xiangze/pyro_baseball.ipynb Secret

## pyro_baseball.ipynb
{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# pyroで打率の推定モデルの実行"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "toc": true
   },
   "source": [
    "<h1>Table of Contents<span class=\"tocSkip\"></span></h1>\n",
    "<div class=\"toc\" style=\"margin-top: 1em;\"><ul class=\"toc-item\"><li><span><a href=\"#pyroで打率の推定モデルの実行\" data-toc-modified-id=\"pyroで打率の推定モデルの実行-1\"><span class=\"toc-item-num\">1&nbsp;&nbsp;</span>pyroで打率の推定モデルの実行</a></span></li><li><span><a href=\"#データ\" data-toc-modified-id=\"データ-2\"><span class=\"toc-item-num\">2&nbsp;&nbsp;</span>データ</a></span></li><li><span><a href=\"#Model\" data-toc-modified-id=\"Model-3\"><span class=\"toc-item-num\">3&nbsp;&nbsp;</span>Model</a></span><ul class=\"toc-item\"><li><span><a href=\"#Fully-pooled-model(complete-pooling)\" data-toc-modified-id=\"Fully-pooled-model(complete-pooling)-3.1\"><span class=\"toc-item-num\">3.1&nbsp;&nbsp;</span>Fully pooled model(complete pooling)</a></span></li><li><span><a href=\"#Not-pooled-model\" data-toc-modified-id=\"Not-pooled-model-3.2\"><span class=\"toc-item-num\">3.2&nbsp;&nbsp;</span>Not pooled model</a></span></li><li><span><a href=\"#partially-pooled-model\" data-toc-modified-id=\"partially-pooled-model-3.3\"><span class=\"toc-item-num\">3.3&nbsp;&nbsp;</span>partially pooled model</a></span></li></ul></li><li><span><a href=\"#DATA-SUMMARIZE-UTILS\" data-toc-modified-id=\"DATA-SUMMARIZE-UTILS-4\"><span class=\"toc-item-num\">4&nbsp;&nbsp;</span>DATA SUMMARIZE UTILS</a></span></li><li><span><a href=\"#モデル評価用関数\" data-toc-modified-id=\"モデル評価用関数-5\"><span class=\"toc-item-num\">5&nbsp;&nbsp;</span>モデル評価用関数</a></span></li><li><span><a href=\"#実行\" data-toc-modified-id=\"実行-6\"><span class=\"toc-item-num\">6&nbsp;&nbsp;</span>実行</a></span><ul class=\"toc-item\"><li><span><a href=\"#Full-Pooling-Model\" data-toc-modified-id=\"Full-Pooling-Model-6.1\"><span class=\"toc-item-num\">6.1&nbsp;&nbsp;</span>Full Pooling Model</a></span></li><li><span><a href=\"#No-Pooling-Model\" data-toc-modified-id=\"No-Pooling-Model-6.2\"><span class=\"toc-item-num\">6.2&nbsp;&nbsp;</span>No Pooling Model</a></span></li><li><span><a href=\"#Partially-Pooled-Model\" data-toc-modified-id=\"Partially-Pooled-Model-6.3\"><span class=\"toc-item-num\">6.3&nbsp;&nbsp;</span>Partially Pooled Model</a></span></li><li><span><a href=\"#Partially-Pooled-with-Logit-Model\" data-toc-modified-id=\"Partially-Pooled-with-Logit-Model-6.4\"><span class=\"toc-item-num\">6.4&nbsp;&nbsp;</span>Partially Pooled with Logit Model</a></span></li></ul></li><li><span><a href=\"#ToDo\" data-toc-modified-id=\"ToDo-7\"><span class=\"toc-item-num\">7&nbsp;&nbsp;</span>ToDo</a></span></li><li><span><a href=\"#Link\" data-toc-modified-id=\"Link-8\"><span class=\"toc-item-num\">8&nbsp;&nbsp;</span>Link</a></span></li><li><span><a href=\"#その他\" data-toc-modified-id=\"その他-9\"><span class=\"toc-item-num\">9&nbsp;&nbsp;</span>その他</a></span></li></ul></div>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "[pyro](http://pyro.ai/)はpytorchをベースとした確率的プログラミングのためのフレームワークです。\n",
    "pytorchの性能や早い時期にNUTSが実装されていることや書き方がtensorflow probabilityに比べ簡潔なところもあって注目されています。\n",
    "Uberで開発され使われているようですが[Dropout as variational bayes](https://arxiv.org/abs/1506.02142)などで有名な[Ghahramani先生がチーフサイエンティスト](https://www.uber.com/newsroom/announcing-zoubin-ghahramani-as-ubers-chief-scientist/)らしいので開発に関わっているのかもしれません。"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": true
   },
   "source": [
    "サンプルとして公開されている[野球選手のシーズン中の打数、打率のデータから打率を推定するコード](\n",
    "　https://github.com/uber/pyro/blob/dev/examples/baseball.py)では[stanでの実施レポート]( http://mc-stan.org/users/documentation/case-studies/pool-binary-trials.html)　に沿ってデータの取得、モデルの定義と実行、事後予測分布(posterior predictive distribution)の表示と評価がされており、 　以下ではそれを追って実行します。\n",
    "\n",
    "stanのレポートの方ではさらに\n",
    "+ estimate event probabilities\n",
    "+ evaluate posterior predictive densities to evaluate model predictions on held-out data\n",
    "+ rank items by chance of success\n",
    "+ perform multiple comparisons in several settings\n",
    "+ replicate new data for posterior p-values\n",
    "+ perform graphical posterior predictive checks\n",
    "\n",
    " といった内容があります。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "'0.3.0'"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from __future__ import absolute_import, division, print_function\n",
    "\n",
    "import argparse\n",
    "import logging\n",
    "import math\n",
    "import os\n",
    "\n",
    "import numpy as np\n",
    "import pandas as pd\n",
    "import torch\n",
    "\n",
    "import pyro\n",
    "import pyro.poutine as poutine\n",
    "from pyro.distributions import Beta, Binomial, HalfCauchy, Normal, Pareto, Uniform\n",
    "from pyro.distributions.util import logsumexp\n",
    "from pyro.infer import EmpiricalMarginal\n",
    "from pyro.infer.abstract_infer import TracePredictive\n",
    "from pyro.infer.mcmc import MCMC, NUTS\n",
    "pyro.__version__"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "plt.style.use(\"ggplot\")\n",
    "import seaborn as sns"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "logging.basicConfig(format='%(message)s', level=logging.INFO)\n",
    "# Enable validation checks"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# データ"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "データのダウンロードと表示"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "pyro.enable_validation(True)\n",
    "DATA_URL = \"https://d2fefpcigoriu7.cloudfront.net/datasets/EfronMorrisBB.txt\"\n",
    "baseball_dataset = pd.read_csv(DATA_URL, \"\\t\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "18人の打者のデータ"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "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>FirstName</th>\n",
       "      <th>LastName</th>\n",
       "      <th>At-Bats</th>\n",
       "      <th>Hits</th>\n",
       "      <th>BattingAverage</th>\n",
       "      <th>RemainingAt-Bats</th>\n",
       "      <th>RemainingAverage</th>\n",
       "      <th>SeasonAt-Bats</th>\n",
       "      <th>SeasonHits</th>\n",
       "      <th>SeasonAverage</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>Roberto</td>\n",
       "      <td>Clemente</td>\n",
       "      <td>45</td>\n",
       "      <td>18</td>\n",
       "      <td>0.400</td>\n",
       "      <td>367</td>\n",
       "      <td>0.3460</td>\n",
       "      <td>412</td>\n",
       "      <td>145</td>\n",
       "      <td>0.352</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>Frank</td>\n",
       "      <td>Robinson</td>\n",
       "      <td>45</td>\n",
       "      <td>17</td>\n",
       "      <td>0.378</td>\n",
       "      <td>426</td>\n",
       "      <td>0.2981</td>\n",
       "      <td>471</td>\n",
       "      <td>144</td>\n",
       "      <td>0.306</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>Frank</td>\n",
       "      <td>Howard</td>\n",
       "      <td>45</td>\n",
       "      <td>16</td>\n",
       "      <td>0.356</td>\n",
       "      <td>521</td>\n",
       "      <td>0.2764</td>\n",
       "      <td>566</td>\n",
       "      <td>160</td>\n",
       "      <td>0.283</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>Jay</td>\n",
       "      <td>Johnstone</td>\n",
       "      <td>45</td>\n",
       "      <td>15</td>\n",
       "      <td>0.333</td>\n",
       "      <td>275</td>\n",
       "      <td>0.2218</td>\n",
       "      <td>320</td>\n",
       "      <td>76</td>\n",
       "      <td>0.238</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>Ken</td>\n",
       "      <td>Berry</td>\n",
       "      <td>45</td>\n",
       "      <td>14</td>\n",
       "      <td>0.311</td>\n",
       "      <td>418</td>\n",
       "      <td>0.2727</td>\n",
       "      <td>463</td>\n",
       "      <td>128</td>\n",
       "      <td>0.276</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "  FirstName   LastName  At-Bats  Hits  BattingAverage  RemainingAt-Bats  \\\n",
       "0   Roberto   Clemente       45    18           0.400               367   \n",
       "1     Frank   Robinson       45    17           0.378               426   \n",
       "2     Frank     Howard       45    16           0.356               521   \n",
       "3       Jay  Johnstone       45    15           0.333               275   \n",
       "4       Ken      Berry       45    14           0.311               418   \n",
       "\n",
       "   RemainingAverage  SeasonAt-Bats  SeasonHits  SeasonAverage  \n",
       "0            0.3460            412         145          0.352  \n",
       "1            0.2981            471         144          0.306  \n",
       "2            0.2764            566         160          0.283  \n",
       "3            0.2218            320          76          0.238  \n",
       "4            0.2727            463         128          0.276  "
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "baseball_dataset.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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GHBMIBDBq1KgOcx0OBxwOh7jc1NQU3VZ0cc5PqZaUOu1vgtWdWnLWaX8jrO7UkiLW2xfL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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x119fcc3c8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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kc/p9sWnTJuj1erS0tGDNmjUYNWoUzGZzxBiXywWXywUAqKiogNFojLi/RcLjdJ3TF9Jq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\nHWNKUq3QAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x119d21208>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "baseball_dataset[\"BattingAverage\"].plot.bar()\n",
    "plt.show()\n",
    "baseball_dataset[\"RemainingAverage\"].plot.bar()\n",
    "plt.show()\n",
    "baseball_dataset[\"SeasonAverage\"].plot.bar()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "名字と名前をくっつけてtrain data(打率とヒットの数), test data(全シーズンでの打率とヒット数)を分離する。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "def train_test_split(pd_dataframe):\n",
    "    \"\"\"\n",
    "    Training data - 45 initial at-bats and hits for each player.\n",
    "    Validation data - Full season at-bats and hits for each player.\n",
    "    \"\"\"\n",
    "    train_data = torch.tensor(pd_dataframe[[\"At-Bats\", \"Hits\"]].values, dtype=torch.float)\n",
    "    test_data = torch.tensor(pd_dataframe[[\"SeasonAt-Bats\", \"SeasonHits\"]].values, dtype=torch.float)\n",
    "    first_name = pd_dataframe[\"FirstName\"].values\n",
    "    last_name = pd_dataframe[\"LastName\"].values\n",
    "    player_names = [\" \".join([first, last]) for first, last in zip(first_name, last_name)]\n",
    "    return train_data, test_data, player_names"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "torch.Size([18, 2])\n"
     ]
    }
   ],
   "source": [
    "train, _, player_names = train_test_split(baseball_dataset)\n",
    "at_bats, hits = train[:, 0], train[:, 1]\n",
    "print(train.shape)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 49,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Index(['FirstName', 'LastName', 'At-Bats', 'Hits', 'BattingAverage',\n",
       "       'RemainingAt-Bats', 'RemainingAverage', 'SeasonAt-Bats', 'SeasonHits',\n",
       "       'SeasonAverage'],\n",
       "      dtype='object')"
      ]
     },
     "execution_count": 49,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "baseball_dataset.columns"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 51,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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/IETEBWARQK+h1MR0YRZmnynejukupOCagoYBL0ZRQy8m+lnK+ATqWmpkb/7b/9N7W0tPixeeQi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\nDJtJr+NHpOwmk8m627UNFqmdFaWWorPOFSbjqW6TV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udnxWM//ZfOwz/DjkEQCShx4MU3RkNePgfvW97BpllAyI/I6cwguifn/ju5qr2XIK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\n7T4CpyMTwUw3wqpqdFkkOeaKZNa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sAQvnx2jML8mOGRYM+3lcmF+dMY9x0ewT0H369AEA\nLF26NOnHmjt3LgDge9/7HgoLC+Hz+ZCdnQ0AyMrKgs/nAwB4vd52X27o8Xjg9Xojv9uqvLwc5eXl\nAIB58+ZF/UJEu91uiS9KVMM5yHn4KXhfeDyyRk3Ow08hbcDZyLBp9vcIYaViPxuRX5GIfiwlcgyI\nvk1aM2OGZd+HrfXL2sNT+fqbMb+xkC3j8dYrQvZT9RobnWHRs5RIfanMjxlfv3gYnV8tib4vo2HN\nyTNTho2k134VYTzQHSMzLVt+RTr+RRlfyP6adPl4mj1SG1u2bMGnn34Kv9/f7vbp06d3e99f//rX\nyMnJgc/nw9NPP41+/fq1+3dFUaAoSlz1FBYWorCwMPJzdXV1h9/Jzc2NersZ2c45H675ZegRDKDJ\nkQl/phthr9foslKiq/18etYSYVR+RSLDsdR6DLR+U213x4AM26RFfgHzZliGfdiVtvXHm18RxPL6\nswcnR7aMJ1Kv0dnXewwBiJFh0bOUaH2pyo+srx97cEei78torFqzmXqwWeiZRaPHA91JZNut2oNF\n6lmijC9kfE1iza/mfyL64x//iJdeegnhcBibN2+G0+nEjh074HA4Yrp/Tk4OAMDtdmP06NGorKyE\n2+2OXA5QW1sbWdMmJyen3YtRU1MTuT+REaycX5uiwBn0I7T7YziDftjiPLmlUlhV0eBwoeGsPDQ4\nXPyG2jasmuHW/DqPHGR+JWbV/JpJV8eiFbLPDOsnlfmR6ZyiJeaXZMcMy6G1nwf7fQsA4Dj8haV6\nbWeYX2MkO744fcyghsM6VWo8zSeg3333XfzqV7/C5MmTYbfbMXnyZDzyyCM4fvx4t/dtbGzEiRMn\nIv+/c+dO5OXloaCgABs3bgQAbNy4EaNHjwYAFBQUYNOmTVBVFXv27IHD4ehwyQC1Z1MUOCp3wT/7\nXlQ/OgX+2ffCUbnL8s1aC1bOL3NlDlbNcNv8+h6fzvxKyqr5NROrH4vMsDmo4bAlc8z8kuyYYblY\nfcxwOuZXTtFyHNr6gWlzrPkSHIFAAHl5eS0PbrejubkZgwcPxqefftrtfX0+H1544QUAQCgUwrhx\n43DBBRdg0KBBKCkpwYYNG9CnTx8UFRUBAEaNGoWtW7di5syZ6NmzJ6ZNm6b15piOI+CDv6Q48k2d\n6slG+EuK4ZpfhgZ+S2dSrJxf5ip2NkWBI+CLXKITzHQL8yk+q2aY+Y2PqBm2an7NwqYocPmq4bXw\nscgMy+n0nqg2n7TkOYX5Jdkxw3LpfPz+MhocvQ2uLvWYXzlFy7H3hcfhml+GYKZbyPdcyVBUVdst\neOSRRzB9+nQMHDgQTz75JEaPHg2n04l169ZhyZIlWj5Vwg4fPtzhNpHWWdGT88hB+B7vuBa3+6lS\nNJyVZ0BFqZWK9Rv1Fi2/RjN7rrTqD5G/cH59klHSM+AqKkZw8LCkTyay5BcwJsNd7UMZ8ivKOSrR\nDKdqDehUELEHA+JkJFbt1jX/OlfqlwfgX7usw++KciyaYQwBdJ9h0bMkUn3RemLOQ0+h5pnZHX5X\n9BzLkuFU9mCRshYrq9YsS34BcccRWtM7i52N33N++Rzq84caOlFn1BrQqaB1fkXqWUbU0tX7UAQb\ndJk3iIfwa0DfcsstqK+vBwDcfvvt+Pvf/441a9bgrrvu0vqpKAH2zEwo6RntblPSM2DPzDSoIjIF\nd1bUXMGdZVBBXTNqbcbO/lLvCPhS8vzUCeY3Zswwaa31k8/qlwdgH3iOVMciyUnLHhqtJzZ9sZc5\nJiJKUre9upPxe/MX+zguJUMkNL7oJMf2zExTvufSfAL6wgsvxNChQwEAQ4YMweLFi7FixQpcfPHF\nWj8VJaC5OYys+x+JhFxJz0DW/Y+gudm8C52T/oKZbriKitvlylVUjGCm2+DKOjJ0vTBfXeQk0ko9\n2dhyWQ0ZhvmNAzNMGmrNs/eX98O/dhl8v1/SYYwi6rFIctK8h0bpiYF//AVZM3/FHBMRJSiWXh3M\ndHfstZOmIPCPv3BcSimX6Pgi2vvQnIefQvPJU6Z8z6X5GtBt+Xw+7N69GwMGDED//v31fCqKkd1u\nQ90fV6L3jXcCNgUIq/D/cSWyHnzS6NJIYmFVRXDwMLjml6FHMIAmR6awaxQZut7v13/hbHsy4aei\njNc2v6KvsWX4etXMMGno9DyHvjoI/x9XIvvBJ9F8aD96jLoYfneukMciyUnzHhqlJ4b9dQjnDZLi\nnEJEJKJYenVYVRHOG4TeN98NQAXCKhreWIewv47jUkq5RMcX0d6Hpg04G81fHjDley7NJqC9Xi9+\n97vf4csvv8S5556La6+9Fk888QRsNhsCgQCmT5+O7373u1o9HSWoORAATp1qf+OpUy23uzzGFEUp\np8eXiIVVFQ0OF3Lz8lFbXQ2I+karq09w6jyB1/oXzg5rOWW6xX29BKRnfiMZEHV/GJhfgBkm7ajh\nMOwnguh9811AWEWg/K8IHT+K0FcH0XxoP5QBZ3PymbSncQ+N1hNzHn4K/l7Olux2c04R9UtdiYgM\n1UWvtrX7YrZsKIO+Df9zv+S4lIyVxPji9Peh6QAApeUDGQf3IfCPvyDsrzNFtjWbgH7ppZfgdrtx\n991344MPPsDcuXMxdepUfOc730FFRQXWrVvHCWgRZHvgvP5W+Ncs+6ZJ3zkVyObks1Xo+UV4UjDw\nE5wyfdJWVMyvsZ9AZoZJCzZFQWjrB/C+8Pg3x/GkKZFPLvGTz6QbjXtoZ59cCnu93d7X8uczIqLO\ndNarsz0d+qa7qBiuF1YCtTUcl5JxNBpftI6R/W3GyFkzf4Vw3iAEW/+4LTHN1oDes2cPfvazn2HU\nqFG499574fP5MHr0aADA6NGjcfz4ca2eipIRDkcmn4GvLw1YswwIcw1oq7D6l4gZvd5v6184G87K\nQ4PDJf1JJNWYX+PXq2aGKVmOgC8y+Qx8fRyvXY7MK69v+TQpJ59JJ3r00NN7omKL7e2V1c9nRESd\n6axXIxzu0Dd9JcVAOMRxKRlKq/FFtDFy3aKngXDIFNnW7BPQoVAIdnvLw6WnpyMjIwNKqr4UiWLn\nq+3k0oBawNHboKIopQy+hN9o/ASn5Jhf5pfk18lxbB8yFPUD8pln0o1QPdTi5zMios501qsdh79g\n3yQhaTa+MPnYQNMJ6E8++STyczgc7vAzCYBfIEXMgDzr/VJHzC/zS/Lr5DgOZXs4+Uy6E6aH8nxG\nRNSpqL2afZMEpsn4wuQZ12wJDrfbjd/+9reR/5xOZ7ufXS75Z+vNQITLt8lYzADJjPklkl8w042c\nh5/icUyWxvMZEVF82DfJ7Mw+RtbsE9BLlizR6qFIR20vDegRDKDJkcnLty1GqMtPieLE/BLJL6yq\nSLtwLI9jsjSez4iI4sO+SWZn9jGyZhPQ0bz//vsYN26cnk9BCWi9NCA3Lx+11dW8fNuChLn8lCgB\nzC+R/BSbjccxWR7PZ0RE8WHfJLMz8xhZsyU4olmxYoWeD09EREREREREREREAtN1Alo10Uw9ERER\nEREREREREcVH1wno888/X8+HpwTZFAXOoB+h3R/DGfTDphREAIAAACAASURBVChGl0REUbQeq84j\nB3mskpR4vrEm9i4iMfBYJCIrYK8j0p5NUaAe+0rT40rzNaA//PBDXHLJJQCARx99NHL75s2bMWbM\nGK2fjuJkUxQ4KnfBX1IM9WTjN9+qOXiYaRY2JzIDHqskO2bYmrjficTQ2bGoZvP7eYjIPDjuINJe\n63F1XOPjSvMJ6GXLlkUmoNtavnx5TBPQ4XAYc+bMQU5ODubMmYOqqiosXLgQ9fX1yM/Px4wZM2C3\n29HU1ITS0lLs27cPvXv3xqxZs9C3b1+tN8d0HAFfpDkDgHqyEf6SYrjml7UsdE5JY4ZJC0Ydq8wv\naYUZtiaOM5LD/JJWOjsW+/xmDZCWrtvzMsMkO2ZYLhx3tMf8khb0Oq40W4Lj2LFjOHbsGMLhMKqq\nqiI/Hzt2DDt37kTPnj1jepz/+7//Q//+/SM/r127FldffTUWL16MzMxMbNiwAQCwYcMGZGZmYvHi\nxbj66qvxP//zP1ptirn56iIhaqWebAR8dQYVZD7MMGnCoGOV+SXNMMPWxHFGUphf0kwnx2K41qvr\n0zLDJDtmWDIcd7TD/JImdDquNJuAnjlzJmbOnIlTp05hxowZkZ9nzpyJJUuW4Oabb+72MWpqarB1\n61ZcccUVAFq+xHDXrl2RT05PmDABFRUVAIAtW7ZgwoQJAIAxY8bgk08+4ZcexsKdBSU9o91NSnoG\n4M4yqCBzYYZJMwYcq8wvaYoZtiaOMxLG/JKmOjkWbdk5uj0lM0yyY4YlxHFHBPNLmtHpuNJsCY51\n69YBAJ544gk8+eSTCT3GqlWrMGnSJJw4cQIAUF9fD4fDgbS0NABATk4OvN6Wv9p7vV54PB4AQFpa\nGhwOB+rr6+Fydfw4eHl5OcrLywEA8+bNQ25uboffsdvtUW83GzWcg5yHn4L3hccja7nkPPwU0gac\njQybrt9JKQS997MeGY4lvyIx47FkxDYZcawa2YP1JnsuZazfLBkWIb+xECUjse53UeqNh4xjCCD+\nDIu+b1hfbDo7Fu1nDURuOKzLc5qtB4uyL+PBmpNjtgwbKVX7VcT5DaMyLWN+RTr+RalFhDr0Oq40\nXwM62uTzoUOHsHHjRkyaNKnT+3300Udwu93Iz8/Hrl27NK2psLAQhYWFkZ+rq6s7/E5ubm7U283I\nds75cM0vQ49gAE2OTPgz3Qh79b0cTxRd7ed+/fol9dh6ZTiW/IrEjMeSUdvUeqzCVwe4s7o8VkXN\nLyBGhmXPpaz1x3O+ETXDIuQ3FiJlJJbeJVK9sZJxDAHEn2HR9w3ri120YzEnHI5an6gZNrIHi7Qv\nY2XVmpPNL2DODBsplVmM5z1TKiSy7VbtwSL1LFFqEaUO2znno89v1uBk1THN5iI0n4Bu5ff78f77\n72Pjxo04cOAARo0a1eXvf/bZZ9iyZQu2bduGU6dO4cSJE1i1ahWCwSBCoRDS0tLg9XqRk9Ny2VhO\nTg5qamrg8XgQCoUQDAbRu3dvvTbHVMKqigaHC7l5+aitrgZ4qYUmmGHSWuuxitaF/nU8Vplf0kMq\nzzfMsDhS2bvMgvklPXAcQRQ7ZlheHHcwv6S9sKpCOaM/Glq/uFiD4yqtuLi4OOlH+VpzczMqKirw\nv//7vygrK8NXX32FqqoqzJ07F9dee22X9x0xYgSuueYaXH311Rg0aBDq6urw0EMPYe/evQCAvLw8\n/OlPf8LQoUMxePBgBINB7NixAxdddBE+/PBDnDp1CmPHjo2pzvr6+g63ORwOBIPB+DdaYtzm9pJt\nuKnKcLT8isSMuZJhm2TJL2BMhmXYh12xQv2yZFjUHixbRmSrFzDHGALoPsOi7xvWl5zO6pMlw6ns\nwaLvy2isWrMWE2dmzLCRZMyiVhLZdqv2YJFyIkototQBxF5LrPnVbFGcsrIyTJkyBS+//DJyc3NR\nXFyMxYsXw+FwRNaWScQdd9yBN998EzNmzEBDQwMmTpwIAJg4cSIaGhowY8YMvPnmm7jjjju02hQi\nTTHDJDPml2THDJPMmF+SHTNMsmOGSWbML4lEUTX6qstbbrkFTqcTt956K7773e/C4XAAAO677z48\n//zzcLvdWjyNJg4fPtzhNlHWWUklbnN7WqwdlgrR8isSM+ZKhm2SJb+AMRmWYR92xQr1y5JhUXuw\nbBmRrV7AHGMIoPsMi75vWF9yOqtPlgynsgeLvi+jsWrNsuQXEHccoTUZs6gVI9aAThWt8ytSTkSp\nRZQ6gNhrSfka0IsXL8amTZvwxhtvYNWqVRg1ahTGjRsHjea3iYiIiIiIiIiIiEgymi3B0bdvX9x8\n881YvHgxfvWrX8HpdGLZsmXw+/145ZVX8OWXX2r1VEREREREREREREQkAc0moNs6//zzMXXqVLz0\n0kuYMWMGampq8Itf/EKPpyIiIiIiIiIiIiIiQWm2BEc0PXv2xLhx4zBu3Dh4vV49n4qIiIiIiIiI\niIiIBKP5BHRzczPee+89HDhwAI2Nje3+bfr06Vo/HREREREREREREREJSvMJ6NLSUnzxxRe46KKL\n4Ha7tX54IiIiIiIiIiIiIpKE5hPQO3bsQGlpKTIzM7V+aCIiIiIiIiIiIiKSiOZfQpibm4umpiat\nH5aIiIiIiIiIiIiIJKP5J6Avu+wyPP/88/jhD3+IrKysdv82fPhwrZ+OiIiIiIiIiIiIiASl+QT0\nW2+9BQB45ZVX2t2uKApKS0u1fjoiIiIiIiIiIiIiEpTmE9BLlizR+iFJYzZFgSPgQ2j3ETgdmQhm\nuhFWVaPLIskxVySz1vzCVwe4s5hfshTmn8yGmSYi0g57KlkNM68PzSegASAUCuGzzz6D1+uFx+PB\nueeei7S0ND2eiuJkUxRkVu6Cr6QY6slGKOkZcBcVIzB4GA8oSphNUeCo3AV/m1y5iooRlDxXnFS3\nBrPnlwMn6ordZoNjz07ULXzKVPknY4jQd8za04mIUqVdL8/2QPnqi3bzB+ypJItExiUcR+hH8y8h\n/Oqrr1BUVIRFixbh73//O37zm99g1qxZ+PLLL7V+KkqAI+CPnDwAQD3ZCF9JMRwBv8GVkcwcAV+k\nQQMtufKXFLc0e0lFTjyz70X1o1Pgn30vHJW7YFMUo0sjjZk9v77HpzO/FJVNUeA88kVk8hkwR/7J\nGKL0HTP2dCKiVDm9l6ub3+swf8CeSjJIdFzCcYR+NJ+ALisrQ2FhIX77299i7ty5WLZsGb73ve/h\n5Zdf1vqpKAFptccjB1Ir9WQj0mqrDaqITMFXFzVX8NUZVFDyeOKxEOaXLMoR8KFp98emyz8ZQ5i+\nY8KeTkSUKqf3ckBlTyUpJTwu4ThCN5pPQB84cADXXHMNlDZ/Vbj66qtx4MABrZ+KEqBkOKCkZ7S/\nLT0DSkYvgyoiU3BnRc0V3FkGFaQBnnisg/klq/LVAaGQ+fJPxhCl75ixpxMRpcrpvTyssqeSnBId\nl3AcoRvN14DOycnBp59+iuHDh0du+89//oPs7Oxu73vq1Ck88cQTaG5uRigUwpgxY/DjH/8YVVVV\nWLhwIerr65Gfn48ZM2bAbrejqakJpaWl2LdvH3r37o1Zs2ahb9++Wm+SqTRn9obrzqnwr1n2zXo2\nd05Fc2Zvo0uTnpXzG8x0w1VU3HGdpEw3IOs6SV+feNqetMx+4rFqhplfc7BqfpPizkJg09twTZoC\n/9rlkfxnzXocDTLnX1LSZ1iQvmPKni4B6fNLlscMf+20Xh4o/2vH+QP2VOEwv1EkOC7hOEI/acXF\nxcVaPqDH48GCBQtw8OBBVFZW4p133sGf/vQn/PSnP0X//v27vK/NZsO4ceNw1VVX4YorrsArr7yC\ngQMH4rXXXsPll1+OKVOm4OOPP0ZtbS0GDRqE8vJyBINBPPbYY8jIyMBbb72FSy65pNsa6+vrO9zm\ncDgQDAYT3m5ZNPdIR49wCD3PGoD0kRchfegFUL41CMHcs2CFQ6mr/dy7d3KT8Ebm12gqgGZPXzgn\nfB+9x38fPa66GcEzB0q9SH9zzww4vz0MpyreB0LN35x4zhwo5LGSbH4Bc2e4q2O/bX4zxk5E+rU/\nFi6/8Z6jRMtvLPWzBycnkXFMc88MZA48Gw1/XgPnD25E+gXfgfOmOxE4+9sI6Zx/Gcddeo4hAHEy\nnOi+SVXf6a4+o3u66NnurD724I5E35fRWLVmM/Vgo53eyxFqRvoPb0T69bfH1VNlzKJWEtl2q/Zg\nPXMS77iktRaOI74Ray2x5lfzJTgKCgrw3HPPYeDAgWhsbEReXh7mzZuH0aNHd3tfRVGQkdHyUfdQ\nKIRQKARFUbBr1y6MGTMGADBhwgRUVFQAALZs2YIJEyYAAMaMGYNPPvkEqkATBiIKqyqCeUOgfOdS\n9Bx+EZTvXIpg3hChJlpkZfX8hlUVDQ4X0s4bgQaHS/pMhVUVwcHD4Jpfhtxnl8M1v8z033xr5Qy3\n5rfhrDzT5df9VCnza/L8Jqo1J87Zz0A5/7+gjB4H/5l5aA6HjS7NkmTPsEh9x2w9XQay55eIGW4R\ntZfnDUGDozd7qsCY346SGZdwHKEPzZfgAIB+/frhpptuAtByKYASx7dfh8NhPPLIIzh69Ci+//3v\n44wzzoDD4UBaWhqAliU+vF4vAMDr9cLj8QAA0tLS4HA4UF9fD5fLpfEWmUvrwZSbl4/a6mpeRqAh\n5tdcrHisMMPm0ZpfOL7eH8wv8xuFFXMiMtkzzDxZm+z5JWKGW7CXy4n57YhZFovmE9C///3vMXbs\nWAwePBhbt27FggULoCgKZs2ahYKCgm7vb7PZ8PzzzyMQCOCFF17A4cOHk66pvLwc5eXlAIB58+Yh\nNze3w+/Y7faot5sZt1l7RuVXJGbMlRm3qTNmzbDs+5D1x8as+Y2FbBmRrV4gNTWLkGHR9w3rS46e\n9YmQXy2Jvi+jYc3JMVuGjSTSfk01o7ZdxvyKlBNRahGlDkD7WjSfgH7//fdxyy23AABee+01zJgx\nAw6HA6tXr45pArpVZmYmhg0bhj179iAYDCIUCiEtLQ1erxc5OTkAWv6CU1NTA4/Hg1AohGAwGHXt\nkcLCQhQWFkZ+rq6u7vA7ubm5UW83M25ze/369dPseVKdX5GYMVcybJOW+QXMl2EZ9mFXrFA/e3By\nZMuIbPUCqRtDAMZmWPR9w/qS01l97MEdib4vo7FqzWbqwWYhYxa1ksi2W7UHi5QTUWoRpQ4g9lpi\nza/ma0CfPHkS6enpqK+vx7FjxzBmzBiMHDkypqL9fj8CgQCAlqU7du7cif79+2PYsGHYvHkzAOC9\n996LTGRfdNFFeO+99wAAmzdvxrBhw+Ja7oNIS8wvyY4ZJpkxvyQ7ZphkxvyS7JhhkhnzSzLQ/BPQ\n/fr1wz//+U8cPXoUI0eOBNByMPTs2bPb+9bW1mLJkiUIh8NQVRWXXHIJLrroIgwYMAALFy7Eq6++\ninPOOQcTJ04EAEycOBGlpaWYMWMGnE4nZs2apfXmEMWM+SXZMcMkM+aXZMcMk8yYX5IdM0wyY35J\nBoqq8VddVlZWYtWqVbDb7Zg6dSrOPPNM/POf/8T27dsxY8YMLZ8qYdHWwhHpY+6pwm1uT+tLt/Si\nxVpOejJjrmTYJlnyCxiTYRn2YVesUL8sGRa1B8uWEdnqBcwxhgC6z7Do+4b1JScVS3DoKZU9WPR9\nGY1Va5Ylv4C44wityZhFrRi9BIeetM6vSDkRpRZR6gC0X4JD809ADx48GE8//XS72y699FJceuml\nWj8VEREREREREREREQlM8wloAGhubsbhw4fh9/vb3T58+HA9no6IiIiIiIiIiIiIBKT5BPTu3bvx\n4osvoqmpCSdOnECvXr3Q2NgIj8eD0tJSrZ+OiIiIiIiIiIiIiARl0/oBV69ejeuuuw4rV65Er169\nsHLlStx000248sortX4qIiIiIiIiIiIiIhKY5hPQhw8fxlVXXdXuthtuuAF/+9vftH4qIiIiIiIi\nIiIiIhKY5hPQDocDJ06cAABkZWXhyy+/RENDAxobG7V+KkqQTVHgDPoR2v0xnEE/bIpidElkMa0Z\ndB45yAySdJhfEgnP6SQL9k4iImOw/5KVMO/i0nwN6Isvvhjbtm3DuHHjcPnll+PJJ59EWloaxowZ\no/VTUQJsigJH5S74S4qhnmyEkp4BV1ExgoOHIayqRpdHFsAMksy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xdrz5496t+/v847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\nTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x12092b630>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "sns.pairplot(baseball_dataset[['At-Bats', 'Hits', 'BattingAverage',\n",
    "       'RemainingAt-Bats', 'RemainingAverage', 'SeasonAt-Bats', 'SeasonHits',\n",
    "       'SeasonAverage']])\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Model"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "打率(at_bats)からのヒットの数の推定に4つのモデル\n",
    "- Fully pooled model\n",
    "- Not pooled model\n",
    "- partially pooled model\n",
    "- partially pooled model(with logit)\n",
    "\n",
    "を試している。階層モデルになってるがpyro.sampleの出力を別の確率変数にパラメータとして代入するような書き方になっている。"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Fully pooled model(complete pooling)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "それぞれの打者の打率を独立のベルヌーイ分布に従うとするモデル、pyroでは統計モデルは関数として定義する。\n",
    "\n",
    "$\\phi \\sim Uniform(0,1)$\n",
    "\n",
    "$y_n \\sim  Binominal(K_n,\\phi)$\n",
    "\n",
    "$K_n$は選手nの打率(モデルの引数)\n",
    "ハイパーパラメータ$\\phi＄は[0,1]間の一様分布、new_tensor(0),new_tensor(1)はモデルで使う定数\n",
    "\n",
    "観測データは出力されるsample関数にobs引数として追加することで関係を示している。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [],
   "source": [
    "def fully_pooled(at_bats, hits):\n",
    "    r\"\"\"\n",
    "    Number of hits in $K$ at bats for each player has a Binomial\n",
    "    distribution with a common probability of success, $\\phi$.\n",
    "    \n",
    "    :param (torch.Tensor) at_bats: Number of at bats for each player.\n",
    "    :return: Number of hits predicted by the model.\n",
    "    \"\"\"\n",
    "    phi_prior = Uniform(at_bats.new_tensor(0), at_bats.new_tensor(1))\n",
    "    phi = pyro.sample(\"phi\", phi_prior)\n",
    "    return pyro.sample(\"obs\", Binomial(at_bats, phi), obs=hits)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Not pooled model"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": true
   },
   "source": [
    "$\\theta_n \\sim Uniform(0,1)$\n",
    "\n",
    "$y_n \\sim  Binominal(K_n,\\theta_n)$\n",
    "\n",
    "それぞれの選手のハイパーパラメータ$\\theta_n$が独立になっている。\n",
    "\n",
    "pyro.plateという関数で内部で使うパラメータを定義している(ように見える)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [],
   "source": [
    "def not_pooled(at_bats, hits):\n",
    "    r\"\"\"\n",
    "    Number of hits in $K$ at bats for each player has a Binomial\n",
    "    distribution with independent probability of success, $\\phi_i$.\n",
    "    \n",
    "    :param (torch.Tensor) at_bats: Number of at bats for each player.\n",
    "    :param (torch.Tensor) hits: Number of hits for the given at bats.\n",
    "    :return: Number of hits predicted by the model.\n",
    "    \"\"\"\n",
    "    num_players = at_bats.shape[0]\n",
    "    with pyro.plate(\"num_players\", num_players):\n",
    "        phi_prior = Uniform(at_bats.new_tensor(0), at_bats.new_tensor(1))\n",
    "        phi = pyro.sample(\"phi\", phi_prior)\n",
    "        return pyro.sample(\"obs\", Binomial(at_bats, phi), obs=hits)\n",
    "    "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## partially pooled model"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "\n",
    "$\\theta_n \\sim Beta(\\alpha,\\beta)$\n",
    "\n",
    "$\\alpha=\\kappa\\phi,\\beta=\\kappa(1-\\phi)$\n",
    "\n",
    "$\\phi \\sim Uniform(0,1)$\n",
    "\n",
    "$\\kappa \\sim Pareto(1,1.5) \\propto \\kappa^{2.5}$\n",
    "\n",
    "$y_n \\sim  Binominal(K_n,\\theta_n)$\n",
    "\n",
    "\n",
    "$\\theta$を[0,1]内に収めるためにbeta分布を用いている階層モデル。さらにサンプリングで$\\alpha,\\beta$を範囲内に収めるために$\\kappa,\\phi$を定義している。pyroではPareto分布も使える！"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [],
   "source": [
    "def partially_pooled(at_bats, hits):\n",
    "    r\"\"\"\n",
    "    Number of hits has a Binomial distribution with independent\n",
    "    probability of success, $\\phi_i$. Each $\\phi_i$ follows a Beta\n",
    "    distribution with concentration parameters $c_1$ and $c_2$, where\n",
    "    $c_1 = m * kappa$, $c_2 = (1 - m) * kappa$, $m ~ Uniform(0, 1)$,\n",
    "    and $kappa ~ Pareto(1, 1.5)$.\n",
    "    :param (torch.Tensor) at_bats: Number of at bats for each player.\n",
    "    :param (torch.Tensor) hits: Number of hits for the given at bats.\n",
    "    :return: Number of hits predicted by the model.\n",
    "    \"\"\"\n",
    "    num_players = at_bats.shape[0]\n",
    "    m = pyro.sample(\"m\", Uniform(at_bats.new_tensor(0), at_bats.new_tensor(1)))\n",
    "    kappa = pyro.sample(\"kappa\", Pareto(at_bats.new_tensor(1), at_bats.new_tensor(1.5)))\n",
    "    with pyro.plate(\"num_players\", num_players):\n",
    "        phi_prior = Beta(m * kappa, (1 - m) * kappa)\n",
    "        phi = pyro.sample(\"phi\", phi_prior)\n",
    "        return pyro.sample(\"obs\", Binomial(at_bats, phi), obs=hits)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$\\alpha_n = \\rm  logit(\\theta_n) =\\frac{\\theta_n}{1-\\theta_n}$\n",
    "\n",
    "サンプルするパラメータの出力にlogitをかませたversion。$\\alpha \\in (-\\infty,\\infty)＄でありこれによって$\\theta$が0,1近辺の時に浮動小数点演算の桁あふれ、不安定性を防ぐ。\n",
    "Binominalにはオプションとしてlogits引数がある。\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [],
   "source": [
    "def partially_pooled_with_logit(at_bats, hits):\n",
    "    r\"\"\"\n",
    "    Number of hits has a Binomial distribution with a logit link function.\n",
    "    The logits $\\alpha$ for each player is normally distributed with the\n",
    "    mean and scale parameters sharing a common prior.\n",
    "    \n",
    "    :param (torch.Tensor) at_bats: Number of at bats for each player.\n",
    "    :param (torch.Tensor) hits: Number of hits for the given at bats.\n",
    "    :return: Number of hits predicted by the model.\n",
    "    \"\"\"\n",
    "    \n",
    "    num_players = at_bats.shape[0]\n",
    "    loc = pyro.sample(\"loc\", Normal(at_bats.new_tensor(-1), at_bats.new_tensor(1)))\n",
    "    scale = pyro.sample(\"scale\", HalfCauchy(scale=at_bats.new_tensor(1)))\n",
    "    with pyro.plate(\"num_players\", num_players):\n",
    "        alpha = pyro.sample(\"alpha\", Normal(loc, scale))\n",
    "        return pyro.sample(\"obs\", Binomial(at_bats, logits=alpha), obs=hits)\n",
    "    "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "stanのレポートではさらに事後分布を均一化させるためにNon-Centered Parameterizationという変数変換を行なっている([参考](https://discourse.mc-stan.org/t/centered-or-non-centered-parametrization-for-random-effects/728/16) )。"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# DATA SUMMARIZE UTILS"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "平均、分散、四分位点の計算、traceからの要約統計やRhatの表示のための関数"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {
    "code_folding": []
   },
   "outputs": [],
   "source": [
    "def get_site_stats(array, player_names):\n",
    "    \"\"\"\n",
    "    Return the summarized statistics for a given array corresponding\n",
    "    to the values sampled for a latent or response site.\n",
    "    \"\"\"\n",
    "    # TODO: only use pandas (or any lightweight tabular package) to display final result\n",
    "    if len(array.shape) == 1:\n",
    "        df = pd.DataFrame(array).transpose()\n",
    "    else:\n",
    "        df = pd.DataFrame(array, columns=player_names).transpose()\n",
    "    return df.apply(pd.Series.describe, axis=1)[[\"mean\", \"std\", \"25%\", \"50%\", \"75%\"]]\n",
    "\n",
    "\n",
    "def summary(trace_posterior, sites, player_names, transforms={}, diagnostics=True):\n",
    "    \"\"\"\n",
    "    Return summarized statistics for each of the ``sites`` in the\n",
    "    traces corresponding to the approximate posterior.\n",
    "    \"\"\"\n",
    "    marginal = trace_posterior.marginal(sites)\n",
    "    site_stats = {}\n",
    "    for site_name in sites:\n",
    "        marginal_site = marginal.support(flatten=True)[site_name]\n",
    "        if site_name in transforms:\n",
    "            marginal_site = transforms[site_name](marginal_site)\n",
    "\n",
    "        site_stats[site_name] = get_site_stats(marginal_site.numpy(), player_names)\n",
    "        if diagnostics and trace_posterior.num_chains > 1:\n",
    "            diag = marginal.diagnostics()[site_name]\n",
    "            site_stats[site_name] = site_stats[site_name].assign(n_eff=diag[\"n_eff\"].numpy(),\n",
    "                                                                 r_hat=diag[\"r_hat\"].numpy())\n",
    "    return site_stats\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# モデル評価用関数"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    " posterior predictive densities評価のための関数\n",
    " \n",
    " Inference Utiliyとして周辺分布の取得などが用意されているのでそれを利用している。\n",
    "\n",
    "http://docs.pyro.ai/en/0.2.1-release/inference_algos.html#module-pyro.infer.abstract_infer "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [],
   "source": [
    "def sample_posterior_predictive(posterior_predictive, baseball_dataset):\n",
    "    \"\"\"\n",
    "    Generate samples from posterior predictive distribution.\n",
    "    \"\"\"\n",
    "    train, test, player_names = train_test_split(baseball_dataset)\n",
    "    at_bats = train[:, 0]\n",
    "    at_bats_season = test[:, 0]\n",
    "    logging.Formatter(\"%(message)s\")\n",
    "    logging.info(\"\\nPosterior Predictive:\")\n",
    "    logging.info(\"Hit Rate - Initial 45 At Bats\")\n",
    "    logging.info(\"-----------------------------\")\n",
    "    # set hits=None to convert it from observation node to sample node\n",
    "    train_predict = posterior_predictive.run(at_bats, None)\n",
    "    train_summary = summary(train_predict, sites=[\"obs\"],\n",
    "                            player_names=player_names, diagnostics=False)[\"obs\"]\n",
    "    train_summary = train_summary.assign(ActualHits=baseball_dataset[[\"Hits\"]].values)\n",
    "    logging.info(train_summary)\n",
    "    logging.info(\"\\nHit Rate - Season Predictions\")\n",
    "    logging.info(\"-----------------------------\")\n",
    "    test_predict = posterior_predictive.run(at_bats_season, None)\n",
    "    test_summary = summary(test_predict, sites=[\"obs\"],\n",
    "                           player_names=player_names, diagnostics=False)[\"obs\"]\n",
    "    test_summary = test_summary.assign(ActualHits=baseball_dataset[[\"SeasonHits\"]].values)\n",
    "    logging.info(test_summary)\n",
    "\n",
    "\n",
    "def evaluate_log_predictive_density(posterior_predictive, baseball_dataset):\n",
    "    \"\"\"\n",
    "    Evaluate the log probability density of observing the unseen data (season hits)\n",
    "    given a model and empirical distribution over the parameters.\n",
    "    \"\"\"\n",
    "    _, test, player_names = train_test_split(baseball_dataset)\n",
    "    at_bats_season, hits_season = test[:, 0], test[:, 1]\n",
    "    test_eval = posterior_predictive.run(at_bats_season, hits_season)\n",
    "    trace_log_pdf = []\n",
    "    for tr in test_eval.exec_traces:\n",
    "        trace_log_pdf.append(tr.log_prob_sum())\n",
    "    # Use LogSumExp trick to evaluate $log(1/num_samples \\sum_i p(new_data | \\theta^{i})) $,\n",
    "    # where $\\theta^{i}$ are parameter samples from the model's posterior.\n",
    "    posterior_pred_density = logsumexp(torch.stack(trace_log_pdf), dim=-1) - math.log(len(trace_log_pdf))\n",
    "    logging.info(\"\\nLog posterior predictive density\")\n",
    "    logging.info(\"--------------------------------\")\n",
    "    logging.info(\"{:.4f}\\n\".format(posterior_pred_density))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# 実行"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "オブジェクトとしてNUTS kernelを作りそこにmodelを代入する。\n",
    "\n",
    "MCMCクラス、run関数でサンプリングを実行する。その後上で定義した関数(sample_posterior_predictive, evaluate_log_predictive_density)を用いて事後分布の値の範囲、Rhat, Log posterior predictive densityを表示する。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [],
   "source": [
    "num_samples=200\n",
    "num_chains=3\n",
    "warmup_steps=100\n",
    "\n",
    "num_predictive_samples = num_samples * num_chains"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [],
   "source": [
    "rng_seed=52\n",
    "pyro.set_rng_seed(rng_seed)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "##  Full Pooling Model"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Widget Javascript not detected.  It may not be installed or enabled properly.\n"
     ]
    },
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       "model_id": "4d51b664111e4db89aff00ce804b0378"
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     "output_type": "display_data"
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Widget Javascript not detected.  It may not be installed or enabled properly.\n"
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    },
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     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Widget Javascript not detected.  It may not be installed or enabled properly.\n"
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     "data": {
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    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "\n",
      "Model: Fully Pooled\n",
      "===================\n",
      "\n",
      "phi:\n",
      "       mean       std       25%       50%       75%  n_eff     r_hat\n",
      "0  0.267115  0.015634  0.254908  0.267284  0.278384    NaN  1.012708\n",
      "\n",
      "Posterior Predictive:\n",
      "Hit Rate - Initial 45 At Bats\n",
      "-----------------------------\n",
      "                  mean  std   25%   50%   75%  ActualHits\n",
      "Roberto Clemente  18.0  0.0  18.0  18.0  18.0          18\n",
      "Frank Robinson    17.0  0.0  17.0  17.0  17.0          17\n",
      "Frank Howard      16.0  0.0  16.0  16.0  16.0          16\n",
      "Jay Johnstone     15.0  0.0  15.0  15.0  15.0          15\n",
      "Ken Berry         14.0  0.0  14.0  14.0  14.0          14\n",
      "Jim Spencer       14.0  0.0  14.0  14.0  14.0          14\n",
      "Don Kessinger     13.0  0.0  13.0  13.0  13.0          13\n",
      "Luis Alvarado     12.0  0.0  12.0  12.0  12.0          12\n",
      "Ron Santo         11.0  0.0  11.0  11.0  11.0          11\n",
      "Ron Swaboda       11.0  0.0  11.0  11.0  11.0          11\n",
      "Rico Petrocelli   10.0  0.0  10.0  10.0  10.0          10\n",
      "Ellie Rodriguez   10.0  0.0  10.0  10.0  10.0          10\n",
      "George Scott      10.0  0.0  10.0  10.0  10.0          10\n",
      "Del Unser         10.0  0.0  10.0  10.0  10.0          10\n",
      "Billy Williams    10.0  0.0  10.0  10.0  10.0          10\n",
      "Bert Campaneris    9.0  0.0   9.0   9.0   9.0           9\n",
      "Thurman Munson     8.0  0.0   8.0   8.0   8.0           8\n",
      "Max Alvis          7.0  0.0   7.0   7.0   7.0           7\n",
      "\n",
      "Hit Rate - Season Predictions\n",
      "-----------------------------\n",
      "                  mean  std   25%   50%   75%  ActualHits\n",
      "Roberto Clemente  18.0  0.0  18.0  18.0  18.0         145\n",
      "Frank Robinson    17.0  0.0  17.0  17.0  17.0         144\n",
      "Frank Howard      16.0  0.0  16.0  16.0  16.0         160\n",
      "Jay Johnstone     15.0  0.0  15.0  15.0  15.0          76\n",
      "Ken Berry         14.0  0.0  14.0  14.0  14.0         128\n",
      "Jim Spencer       14.0  0.0  14.0  14.0  14.0         140\n",
      "Don Kessinger     13.0  0.0  13.0  13.0  13.0         168\n",
      "Luis Alvarado     12.0  0.0  12.0  12.0  12.0          41\n",
      "Ron Santo         11.0  0.0  11.0  11.0  11.0         148\n",
      "Ron Swaboda       11.0  0.0  11.0  11.0  11.0          57\n",
      "Rico Petrocelli   10.0  0.0  10.0  10.0  10.0         152\n",
      "Ellie Rodriguez   10.0  0.0  10.0  10.0  10.0          52\n",
      "George Scott      10.0  0.0  10.0  10.0  10.0         142\n",
      "Del Unser         10.0  0.0  10.0  10.0  10.0          83\n",
      "Billy Williams    10.0  0.0  10.0  10.0  10.0         205\n",
      "Bert Campaneris    9.0  0.0   9.0   9.0   9.0         168\n",
      "Thurman Munson     8.0  0.0   8.0   8.0   8.0         137\n",
      "Max Alvis          7.0  0.0   7.0   7.0   7.0          21\n",
      "\n",
      "Log posterior predictive density\n",
      "--------------------------------\n",
      "-77.0128\n",
      "\n"
     ]
    }
   ],
   "source": [
    "nuts_kernel = NUTS(fully_pooled)\n",
    "posterior_fully_pooled = MCMC(nuts_kernel,\n",
    "                              num_samples=num_samples,\n",
    "                              warmup_steps=warmup_steps,\n",
    "                              num_chains=num_chains).run(at_bats, hits)\n",
    "logging.info(\"\\nModel: Fully Pooled\")\n",
    "logging.info(\"===================\")\n",
    "logging.info(\"\\nphi:\")\n",
    "logging.info(summary(posterior_fully_pooled, sites=[\"phi\"], player_names=player_names)[\"phi\"])\n",
    "posterior_predictive = TracePredictive(fully_pooled,\n",
    "                                       posterior_fully_pooled,\n",
    "                                       num_samples=num_predictive_samples)\n",
    "sample_posterior_predictive(posterior_predictive, baseball_dataset)\n",
    "evaluate_log_predictive_density(posterior_predictive, baseball_dataset)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## No Pooling Model"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Widget Javascript not detected.  It may not be installed or enabled properly.\n"
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    },
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    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Widget Javascript not detected.  It may not be installed or enabled properly.\n"
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    },
    {
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    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Widget Javascript not detected.  It may not be installed or enabled properly.\n"
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    },
    {
     "data": {
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    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "\n",
      "Model: Not Pooled\n",
      "=================\n",
      "\n",
      "phi:\n",
      "                      mean       std       25%       50%       75%  n_eff  \\\n",
      "Roberto Clemente  0.399943  0.075035  0.346843  0.396658  0.452164    NaN   \n",
      "Frank Robinson    0.380921  0.070193  0.334455  0.375778  0.428543    NaN   \n",
      "Frank Howard      0.362561  0.071634  0.312462  0.358348  0.413378    NaN   \n",
      "Jay Johnstone     0.336355  0.071878  0.289077  0.329880  0.382827    NaN   \n",
      "Ken Berry         0.314747  0.065654  0.270413  0.310458  0.356329    NaN   \n",
      "Jim Spencer       0.315158  0.062964  0.268278  0.311988  0.358840    NaN   \n",
      "Don Kessinger     0.301659  0.068475  0.252892  0.298465  0.349038    NaN   \n",
      "Luis Alvarado     0.283721  0.062200  0.239647  0.282782  0.324852    NaN   \n",
      "Ron Santo         0.258056  0.059806  0.215130  0.255764  0.297286    NaN   \n",
      "Ron Swaboda       0.256684  0.067631  0.208116  0.255430  0.299480    NaN   \n",
      "Rico Petrocelli   0.229894  0.059704  0.186203  0.224607  0.270622    NaN   \n",
      "Ellie Rodriguez   0.236017  0.057246  0.191330  0.234975  0.274804    NaN   \n",
      "George Scott      0.234043  0.059666  0.190660  0.231042  0.274553    NaN   \n",
      "Del Unser         0.236534  0.061990  0.193895  0.231431  0.276140    NaN   \n",
      "Billy Williams    0.236507  0.057134  0.193631  0.233240  0.275560    NaN   \n",
      "Bert Campaneris   0.212033  0.061096  0.168675  0.206219  0.252786    NaN   \n",
      "Thurman Munson    0.191130  0.057044  0.146603  0.187605  0.228246    NaN   \n",
      "Max Alvis         0.171947  0.054420  0.131149  0.166210  0.210815    NaN   \n",
      "\n",
      "                     r_hat  \n",
      "Roberto Clemente  0.996561  \n",
      "Frank Robinson    0.996544  \n",
      "Frank Howard      0.997555  \n",
      "Jay Johnstone     0.997095  \n",
      "Ken Berry         1.001117  \n",
      "Jim Spencer       0.997749  \n",
      "Don Kessinger     0.998231  \n",
      "Luis Alvarado     1.000688  \n",
      "Ron Santo         0.999810  \n",
      "Ron Swaboda       0.998106  \n",
      "Rico Petrocelli   0.996533  \n",
      "Ellie Rodriguez   0.999227  \n",
      "George Scott      0.998112  \n",
      "Del Unser         0.998835  \n",
      "Billy Williams    0.995157  \n",
      "Bert Campaneris   1.002228  \n",
      "Thurman Munson    0.999830  \n",
      "Max Alvis         0.996702  \n",
      "\n",
      "Posterior Predictive:\n",
      "Hit Rate - Initial 45 At Bats\n",
      "-----------------------------\n",
      "                  mean  std   25%   50%   75%  ActualHits\n",
      "Roberto Clemente  18.0  0.0  18.0  18.0  18.0          18\n",
      "Frank Robinson    17.0  0.0  17.0  17.0  17.0          17\n",
      "Frank Howard      16.0  0.0  16.0  16.0  16.0          16\n",
      "Jay Johnstone     15.0  0.0  15.0  15.0  15.0          15\n",
      "Ken Berry         14.0  0.0  14.0  14.0  14.0          14\n",
      "Jim Spencer       14.0  0.0  14.0  14.0  14.0          14\n",
      "Don Kessinger     13.0  0.0  13.0  13.0  13.0          13\n",
      "Luis Alvarado     12.0  0.0  12.0  12.0  12.0          12\n",
      "Ron Santo         11.0  0.0  11.0  11.0  11.0          11\n",
      "Ron Swaboda       11.0  0.0  11.0  11.0  11.0          11\n",
      "Rico Petrocelli   10.0  0.0  10.0  10.0  10.0          10\n",
      "Ellie Rodriguez   10.0  0.0  10.0  10.0  10.0          10\n",
      "George Scott      10.0  0.0  10.0  10.0  10.0          10\n",
      "Del Unser         10.0  0.0  10.0  10.0  10.0          10\n",
      "Billy Williams    10.0  0.0  10.0  10.0  10.0          10\n",
      "Bert Campaneris    9.0  0.0   9.0   9.0   9.0           9\n",
      "Thurman Munson     8.0  0.0   8.0   8.0   8.0           8\n",
      "Max Alvis          7.0  0.0   7.0   7.0   7.0           7\n",
      "\n",
      "Hit Rate - Season Predictions\n",
      "-----------------------------\n",
      "                  mean  std   25%   50%   75%  ActualHits\n",
      "Roberto Clemente  18.0  0.0  18.0  18.0  18.0         145\n",
      "Frank Robinson    17.0  0.0  17.0  17.0  17.0         144\n",
      "Frank Howard      16.0  0.0  16.0  16.0  16.0         160\n",
      "Jay Johnstone     15.0  0.0  15.0  15.0  15.0          76\n",
      "Ken Berry         14.0  0.0  14.0  14.0  14.0         128\n",
      "Jim Spencer       14.0  0.0  14.0  14.0  14.0         140\n",
      "Don Kessinger     13.0  0.0  13.0  13.0  13.0         168\n",
      "Luis Alvarado     12.0  0.0  12.0  12.0  12.0          41\n",
      "Ron Santo         11.0  0.0  11.0  11.0  11.0         148\n",
      "Ron Swaboda       11.0  0.0  11.0  11.0  11.0          57\n",
      "Rico Petrocelli   10.0  0.0  10.0  10.0  10.0         152\n",
      "Ellie Rodriguez   10.0  0.0  10.0  10.0  10.0          52\n",
      "George Scott      10.0  0.0  10.0  10.0  10.0         142\n",
      "Del Unser         10.0  0.0  10.0  10.0  10.0          83\n",
      "Billy Williams    10.0  0.0  10.0  10.0  10.0         205\n",
      "Bert Campaneris    9.0  0.0   9.0   9.0   9.0         168\n",
      "Thurman Munson     8.0  0.0   8.0   8.0   8.0         137\n",
      "Max Alvis          7.0  0.0   7.0   7.0   7.0          21\n",
      "\n",
      "Log posterior predictive density\n",
      "--------------------------------\n",
      "-99.6108\n",
      "\n"
     ]
    }
   ],
   "source": [
    "nuts_kernel = NUTS(not_pooled)\n",
    "posterior_not_pooled = MCMC(nuts_kernel,\n",
    "                            num_samples=num_samples,\n",
    "                            warmup_steps=warmup_steps,\n",
    "                            num_chains=num_chains).run(at_bats, hits)\n",
    "\n",
    "logging.info(\"\\nModel: Not Pooled\")\n",
    "logging.info(\"=================\")\n",
    "logging.info(\"\\nphi:\")\n",
    "logging.info(summary(posterior_not_pooled, sites=[\"phi\"], player_names=player_names)[\"phi\"])\n",
    "posterior_predictive = TracePredictive(not_pooled,\n",
    "                                       posterior_not_pooled,\n",
    "                                       num_samples=num_predictive_samples)\n",
    "sample_posterior_predictive(posterior_predictive, baseball_dataset)\n",
    "evaluate_log_predictive_density(posterior_predictive, baseball_dataset)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Rhatが1以下の$\\phi$選手が多く収束していない。posterior predictive densityの値も小さい。"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Partially Pooled Model"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Widget Javascript not detected.  It may not be installed or enabled properly.\n"
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     "output_type": "stream",
     "text": [
      "Widget Javascript not detected.  It may not be installed or enabled properly.\n"
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     "output_type": "stream",
     "text": [
      "Widget Javascript not detected.  It may not be installed or enabled properly.\n"
     ]
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    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Widget Javascript not detected.  It may not be installed or enabled properly.\n",
      "Widget Javascript not detected.  It may not be installed or enabled properly.\n",
      "\n",
      "Model: Partially Pooled\n",
      "=======================\n",
      "\n",
      "phi:\n",
      "                      mean       std       25%       50%       75%  n_eff  \\\n",
      "Roberto Clemente  0.330732  0.056697  0.287433  0.329061  0.367337    NaN   \n",
      "Frank Robinson    0.318623  0.053476  0.281985  0.313461  0.349818    NaN   \n",
      "Frank Howard      0.312894  0.053505  0.274333  0.307558  0.347047    NaN   \n",
      "Jay Johnstone     0.295636  0.050027  0.261132  0.291267  0.324851    NaN   \n",
      "Ken Berry         0.288313  0.046968  0.256531  0.284000  0.318049    NaN   \n",
      "Jim Spencer       0.287504  0.045141  0.256558  0.284777  0.318844    NaN   \n",
      "Don Kessinger     0.278573  0.048426  0.246480  0.277425  0.309384    NaN   \n",
      "Luis Alvarado     0.266445  0.045962  0.236697  0.264992  0.295940    NaN   \n",
      "Ron Santo         0.259523  0.047678  0.228490  0.259872  0.289555    NaN   \n",
      "Ron Swaboda       0.259049  0.046129  0.228279  0.256043  0.290896    NaN   \n",
      "Rico Petrocelli   0.246646  0.045131  0.216728  0.246783  0.272855    NaN   \n",
      "Ellie Rodriguez   0.244179  0.048296  0.213908  0.244600  0.277833    NaN   \n",
      "George Scott      0.249798  0.044556  0.220636  0.249137  0.280757    NaN   \n",
      "Del Unser         0.245764  0.041945  0.217120  0.245693  0.273705    NaN   \n",
      "Billy Williams    0.248844  0.043270  0.220262  0.249451  0.277614    NaN   \n",
      "Bert Campaneris   0.234063  0.045807  0.203822  0.234369  0.263453    NaN   \n",
      "Thurman Munson    0.226682  0.046412  0.198276  0.225546  0.260829    NaN   \n",
      "Max Alvis         0.215490  0.043255  0.185727  0.214943  0.244984    NaN   \n",
      "\n",
      "                     r_hat  \n",
      "Roberto Clemente  1.008639  \n",
      "Frank Robinson    1.004020  \n",
      "Frank Howard      1.005832  \n",
      "Jay Johnstone     1.014933  \n",
      "Ken Berry         1.005918  \n",
      "Jim Spencer       1.021570  \n",
      "Don Kessinger     1.002926  \n",
      "Luis Alvarado     1.003754  \n",
      "Ron Santo         0.997998  \n",
      "Ron Swaboda       1.003618  \n",
      "Rico Petrocelli   1.004025  \n",
      "Ellie Rodriguez   1.004003  \n",
      "George Scott      0.999369  \n",
      "Del Unser         1.002674  \n",
      "Billy Williams    1.000619  \n",
      "Bert Campaneris   1.006408  \n",
      "Thurman Munson    1.010476  \n",
      "Max Alvis         1.008355  \n",
      "\n",
      "Posterior Predictive:\n",
      "Hit Rate - Initial 45 At Bats\n",
      "-----------------------------\n",
      "                  mean  std   25%   50%   75%  ActualHits\n",
      "Roberto Clemente  18.0  0.0  18.0  18.0  18.0          18\n",
      "Frank Robinson    17.0  0.0  17.0  17.0  17.0          17\n",
      "Frank Howard      16.0  0.0  16.0  16.0  16.0          16\n",
      "Jay Johnstone     15.0  0.0  15.0  15.0  15.0          15\n",
      "Ken Berry         14.0  0.0  14.0  14.0  14.0          14\n",
      "Jim Spencer       14.0  0.0  14.0  14.0  14.0          14\n",
      "Don Kessinger     13.0  0.0  13.0  13.0  13.0          13\n",
      "Luis Alvarado     12.0  0.0  12.0  12.0  12.0          12\n",
      "Ron Santo         11.0  0.0  11.0  11.0  11.0          11\n",
      "Ron Swaboda       11.0  0.0  11.0  11.0  11.0          11\n",
      "Rico Petrocelli   10.0  0.0  10.0  10.0  10.0          10\n",
      "Ellie Rodriguez   10.0  0.0  10.0  10.0  10.0          10\n",
      "George Scott      10.0  0.0  10.0  10.0  10.0          10\n",
      "Del Unser         10.0  0.0  10.0  10.0  10.0          10\n",
      "Billy Williams    10.0  0.0  10.0  10.0  10.0          10\n",
      "Bert Campaneris    9.0  0.0   9.0   9.0   9.0           9\n",
      "Thurman Munson     8.0  0.0   8.0   8.0   8.0           8\n",
      "Max Alvis          7.0  0.0   7.0   7.0   7.0           7\n",
      "\n",
      "Hit Rate - Season Predictions\n",
      "-----------------------------\n",
      "                  mean  std   25%   50%   75%  ActualHits\n",
      "Roberto Clemente  18.0  0.0  18.0  18.0  18.0         145\n",
      "Frank Robinson    17.0  0.0  17.0  17.0  17.0         144\n",
      "Frank Howard      16.0  0.0  16.0  16.0  16.0         160\n",
      "Jay Johnstone     15.0  0.0  15.0  15.0  15.0          76\n",
      "Ken Berry         14.0  0.0  14.0  14.0  14.0         128\n",
      "Jim Spencer       14.0  0.0  14.0  14.0  14.0         140\n",
      "Don Kessinger     13.0  0.0  13.0  13.0  13.0         168\n",
      "Luis Alvarado     12.0  0.0  12.0  12.0  12.0          41\n",
      "Ron Santo         11.0  0.0  11.0  11.0  11.0         148\n",
      "Ron Swaboda       11.0  0.0  11.0  11.0  11.0          57\n",
      "Rico Petrocelli   10.0  0.0  10.0  10.0  10.0         152\n",
      "Ellie Rodriguez   10.0  0.0  10.0  10.0  10.0          52\n",
      "George Scott      10.0  0.0  10.0  10.0  10.0         142\n",
      "Del Unser         10.0  0.0  10.0  10.0  10.0          83\n",
      "Billy Williams    10.0  0.0  10.0  10.0  10.0         205\n",
      "Bert Campaneris    9.0  0.0   9.0   9.0   9.0         168\n",
      "Thurman Munson     8.0  0.0   8.0   8.0   8.0         137\n",
      "Max Alvis          7.0  0.0   7.0   7.0   7.0          21\n",
      "\n",
      "Log posterior predictive density\n",
      "--------------------------------\n",
      "-46.9007\n",
      "\n"
     ]
    }
   ],
   "source": [
    "    nuts_kernel = NUTS(partially_pooled)\n",
    "    posterior_partially_pooled = MCMC(nuts_kernel,\n",
    "                                      num_samples=num_samples,\n",
    "                                      warmup_steps=warmup_steps,\n",
    "                                      num_chains=num_chains).run(at_bats, hits)\n",
    "    logging.info(\"\\nModel: Partially Pooled\")\n",
    "    logging.info(\"=======================\")\n",
    "    logging.info(\"\\nphi:\")\n",
    "    logging.info(summary(posterior_partially_pooled, sites=[\"phi\"],\n",
    "                         player_names=player_names)[\"phi\"])\n",
    "    posterior_predictive = TracePredictive(partially_pooled,\n",
    "                                           posterior_partially_pooled,\n",
    "                                           num_samples=num_predictive_samples)\n",
    "    sample_posterior_predictive(posterior_predictive, baseball_dataset)\n",
    "    evaluate_log_predictive_density(posterior_predictive, baseball_dataset)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Partially Pooled with Logit Model"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Widget Javascript not detected.  It may not be installed or enabled properly.\n"
     ]
    },
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    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Widget Javascript not detected.  It may not be installed or enabled properly.\n"
     ]
    },
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     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Widget Javascript not detected.  It may not be installed or enabled properly.\n"
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     "name": "stderr",
     "output_type": "stream",
     "text": [
      "\n",
      "Model: Partially Pooled with Logit\n",
      "==================================\n",
      "\n",
      "Sigmoid(alpha):\n",
      "                      mean       std       25%       50%       75%  n_eff  \\\n",
      "Roberto Clemente  0.296156  0.040719  0.266291  0.290531  0.320242    NaN   \n",
      "Frank Robinson    0.290568  0.039773  0.264530  0.284151  0.312349    NaN   \n",
      "Frank Howard      0.287571  0.039618  0.261698  0.280873  0.308512    NaN   \n",
      "Jay Johnstone     0.281311  0.036731  0.254630  0.278680  0.301954    NaN   \n",
      "Ken Berry         0.275172  0.034034  0.251361  0.273174  0.296399    NaN   \n",
      "Jim Spencer       0.275183  0.038243  0.248527  0.271953  0.294773    NaN   \n",
      "Don Kessinger     0.269896  0.034686  0.246947  0.265581  0.290342    NaN   \n",
      "Luis Alvarado     0.265240  0.035537  0.244533  0.264933  0.287217    NaN   \n",
      "Ron Santo         0.259697  0.034639  0.239275  0.262939  0.279452    NaN   \n",
      "Ron Swaboda       0.260685  0.035905  0.235296  0.259989  0.281871    NaN   \n",
      "Rico Petrocelli   0.253204  0.034641  0.232819  0.255023  0.273528    NaN   \n",
      "Ellie Rodriguez   0.254260  0.031659  0.235744  0.254733  0.273609    NaN   \n",
      "George Scott      0.253762  0.032302  0.234679  0.255867  0.275410    NaN   \n",
      "Del Unser         0.255131  0.031011  0.237398  0.257930  0.274724    NaN   \n",
      "Billy Williams    0.253935  0.032343  0.235494  0.254280  0.274392    NaN   \n",
      "Bert Campaneris   0.249635  0.037554  0.228033  0.251631  0.272752    NaN   \n",
      "Thurman Munson    0.243726  0.035686  0.222682  0.246175  0.265775    NaN   \n",
      "Max Alvis         0.240035  0.036551  0.218575  0.244242  0.265604    NaN   \n",
      "\n",
      "                     r_hat  \n",
      "Roberto Clemente  1.013094  \n",
      "Frank Robinson    1.026909  \n",
      "Frank Howard      1.026840  \n",
      "Jay Johnstone     1.012468  \n",
      "Ken Berry         1.004120  \n",
      "Jim Spencer       1.003538  \n",
      "Don Kessinger     0.998158  \n",
      "Luis Alvarado     0.995409  \n",
      "Ron Santo         0.998881  \n",
      "Ron Swaboda       1.007532  \n",
      "Rico Petrocelli   0.998102  \n",
      "Ellie Rodriguez   0.999133  \n",
      "George Scott      0.998382  \n",
      "Del Unser         1.008240  \n",
      "Billy Williams    1.000821  \n",
      "Bert Campaneris   0.995667  \n",
      "Thurman Munson    1.002400  \n",
      "Max Alvis         1.012194  \n",
      "\n",
      "Posterior Predictive:\n",
      "Hit Rate - Initial 45 At Bats\n",
      "-----------------------------\n",
      "                  mean  std   25%   50%   75%  ActualHits\n",
      "Roberto Clemente  18.0  0.0  18.0  18.0  18.0          18\n",
      "Frank Robinson    17.0  0.0  17.0  17.0  17.0          17\n",
      "Frank Howard      16.0  0.0  16.0  16.0  16.0          16\n",
      "Jay Johnstone     15.0  0.0  15.0  15.0  15.0          15\n",
      "Ken Berry         14.0  0.0  14.0  14.0  14.0          14\n",
      "Jim Spencer       14.0  0.0  14.0  14.0  14.0          14\n",
      "Don Kessinger     13.0  0.0  13.0  13.0  13.0          13\n",
      "Luis Alvarado     12.0  0.0  12.0  12.0  12.0          12\n",
      "Ron Santo         11.0  0.0  11.0  11.0  11.0          11\n",
      "Ron Swaboda       11.0  0.0  11.0  11.0  11.0          11\n",
      "Rico Petrocelli   10.0  0.0  10.0  10.0  10.0          10\n",
      "Ellie Rodriguez   10.0  0.0  10.0  10.0  10.0          10\n",
      "George Scott      10.0  0.0  10.0  10.0  10.0          10\n",
      "Del Unser         10.0  0.0  10.0  10.0  10.0          10\n",
      "Billy Williams    10.0  0.0  10.0  10.0  10.0          10\n",
      "Bert Campaneris    9.0  0.0   9.0   9.0   9.0           9\n",
      "Thurman Munson     8.0  0.0   8.0   8.0   8.0           8\n",
      "Max Alvis          7.0  0.0   7.0   7.0   7.0           7\n",
      "\n",
      "Hit Rate - Season Predictions\n",
      "-----------------------------\n",
      "                  mean  std   25%   50%   75%  ActualHits\n",
      "Roberto Clemente  18.0  0.0  18.0  18.0  18.0         145\n",
      "Frank Robinson    17.0  0.0  17.0  17.0  17.0         144\n",
      "Frank Howard      16.0  0.0  16.0  16.0  16.0         160\n",
      "Jay Johnstone     15.0  0.0  15.0  15.0  15.0          76\n",
      "Ken Berry         14.0  0.0  14.0  14.0  14.0         128\n",
      "Jim Spencer       14.0  0.0  14.0  14.0  14.0         140\n",
      "Don Kessinger     13.0  0.0  13.0  13.0  13.0         168\n",
      "Luis Alvarado     12.0  0.0  12.0  12.0  12.0          41\n",
      "Ron Santo         11.0  0.0  11.0  11.0  11.0         148\n",
      "Ron Swaboda       11.0  0.0  11.0  11.0  11.0          57\n",
      "Rico Petrocelli   10.0  0.0  10.0  10.0  10.0         152\n",
      "Ellie Rodriguez   10.0  0.0  10.0  10.0  10.0          52\n",
      "George Scott      10.0  0.0  10.0  10.0  10.0         142\n",
      "Del Unser         10.0  0.0  10.0  10.0  10.0          83\n",
      "Billy Williams    10.0  0.0  10.0  10.0  10.0         205\n",
      "Bert Campaneris    9.0  0.0   9.0   9.0   9.0         168\n",
      "Thurman Munson     8.0  0.0   8.0   8.0   8.0         137\n",
      "Max Alvis          7.0  0.0   7.0   7.0   7.0          21\n",
      "\n",
      "Log posterior predictive density\n",
      "--------------------------------\n",
      "-52.6788\n",
      "\n"
     ]
    }
   ],
   "source": [
    "nuts_kernel = NUTS(partially_pooled_with_logit)\n",
    "posterior_partially_pooled_with_logit = MCMC(nuts_kernel,\n",
    "                                             num_samples=num_samples,\n",
    "                                             warmup_steps=warmup_steps,\n",
    "                                             num_chains=num_chains).run(at_bats, hits)\n",
    "logging.info(\"\\nModel: Partially Pooled with Logit\")\n",
    "logging.info(\"==================================\")\n",
    "logging.info(\"\\nSigmoid(alpha):\")\n",
    "logging.info(summary(posterior_partially_pooled_with_logit,\n",
    "                     sites=[\"alpha\"],\n",
    "                     player_names=player_names,\n",
    "                     transforms={\"alpha\": lambda x: 1. / (1 + (-x).exp())})[\"alpha\"])\n",
    "posterior_predictive = TracePredictive(partially_pooled_with_logit,\n",
    "                                       posterior_partially_pooled_with_logit,\n",
    "                                       num_samples=num_predictive_samples)\n",
    "sample_posterior_predictive(posterior_predictive, baseball_dataset)\n",
    "evaluate_log_predictive_density(posterior_predictive, baseball_dataset)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# ToDo"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "- レポートの可視化（stan、pymcのforestplotのようなもの）\n",
    "\n",
    "- ハイパーパラメータの分布のプロット\n",
    "-  Centered Parameterization, Non-Centered Parameterizationの比較(plot)\n",
    "-  stanの例の続き\n",
    "\n",
    "    + estimate event probabilities\n",
    "    + evaluate posterior predictive densities to evaluate model predictions on held-out data\n",
    "    + rank items by chance of success\n",
    "    + perform multiple comparisons in several settings\n",
    "    + replicate new data for posterior p-values\n",
    "    + perform graphical posterior predictive checks"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Link"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "pymcの階層ベイズモデルの例\n",
    "- https://docs.pymc.io/notebooks/rugby_analytics.html\n",
    "- https://docs.pymc.io/notebooks/multilevel_modeling.html\n",
    "- http://danielweitzenfeld.github.io/passtheroc/blog/2014/10/28/bayes-premier-league/ \n",
    "\n",
    "なぜかスポーツのデータが多い。"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# その他"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "poutineとは統計モデルをデータを結びつけるための関数でwith構文にしたりデコレーターとしたりといろいろな使い方ができる。少し古いversionではこれを直接使ってMCMC用のkernelを作っていた。\n",
    "http://docs.pyro.ai/en/0.2.1-release/poutine.html"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def conditioned_model(model, at_bats, hits):\n",
    "    return poutine.condition(model, data={\"obs\": hits})(at_bats)"
   ]
  }
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