SimpleModels.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Make and condition a Bernoulli Distribution\n",
    "\n",
    "A Bernoulli distribution is the distribution of probabilities of a binary even"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import pymc3 as pm\n",
    "import numpy as np\n",
    "import seaborn as sns"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Auto-assigning NUTS sampler...\n",
      "Initializing NUTS using jitter+adapt_diag...\n",
      "Multiprocess sampling (2 chains in 2 jobs)\n",
      "NUTS: [p_interval__]\n",
      "100%|██████████| 2500/2500 [00:02<00:00, 1163.42it/s]\n",
      "The acceptance probability does not match the target. It is 0.8841238753627214, but should be close to 0.8. Try to increase the number of tuning steps.\n"
     ]
    }
   ],
   "source": [
    "results = [0,1]*100\n",
    "with pm.Model() as model:\n",
    "    p = pm.Uniform(\"p\", lower=0, upper=1)\n",
    "    y_obs = pm.Bernoulli(\"bern\", p=p, observed=results)\n",
    "    posterior = pm.sample(2000, tune=500)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
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       "    .dataframe tbody tr th:only-of-type {\n",
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       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
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       "    }\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>mc_error</th>\n",
       "      <th>hpd_2.5</th>\n",
       "      <th>hpd_97.5</th>\n",
       "      <th>n_eff</th>\n",
       "      <th>Rhat</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>p</th>\n",
       "      <td>0.501389</td>\n",
       "      <td>0.035378</td>\n",
       "      <td>0.00096</td>\n",
       "      <td>0.435253</td>\n",
       "      <td>0.572803</td>\n",
       "      <td>1510.271875</td>\n",
       "      <td>0.999868</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "       mean        sd  mc_error   hpd_2.5  hpd_97.5        n_eff      Rhat\n",
       "p  0.501389  0.035378   0.00096  0.435253  0.572803  1510.271875  0.999868"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "pm.summary(posterior)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/Users/canyon/.miniconda3/lib/python3.5/site-packages/matplotlib/axes/_axes.py:6462: UserWarning: The 'normed' kwarg is deprecated, and has been replaced by the 'density' kwarg.\n",
      "  warnings.warn(\"The 'normed' kwarg is deprecated, and has been \"\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "<matplotlib.axes._subplots.AxesSubplot at 0x1c172c2f60>"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "sns.distplot(posterior[\"p\"])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Make a similar distribution for Binomial\n",
    "Binomial distriution"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Auto-assigning NUTS sampler...\n",
      "Initializing NUTS using jitter+adapt_diag...\n",
      "Multiprocess sampling (2 chains in 2 jobs)\n",
      "NUTS: [p_interval__]\n",
      "100%|██████████| 4000/4000 [00:04<00:00, 904.17it/s]\n"
     ]
    }
   ],
   "source": [
    "n=6\n",
    "results = [[2]]*10000\n",
    "with pm.Model() as model:\n",
    "    p = pm.Uniform(\"p\", lower=0, upper=1)\n",
    "    y_obs = pm.Binomial(\"binom\", p=p, n=n, observed=results)\n",
    "    posterior = pm.sample(3000, tune=1000)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "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>mc_error</th>\n",
       "      <th>hpd_2.5</th>\n",
       "      <th>hpd_97.5</th>\n",
       "      <th>n_eff</th>\n",
       "      <th>Rhat</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>p</th>\n",
       "      <td>0.33339</td>\n",
       "      <td>0.001913</td>\n",
       "      <td>0.000041</td>\n",
       "      <td>0.329866</td>\n",
       "      <td>0.337311</td>\n",
       "      <td>2548.631051</td>\n",
       "      <td>0.999847</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "      mean        sd  mc_error   hpd_2.5  hpd_97.5        n_eff      Rhat\n",
       "p  0.33339  0.001913  0.000041  0.329866  0.337311  2548.631051  0.999847"
      ]
     },
     "execution_count": 26,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "pm.summary(posterior)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/Users/canyon/.miniconda3/lib/python3.5/site-packages/matplotlib/axes/_axes.py:6462: UserWarning: The 'normed' kwarg is deprecated, and has been replaced by the 'density' kwarg.\n",
      "  warnings.warn(\"The 'normed' kwarg is deprecated, and has been \"\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "<matplotlib.axes._subplots.AxesSubplot at 0x1c188eb860>"
      ]
     },
     "execution_count": 28,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "sns.distplot(posterior[\"p\"], kde=False)"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "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": "3.5.4"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}