071,\n",
       "           0.72501071,  0.72501071,  0.72501071,  0.72501071,  0.72501071,\n",
       "           0.72501071,  0.72501071,  0.72501071,  0.72501071,  0.72501071,\n",
       "           0.72501071,  0.72501071,  0.72501071,  0.72501071,  0.72501071,\n",
       "           0.72501071,  0.72501071,  0.72501071,  0.72501071,  0.72501071,\n",
       "           0.72501071,  0.72501071,  0.72501071,  0.72501071,  0.72501071,\n",
       "           0.72501071,  0.72501071,  0.72501071,  0.72501071,  0.72501071,\n",
       "           0.72501071,  0.72501071,  0.72501071,  0.72501071,  0.72501071,\n",
       "           0.72501071,  0.72501071,  0.72501071,  0.72501071,  0.72501071,\n",
       "           0.72501071]),\n",
       "   25: array([ 2.86270665,  2.86270665,  2.86270665,  2.86270665,  2.86270665,\n",
       "           2.86270665,  2.86270665,  2.86270665,  2.86270665,  2.86270665,\n",
       "           2.86270665,  2.86270665,  2.86270665,  2.86270665,  2.86270665,\n",
       "           2.86270665,  2.86270665,  2.86270665,  2.86270665,  2.86270665,\n",
       "           2.86270665,  2.86270665,  2.86270665,  2.86270665,  2.86270665,\n",
       "           2.86270665,  2.86270665,  2.86270665,  2.86270665,  2.86270665,\n",
       "           2.86270665,  2.86270665,  2.86270665,  2.86270665,  2.86139381,\n",
       "           2.85902481,  2.80400851,  2.71678786,  2.62747014,  1.03513513,\n",
       "           0.95007804,  0.8918194 ,  0.87009636,  0.86497913,  0.86309942,\n",
       "           0.86283482,  0.8565055 ,  0.85542631,  0.85542631,  0.85542631,\n",
       "           0.85542631,  0.85542631,  0.85542631,  0.85542631,  0.85542631,\n",
       "           0.85542631,  0.85542631,  0.85542631,  0.85542631,  0.85542631,\n",
       "           0.85542631,  0.85542631,  0.85542631,  0.85542631,  0.85542631,\n",
       "           0.85542631,  0.85542631,  0.85542631,  0.85542631,  0.85542631,\n",
       "           0.85542631,  0.85542631,  0.85542631,  0.85542631,  0.85542631,\n",
       "           0.85542631,  0.85542631,  0.85542631,  0.85542631,  0.85542631,\n",
       "           0.85542631,  0.85542631,  0.85542631,  0.85542631,  0.85542631,\n",
       "           0.85542631,  0.85542631,  0.85542631,  0.85542631,  0.85542631,\n",
       "           0.85542631,  0.85542631,  0.85542631,  0.85542631,  0.85542631,\n",
       "           0.85542631,  0.85542631,  0.85542631,  0.85542631,  0.85542631,\n",
       "           0.85542631,  0.85542631,  0.85542631,  0.85542631,  0.85542631,\n",
       "           0.85542631,  0.85542631,  0.85542631,  0.85542631,  0.85542631,\n",
       "           0.85542631]),\n",
       "   50: array([ 3.03444478,  3.03444478,  3.03444478,  3.03444478,  3.03444478,\n",
       "           3.03444478,  3.03444478,  3.03444478,  3.03444478,  3.03444478,\n",
       "           3.03444478,  3.03444478,  3.03444478,  3.03444478,  3.03444478,\n",
       "           3.03444478,  3.03444478,  3.03444478,  3.03444478,  3.03444478,\n",
       "           3.03444478,  3.03444478,  3.03444478,  3.03444478,  3.03444478,\n",
       "           3.03444478,  3.03444478,  3.03444478,  3.03444478,  3.03444478,\n",
       "           3.03444478,  3.03444478,  3.03444478,  3.03444478,  3.03207067,\n",
       "           3.02676707,  2.99636689,  2.96248568,  2.94064646,  2.82870952,\n",
       "           1.1751514 ,  0.99324813,  0.96392304,  0.94894733,  0.94612981,\n",
       "           0.94514684,  0.93644557,  0.93619061,  0.93619061,  0.93619061,\n",
       "           0.93619061,  0.93619061,  0.93619061,  0.93619061,  0.93619061,\n",
       "           0.93619061,  0.93619061,  0.93619061,  0.93619061,  0.93619061,\n",
       "           0.93619061,  0.93619061,  0.93619061,  0.93619061,  0.93619061,\n",
       "           0.93619061,  0.93619061,  0.93619061,  0.93619061,  0.93619061,\n",
       "           0.93619061,  0.93619061,  0.93619061,  0.93619061,  0.93619061,\n",
       "           0.93619061,  0.93619061,  0.93619061,  0.93619061,  0.93619061,\n",
       "           0.93619061,  0.93619061,  0.93619061,  0.93619061,  0.93619061,\n",
       "           0.93619061,  0.93619061,  0.93619061,  0.93619061,  0.93619061,\n",
       "           0.93619061,  0.93619061,  0.93619061,  0.93619061,  0.93619061,\n",
       "           0.93619061,  0.93619061,  0.93619061,  0.93619061,  0.93619061,\n",
       "           0.93619061,  0.93619061,  0.93619061,  0.93619061,  0.93619061,\n",
       "           0.93619061,  0.93619061,  0.93619061,  0.93619061,  0.93619061,\n",
       "           0.93619061]),\n",
       "   75: array([ 3.23447552,  3.23447552,  3.23447552,  3.23447552,  3.23447552,\n",
       "           3.23447552,  3.23447552,  3.23447552,  3.23447552,  3.23447552,\n",
       "           3.23447552,  3.23447552,  3.23447552,  3.23447552,  3.23447552,\n",
       "           3.23447552,  3.23447552,  3.23447552,  3.23447552,  3.23447552,\n",
       "           3.23447552,  3.23447552,  3.23447552,  3.23447552,  3.23447552,\n",
       "           3.23447552,  3.23447552,  3.23447552,  3.23447552,  3.23447552,\n",
       "           3.23447552,  3.23447552,  3.23447552,  3.23447552,  3.23228603,\n",
       "           3.23183046,  3.20835552,  3.17117708,  3.16559563,  3.08684892,\n",
       "           2.9712388 ,  1.18959291,  1.0635764 ,  1.03841408,  1.03513513,\n",
       "           1.03161428,  1.01652898,  1.01450645,  1.01450645,  1.01450645,\n",
       "           1.01450645,  1.01450645,  1.01450645,  1.01450645,  1.01450645,\n",
       "           1.01450645,  1.01450645,  1.01450645,  1.01450645,  1.01450645,\n",
       "           1.01450645,  1.01450645,  1.01450645,  1.01450645,  1.01450645,\n",
       "           1.01450645,  1.01450645,  1.01450645,  1.01450645,  1.01450645,\n",
       "           1.01450645,  1.01450645,  1.01450645,  1.01450645,  1.01450645,\n",
       "           1.01450645,  1.01450645,  1.01450645,  1.01450645,  1.01450645,\n",
       "           1.01450645,  1.01450645,  1.01450645,  1.01450645,  1.01450645,\n",
       "           1.01450645,  1.01450645,  1.01450645,  1.01450645,  1.01450645,\n",
       "           1.01450645,  1.01450645,  1.01450645,  1.01450645,  1.01450645,\n",
       "           1.01450645,  1.01450645,  1.01450645,  1.01450645,  1.01450645,\n",
       "           1.01450645,  1.01450645,  1.01450645,  1.01450645,  1.01450645,\n",
       "           1.01450645,  1.01450645,  1.01450645,  1.01450645,  1.01450645,\n",
       "           1.01450645]),\n",
       "   97.5: array([ 3.64320767,  3.64320767,  3.64320767,  3.64320767,  3.64320767,\n",
       "           3.64320767,  3.64320767,  3.64320767,  3.64320767,  3.64320767,\n",
       "           3.64320767,  3.64320767,  3.64320767,  3.64320767,  3.64320767,\n",
       "           3.64320767,  3.64320767,  3.64320767,  3.64320767,  3.64320767,\n",
       "           3.64320767,  3.64320767,  3.64320767,  3.64320767,  3.64320767,\n",
       "           3.64320767,  3.64320767,  3.64320767,  3.64320767,  3.64320767,\n",
       "           3.64320767,  3.64320767,  3.64320767,  3.64320767,  3.64320767,\n",
       "           3.64320767,  3.62444114,  3.59666899,  3.58309767,  3.50511214,\n",
       "           3.4272103 ,  3.25756039,  3.09237496,  2.98102334,  2.89873888,\n",
       "           2.86453187,  1.19924348,  1.18959291,  1.18662017,  1.18662017,\n",
       "           1.18662017,  1.18662017,  1.18662017,  1.18662017,  1.18662017,\n",
       "           1.18662017,  1.18662017,  1.18662017,  1.18662017,  1.18662017,\n",
       "           1.18662017,  1.18662017,  1.18662017,  1.18662017,  1.18662017,\n",
       "           1.18662017,  1.18662017,  1.18662017,  1.18662017,  1.18662017,\n",
       "           1.18662017,  1.18662017,  1.18662017,  1.18662017,  1.18662017,\n",
       "           1.18662017,  1.18662017,  1.18662017,  1.18662017,  1.18662017,\n",
       "           1.18662017,  1.18662017,  1.18662017,  1.18662017,  1.18662017,\n",
       "           1.18662017,  1.18662017,  1.18662017,  1.18662017,  1.18662017,\n",
       "           1.18662017,  1.18662017,  1.18662017,  1.18662017,  1.18662017,\n",
       "           1.18662017,  1.18662017,  1.18662017,  1.18662017,  1.18662017,\n",
       "           1.18662017,  1.18662017,  1.18662017,  1.18662017,  1.18662017,\n",
       "           1.18662017,  1.18662017,  1.18662017,  1.18662017,  1.18662017,\n",
       "           1.18662017])},\n",
       "  'standard deviation': array([ 0.27482334,  0.27482334,  0.27482334,  0.27482334,  0.27482334,\n",
       "          0.27482334,  0.27482334,  0.27482334,  0.27482334,  0.27482334,\n",
       "          0.27482334,  0.27482334,  0.27482334,  0.27482334,  0.27482334,\n",
       "          0.27482334,  0.27482334,  0.27482334,  0.27482334,  0.27482334,\n",
       "          0.27482334,  0.27482334,  0.27482334,  0.27482334,  0.27482334,\n",
       "          0.27482334,  0.27482334,  0.27482334,  0.27482334,  0.27482334,\n",
       "          0.27482334,  0.27482334,  0.27482334,  0.27482334,  0.29756955,\n",
       "          0.33896158,  0.60796176,  0.79612217,  0.85288465,  0.99933095,\n",
       "          1.03904182,  0.85489342,  0.64852676,  0.50959416,  0.4605806 ,\n",
       "          0.41918924,  0.17856708,  0.13416132,  0.11692962,  0.11692962,\n",
       "          0.11692962,  0.11692962,  0.11692962,  0.11692962,  0.11692962,\n",
       "          0.11692962,  0.11692962,  0.11692962,  0.11692962,  0.11692962,\n",
       "          0.11692962,  0.11692962,  0.11692962,  0.11692962,  0.11692962,\n",
       "          0.11692962,  0.11692962,  0.11692962,  0.11692962,  0.11692962,\n",
       "          0.11692962,  0.11692962,  0.11692962,  0.11692962,  0.11692962,\n",
       "          0.11692962,  0.11692962,  0.11692962,  0.11692962,  0.11692962,\n",
       "          0.11692962,  0.11692962,  0.11692962,  0.11692962,  0.11692962,\n",
       "          0.11692962,  0.11692962,  0.11692962,  0.11692962,  0.11692962,\n",
       "          0.11692962,  0.11692962,  0.11692962,  0.11692962,  0.11692962,\n",
       "          0.11692962,  0.11692962,  0.11692962,  0.11692962,  0.11692962,\n",
       "          0.11692962,  0.11692962,  0.11692962,  0.11692962,  0.11692962,\n",
       "          0.11692962,  0.11692962,  0.11692962,  0.11692962,  0.11692962,\n",
       "          0.11692962])},\n",
       " 'switchpoint': {'95% HPD interval': array([ 35.,  45.]),\n",
       "  'mc error': 0.077369962589567728,\n",
       "  'mean': 40.194444444444443,\n",
       "  'n': 900,\n",
       "  'quantiles': {2.5: 36.0, 25: 39.0, 50: 40.0, 75: 41.0, 97.5: 46.0},\n",
       "  'standard deviation': 2.3965188230297301}}"
      ]
     },
     "execution_count": 36,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "M.stats()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  }
 ],
 "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": "2.7.10"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 0
}