AustinRochford/quantifying_reading.ipynb

## quantifying_reading.ipynb
{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "---\n",
    "title: Quantifying Three Years of Reading\n",
    "tags: Bayesian Statistics, PyMC3, Books, Personal\n",
    "---"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Since December 2014, I have [tracked](https://cdn.knightlab.com/libs/timeline3/latest/embed/index.html?source=1wNbJv1Zf4Oichj3-dEQXE_lXVCwuYQjaoyU1gGQQqk4&font=Default&lang=en&start_at_end=true&initial_zoom=2&height=650) the books I read in a Google spreadsheet.  It recently occurred to me to use this data to quantify how my reading habits have changed over time.  This post will use [PyMC3](https://github.com/pymc-devs/pymc3) to model my reading habits."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "from itertools import product"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "from matplotlib import dates as mdates\n",
    "from matplotlib import pyplot as plt\n",
    "import numpy as np\n",
    "import pandas as pd\n",
    "import pymc3 as pm\n",
    "import scipy as sp\n",
    "import seaborn as sns\n",
    "from theano import shared, tensor as tt"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "sns.set()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "SEED = 27432 # from random.org, for reproductibility"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "First we load the data from the Google Spreadsheet.  Conveniently, [`pandas`](https://github.com/pymc-devs/pymc3/pull/2766) can load CSVs from a web link."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "GDOC_URI = 'https://docs.google.com/spreadsheets/d/1wNbJv1Zf4Oichj3-dEQXE_lXVCwuYQjaoyU1gGQQqk4/export?gid=0&format=csv'"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "raw_df = (pd.read_csv(\n",
    "                GDOC_URI,\n",
    "                usecols=[\n",
    "                    'Year', 'Month', 'Day',\n",
    "                    'End Year', 'End Month', 'End Day',\n",
    "                    'Headline', 'Text'\n",
    "                ]\n",
    "            )\n",
    "            .dropna(axis=1, how='all')\n",
    "            .dropna(axis=0))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
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       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Year</th>\n",
       "      <th>Month</th>\n",
       "      <th>Day</th>\n",
       "      <th>End Year</th>\n",
       "      <th>End Month</th>\n",
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       "      <th>0</th>\n",
       "      <td>2014</td>\n",
       "      <td>12</td>\n",
       "      <td>13</td>\n",
       "      <td>2014.0</td>\n",
       "      <td>12.0</td>\n",
       "      <td>23.0</td>\n",
       "      <td>The Bloody Chamber</td>\n",
       "      <td>Angela Carter, 126 pages</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>2014</td>\n",
       "      <td>12</td>\n",
       "      <td>23</td>\n",
       "      <td>2015.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>4.0</td>\n",
       "      <td>The Last Place on Earth</td>\n",
       "      <td>Roland Huntford, 564 pages</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>2015</td>\n",
       "      <td>1</td>\n",
       "      <td>24</td>\n",
       "      <td>2015.0</td>\n",
       "      <td>2.0</td>\n",
       "      <td>13.0</td>\n",
       "      <td>Empire Falls</td>\n",
       "      <td>Richard Russo, 483 pages</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>2015</td>\n",
       "      <td>2</td>\n",
       "      <td>14</td>\n",
       "      <td>2015.0</td>\n",
       "      <td>2.0</td>\n",
       "      <td>20.0</td>\n",
       "      <td>Wonder Boys</td>\n",
       "      <td>Michael Chabon, 368 pages</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>2015</td>\n",
       "      <td>2</td>\n",
       "      <td>25</td>\n",
       "      <td>2015.0</td>\n",
       "      <td>3.0</td>\n",
       "      <td>4.0</td>\n",
       "      <td>Red State, Blue State, Rich State, Poor State:...</td>\n",
       "      <td>Andrew Gelman, 196 pages</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   Year  Month  Day  End Year  End Month  End Day  \\\n",
       "0  2014     12   13    2014.0       12.0     23.0   \n",
       "1  2014     12   23    2015.0        1.0      4.0   \n",
       "2  2015      1   24    2015.0        2.0     13.0   \n",
       "3  2015      2   14    2015.0        2.0     20.0   \n",
       "4  2015      2   25    2015.0        3.0      4.0   \n",
       "\n",
       "                                            Headline  \\\n",
       "0                                 The Bloody Chamber   \n",
       "1                            The Last Place on Earth   \n",
       "2                                       Empire Falls   \n",
       "3                                        Wonder Boys   \n",
       "4  Red State, Blue State, Rich State, Poor State:...   \n",
       "\n",
       "                         Text  \n",
       "0    Angela Carter, 126 pages  \n",
       "1  Roland Huntford, 564 pages  \n",
       "2    Richard Russo, 483 pages  \n",
       "3   Michael Chabon, 368 pages  \n",
       "4    Andrew Gelman, 196 pages  "
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "raw_df.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
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       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Year</th>\n",
       "      <th>Month</th>\n",
       "      <th>Day</th>\n",
       "      <th>End Year</th>\n",
       "      <th>End Month</th>\n",
       "      <th>End Day</th>\n",
       "      <th>Headline</th>\n",
       "      <th>Text</th>\n",
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       "  <tbody>\n",
       "    <tr>\n",
       "      <th>58</th>\n",
       "      <td>2017</td>\n",
       "      <td>9</td>\n",
       "      <td>16</td>\n",
       "      <td>2017.0</td>\n",
       "      <td>10.0</td>\n",
       "      <td>14.0</td>\n",
       "      <td>Civilization of the Middle Ages</td>\n",
       "      <td>Norman F. Cantor, 566 pages</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>59</th>\n",
       "      <td>2017</td>\n",
       "      <td>10</td>\n",
       "      <td>14</td>\n",
       "      <td>2017.0</td>\n",
       "      <td>10.0</td>\n",
       "      <td>16.0</td>\n",
       "      <td>The Bloody Chamber</td>\n",
       "      <td>Angela Carter, 126 pages</td>\n",
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       "    <tr>\n",
       "      <th>60</th>\n",
       "      <td>2017</td>\n",
       "      <td>10</td>\n",
       "      <td>16</td>\n",
       "      <td>2017.0</td>\n",
       "      <td>10.0</td>\n",
       "      <td>27.0</td>\n",
       "      <td>Big Data Baseball</td>\n",
       "      <td>Travis Sawchik, 233 pages</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>61</th>\n",
       "      <td>2017</td>\n",
       "      <td>10</td>\n",
       "      <td>27</td>\n",
       "      <td>2017.0</td>\n",
       "      <td>12.0</td>\n",
       "      <td>7.0</td>\n",
       "      <td>The History of Statistics: The Measurement of ...</td>\n",
       "      <td>Stephen M. Stigler, 361 pages</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>62</th>\n",
       "      <td>2017</td>\n",
       "      <td>12</td>\n",
       "      <td>8</td>\n",
       "      <td>2017.0</td>\n",
       "      <td>12.0</td>\n",
       "      <td>21.0</td>\n",
       "      <td>An Arsonist's Guide to Writers' Homes in New E...</td>\n",
       "      <td>Brock Clarke, 303 pages</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "    Year  Month  Day  End Year  End Month  End Day  \\\n",
       "58  2017      9   16    2017.0       10.0     14.0   \n",
       "59  2017     10   14    2017.0       10.0     16.0   \n",
       "60  2017     10   16    2017.0       10.0     27.0   \n",
       "61  2017     10   27    2017.0       12.0      7.0   \n",
       "62  2017     12    8    2017.0       12.0     21.0   \n",
       "\n",
       "                                             Headline  \\\n",
       "58                    Civilization of the Middle Ages   \n",
       "59                                 The Bloody Chamber   \n",
       "60                                  Big Data Baseball   \n",
       "61  The History of Statistics: The Measurement of ...   \n",
       "62  An Arsonist's Guide to Writers' Homes in New E...   \n",
       "\n",
       "                             Text  \n",
       "58    Norman F. Cantor, 566 pages  \n",
       "59       Angela Carter, 126 pages  \n",
       "60      Travis Sawchik, 233 pages  \n",
       "61  Stephen M. Stigler, 361 pages  \n",
       "62        Brock Clarke, 303 pages  "
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "raw_df.tail()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The spreadhseet is formatted for use with [Knight Lab's](https://knightlab.northwestern.edu/) excellent [TimelineJS](https://timeline.knightlab.com/) package.  We transform the data to a more useful format for our purposes."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [],
   "source": [
    "df = pd.DataFrame({\n",
    "    'start_date': raw_df.apply(\n",
    "        lambda s: pd.datetime(\n",
    "            s['Year'],\n",
    "            s['Month'],\n",
    "            s['Day']\n",
    "        ),\n",
    "        axis=1\n",
    "    ),\n",
    "    'end_date': raw_df.apply(\n",
    "        lambda s: pd.datetime(\n",
    "            int(s['End Year']),\n",
    "            int(s['End Month']),\n",
    "            int(s['End Day'])\n",
    "        ),\n",
    "        axis=1\n",
    "    ),\n",
    "    'title': raw_df['Headline'],\n",
    "    'author': (raw_df['Text']\n",
    "                     .str.extract('(.*),.*', expand=True)\n",
    "                     .iloc[:, 0]),\n",
    "    'pages': (raw_df['Text']\n",
    "                    .str.extract(r'.*, (\\d+) pages', expand=False)\n",
    "                    .astype(np.int64))\n",
    "})\n",
    "\n",
    "df['days'] = (df['end_date']\n",
    "                .sub(df['start_date'])\n",
    "                .dt.days)\n",
    "\n",
    "df = df[[\n",
    "    'author', 'title',\n",
    "    'start_date', 'end_date', 'days',\n",
    "    'pages'\n",
    "]]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Each row of the dataframe corresponds to a book I have read, and the columns are\n",
    "\n",
    "* `author`, the book's author,\n",
    "* `title`, the book's title,\n",
    "* `start_date`, the date I started reading the book,\n",
    "* `end_date`, the date I finished reading the book,\n",
    "* `days`, then number of days it took me to read the book, and\n",
    "* `pages`, the number of pages in the book."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "      <th>start_date</th>\n",
       "      <th>end_date</th>\n",
       "      <th>days</th>\n",
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       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>Angela Carter</td>\n",
       "      <td>The Bloody Chamber</td>\n",
       "      <td>2014-12-13</td>\n",
       "      <td>2014-12-23</td>\n",
       "      <td>10</td>\n",
       "      <td>126</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>Roland Huntford</td>\n",
       "      <td>The Last Place on Earth</td>\n",
       "      <td>2014-12-23</td>\n",
       "      <td>2015-01-04</td>\n",
       "      <td>12</td>\n",
       "      <td>564</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>Richard Russo</td>\n",
       "      <td>Empire Falls</td>\n",
       "      <td>2015-01-24</td>\n",
       "      <td>2015-02-13</td>\n",
       "      <td>20</td>\n",
       "      <td>483</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>Michael Chabon</td>\n",
       "      <td>Wonder Boys</td>\n",
       "      <td>2015-02-14</td>\n",
       "      <td>2015-02-20</td>\n",
       "      <td>6</td>\n",
       "      <td>368</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>Andrew Gelman</td>\n",
       "      <td>Red State, Blue State, Rich State, Poor State:...</td>\n",
       "      <td>2015-02-25</td>\n",
       "      <td>2015-03-04</td>\n",
       "      <td>7</td>\n",
       "      <td>196</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "            author                                              title  \\\n",
       "0    Angela Carter                                 The Bloody Chamber   \n",
       "1  Roland Huntford                            The Last Place on Earth   \n",
       "2    Richard Russo                                       Empire Falls   \n",
       "3   Michael Chabon                                        Wonder Boys   \n",
       "4    Andrew Gelman  Red State, Blue State, Rich State, Poor State:...   \n",
       "\n",
       "  start_date   end_date  days  pages  \n",
       "0 2014-12-13 2014-12-23    10    126  \n",
       "1 2014-12-23 2015-01-04    12    564  \n",
       "2 2015-01-24 2015-02-13    20    483  \n",
       "3 2015-02-14 2015-02-20     6    368  \n",
       "4 2015-02-25 2015-03-04     7    196  "
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
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       "      <th>58</th>\n",
       "      <td>Norman F. Cantor</td>\n",
       "      <td>Civilization of the Middle Ages</td>\n",
       "      <td>2017-09-16</td>\n",
       "      <td>2017-10-14</td>\n",
       "      <td>28</td>\n",
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       "    <tr>\n",
       "      <th>59</th>\n",
       "      <td>Angela Carter</td>\n",
       "      <td>The Bloody Chamber</td>\n",
       "      <td>2017-10-14</td>\n",
       "      <td>2017-10-16</td>\n",
       "      <td>2</td>\n",
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       "    <tr>\n",
       "      <th>60</th>\n",
       "      <td>Travis Sawchik</td>\n",
       "      <td>Big Data Baseball</td>\n",
       "      <td>2017-10-16</td>\n",
       "      <td>2017-10-27</td>\n",
       "      <td>11</td>\n",
       "      <td>233</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>61</th>\n",
       "      <td>Stephen M. Stigler</td>\n",
       "      <td>The History of Statistics: The Measurement of ...</td>\n",
       "      <td>2017-10-27</td>\n",
       "      <td>2017-12-07</td>\n",
       "      <td>41</td>\n",
       "      <td>361</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>62</th>\n",
       "      <td>Brock Clarke</td>\n",
       "      <td>An Arsonist's Guide to Writers' Homes in New E...</td>\n",
       "      <td>2017-12-08</td>\n",
       "      <td>2017-12-21</td>\n",
       "      <td>13</td>\n",
       "      <td>303</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                author                                              title  \\\n",
       "58    Norman F. Cantor                    Civilization of the Middle Ages   \n",
       "59       Angela Carter                                 The Bloody Chamber   \n",
       "60      Travis Sawchik                                  Big Data Baseball   \n",
       "61  Stephen M. Stigler  The History of Statistics: The Measurement of ...   \n",
       "62        Brock Clarke  An Arsonist's Guide to Writers' Homes in New E...   \n",
       "\n",
       "   start_date   end_date  days  pages  \n",
       "58 2017-09-16 2017-10-14    28    566  \n",
       "59 2017-10-14 2017-10-16     2    126  \n",
       "60 2017-10-16 2017-10-27    11    233  \n",
       "61 2017-10-27 2017-12-07    41    361  \n",
       "62 2017-12-08 2017-12-21    13    303  "
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df.tail()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Modeling"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We will model the number of days it takes me to read a book using count regression models based on the number of pages.  It would also be reasonable to analyze this data using [survival models](https://en.wikipedia.org/wiki/Survival_analysis)."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Negative binomial regression\n",
    "\n",
    "While [Poisson regression](https://en.wikipedia.org/wiki/Poisson_regression) is perhaps the simplest count regression model, we see that these data are fairly [overdispersed](https://en.wikipedia.org/wiki/Index_of_dispersion)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "14.466643655077199"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df['days'].var() / df['days'].mean()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "so [negative binomial regression](http://www.karlin.mff.cuni.cz/~pesta/NMFM404/NB.html) is more appropriate.  We further verify that negative binomial regression is appropriate by plotting the logarithm of the number of pages versus the logarithm of the number of days it took me to read the book, since the logarithm is the [link function](https://en.wikipedia.org/wiki/Generalized_linear_model#Link_function) for the negative binomial GLM."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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BCHgAAAxEwAMAYCACHgAAAxHwAAAYiIAHAMBABDwAAAYi4AEAMBABDwCAgQh4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\nIuABADAQAQ8AgIEIeAAADETAAwBgoP8PY54Xt5PXqWYAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f110ce59240>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = plt.subplots(figsize=(8, 6))\n",
    "\n",
    "df.plot(\n",
    "    'pages', 'days',\n",
    "    s=40, kind='scatter',\n",
    "    ax=ax\n",
    ");\n",
    "\n",
    "ax.set_xscale('log');\n",
    "ax.set_xlabel(\"Number of pages\");\n",
    "\n",
    "ax.set_yscale('log');\n",
    "ax.set_ylim(top=1.1e2);\n",
    "ax.set_ylabel(\"Number of days to read\");"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This approximately linear relationship confirms the suitability of a negative binomial model.\n",
    "\n",
    "Now we introduce some notation.  Let $y_i$ be the number of days it took me to read the $i$-th book and $x^{\\textrm{pages}}_i$ be the (standardized) logarithm of the number of pages in the $i$-th book.  Our first model is\n",
    "\n",
    "$$\n",
    "\\begin{align*}\n",
    "    \\beta^0, \\beta^{\\textrm{pages}}\n",
    "        & \\sim N(0, 5^2) \\\\\n",
    "    \\theta_i\n",
    "        & \\sim \\beta^0 + \\beta^{\\textrm{pages}} \\cdot x^{\\textrm{pages}}_i \\\\\n",
    "    \\mu_i\n",
    "        & = \\exp({\\theta_i}) \\\\\n",
    "    \\alpha\n",
    "        & \\sim \\operatorname{Lognormal}(0, 5^2) \\\\\n",
    "    y_i - 1\n",
    "        & \\sim \\operatorname{NegativeBinomial}(\\mu_i, \\alpha).\n",
    "\\end{align*}\n",
    "$$\n",
    "\n",
    "This model is expressed in PyMC3 below."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [],
   "source": [
    "days = df['days'].values\n",
    "\n",
    "pages = df['pages'].values\n",
    "pages_ = shared(pages)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [],
   "source": [
    "with pm.Model() as nb_model:\n",
    "    β0 = pm.Normal('β0', 0., 5.)\n",
    "    β_pages = pm.Normal('β_pages', 0., 5.)\n",
    "    \n",
    "    log_pages = tt.log(pages_)\n",
    "    log_pages_std = (log_pages - log_pages.mean()) / log_pages.std()\n",
    "\n",
    "    θ = β0 + β_pages * log_pages_std\n",
    "    μ = tt.exp(θ)\n",
    "    \n",
    "    α = pm.Lognormal('α', 0., 5.)\n",
    "    \n",
    "    days_obs = pm.NegativeBinomial('days_obs', μ, α, observed=days - 1)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We now sample from the model's posterior distribution."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [],
   "source": [
    "NJOBS = 3\n",
    "SAMPLE_KWARGS = {\n",
    "    'njobs': NJOBS,\n",
    "    'random_seed': [SEED + i for i in range(NJOBS)]\n",
    "}"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Auto-assigning NUTS sampler...\n",
      "Initializing NUTS using jitter+adapt_diag...\n",
      "Multiprocess sampling (3 chains in 3 jobs)\n",
      "NUTS: [α_log__, β_pages, β0]\n",
      "100%|██████████| 1000/1000 [00:05<00:00, 190.41it/s]\n"
     ]
    }
   ],
   "source": [
    "with nb_model:\n",
    "    nb_trace = pm.sample(**SAMPLE_KWARGS)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We check a few convergence diagnostics.  The BFMI and energy distributions for our samples show no cause for concern."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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Fu/4MeDX6BlI7IlJslWlZIWaCBKYQCbQNr1+6MgjM3kgXOlrSx0mOFO/6k2oT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\nsgUFpoiIyBb+BfcauiwioBl4AAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f10f9b870b8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "ax = pm.energyplot(nb_trace)\n",
    "\n",
    "bfmi = pm.bfmi(nb_trace)\n",
    "ax.set_title(f\"BFMI = {bfmi:.2f}\");"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The Gelman-Rubin statistics indicate that the chains have converged."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1.0003248725601743"
      ]
     },
     "execution_count": 20,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "max(np.max(gr_stats) for gr_stats in pm.gelman_rubin(nb_trace).values())"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We use the posterior samples to make predictions so that we can examine residuals."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "100%|██████████| 500/500 [00:00<00:00, 1114.32it/s]\n"
     ]
    }
   ],
   "source": [
    "with nb_model:\n",
    "    nb_pred_trace = pm.sample_ppc(nb_trace)\n",
    "    \n",
    "nb_pred_days = nb_pred_trace['days_obs'].mean(axis=0)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Since the mean and variance of the negative binomial distribution are [related](https://en.wikipedia.org/wiki/Negative_binomial_distribution), we use standardized residuals to untangle this relationship."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [],
   "source": [
    "nb_std_resid = (days - nb_pred_days) / nb_pred_trace['days_obs'].std(axis=0)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We visualize these standardized residuals below."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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99T9GRESOx2RoKxQKfP755/D398f06dPx/fff49ChQ9YoGwFwc5UhONBP72PBgb5sGici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\nREQiwdAmIiISif8Pug2hK/FjT5MAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f10ef12c390>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = plt.subplots(figsize=(8, 6))\n",
    "\n",
    "ax.scatter(nb_pred_days, nb_std_resid);\n",
    "\n",
    "ax.hlines(\n",
    "    sp.stats.norm.isf([0.975, 0.025]),\n",
    "    0, 75,\n",
    "    linestyles='--', label=\"95% confidence band\"\n",
    ");\n",
    "\n",
    "ax.set_xlim(0, 75);\n",
    "ax.set_xlabel(\"Predicted number of days to read\");\n",
    "\n",
    "ax.set_ylabel(\"Standardized residual\");\n",
    "\n",
    "ax.legend(loc=1);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "If the model is correct, approximately 95% of the residuals should lie between the dotted horizontal lines, and indeed most residuals are in this band.\n",
    "\n",
    "We also plot the standardized residuals against the number of pages in the book, and notice no troubling patterns."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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ucxHhIVQOs/+ciIgvcRjqZrOZv/71r9SpU4dx48bx/vvv89lnn7mjbCJOExzoT3RUpN3n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\n1EVERAzi/wHbobAoGSN2iAAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f10eeac9588>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = plt.subplots(figsize=(8, 6))\n",
    "\n",
    "ax.scatter(df['pages'], nb_std_resid);\n",
    "\n",
    "ax.hlines(\n",
    "    sp.stats.norm.isf([0.975, 0.025]),\n",
    "    0, 900,\n",
    "    linestyles='--', label=\"95% confidence band\"\n",
    ");\n",
    "\n",
    "ax.set_xlim(0, 900);\n",
    "ax.set_xlabel(\"Number of pages\");\n",
    "\n",
    "ax.set_ylabel(\"Standardized residual\");\n",
    "\n",
    "ax.legend(loc=1);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We now examine this model's predictions directly by sampling from the posterior predictive distribution."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "100%|██████████| 5000/5000 [00:06<00:00, 825.67it/s] \n"
     ]
    }
   ],
   "source": [
    "PP_PAGES = np.linspace(1, 1000, 300, dtype=np.int64)\n",
    "\n",
    "pages_.set_value(PP_PAGES)\n",
    "\n",
    "with nb_model:\n",
    "    pp_nb_trace = pm.sample_ppc(nb_trace, samples=5000)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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mvqBOQNHxBjVqXEGq6gORRCdNR9bhoNt0dB3reJc/qEXtHK9xBWVNuxuQjWii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\nEo33cjZ9KHqTPhy9wmwzc2cWRTVe2e2WQZ+TK+0RaGx3c6L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oyoDjWsneTzm28Hhcri18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\nPIEDX410JLkAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f10ee9e5160>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = plt.subplots(figsize=(8, 6))\n",
    "\n",
    "ALPHA = 0.05\n",
    "\n",
    "low, high = np.percentile(\n",
    "    pp_nb_trace['days_obs'],\n",
    "    [100 * ALPHA / 2, 100 * (1 - ALPHA / 2)],\n",
    "    axis=0\n",
    ")\n",
    "\n",
    "ax.fill_between(\n",
    "    PP_PAGES, low, high,\n",
    "    alpha=0.35,\n",
    "    label=f\"{1 - ALPHA:.0%} credible interval\"\n",
    ");\n",
    "ax.plot(\n",
    "    PP_PAGES, pp_nb_trace['days_obs'].mean(axis=0),\n",
    "    label=\"Posterior expected value\"\n",
    ");\n",
    "\n",
    "df.plot(\n",
    "    'pages', 'days',\n",
    "    s=40, c='k',\n",
    "    kind='scatter',\n",
    "    label=\"Observed\",\n",
    "    ax=ax\n",
    ");\n",
    "\n",
    "ax.set_xlabel(\"Number of pages\");\n",
    "ax.set_ylabel(\"Number of days to read\");\n",
    "\n",
    "ax.legend(loc=2);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We see that most of the obserations fall within the 95% credible interval.  An important feature of negative binomial regression is that the credible intervals expand as the predictions get larger.  This feature is reflected in the fact that the predictions are less accurate for longer books."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Book effects\n",
    "\n",
    "One advantage to working with such a personal data set is that I can explain the factors that led to certain outliers.  Below are the four books that I read at the slowest average rate of pages per day."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {
    "scrolled": true
   },
   "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>title</th>\n",
       "      <th>author</th>\n",
       "      <th>start_date</th>\n",
       "      <th>pages_per_day</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>41</th>\n",
       "      <td>The Handmaid's Tale</td>\n",
       "      <td>Margaret Atwood</td>\n",
       "      <td>2016-10-16</td>\n",
       "      <td>4.382353</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>48</th>\n",
       "      <td>The Shadow of the Torturer</td>\n",
       "      <td>Gene Wolf</td>\n",
       "      <td>2017-03-11</td>\n",
       "      <td>7.046512</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>24</th>\n",
       "      <td>The Song of the Lark</td>\n",
       "      <td>Willa Cather</td>\n",
       "      <td>2016-02-14</td>\n",
       "      <td>7.446429</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>61</th>\n",
       "      <td>The History of Statistics: The Measurement of ...</td>\n",
       "      <td>Stephen M. Stigler</td>\n",
       "      <td>2017-10-27</td>\n",
       "      <td>8.804878</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                                                title              author  \\\n",
       "41                                The Handmaid's Tale     Margaret Atwood   \n",
       "48                         The Shadow of the Torturer           Gene Wolf   \n",
       "24                               The Song of the Lark        Willa Cather   \n",
       "61  The History of Statistics: The Measurement of ...  Stephen M. Stigler   \n",
       "\n",
       "   start_date  pages_per_day  \n",
       "41 2016-10-16       4.382353  \n",
       "48 2017-03-11       7.046512  \n",
       "24 2016-02-14       7.446429  \n",
       "61 2017-10-27       8.804878  "
      ]
     },
     "execution_count": 27,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "(df.assign(pages_per_day=df['pages'] / df['days'])\n",
    "   .nsmallest(4, 'pages_per_day')\n",
    "   [['title', 'author', 'start_date', 'pages_per_day']])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Several of these books make sense; I found [_The Shadow of the Torturer_](https://en.wikipedia.org/wiki/The_Shadow_of_the_Torturer) to be an unpleasant slog and [_The History of Statistics_](http://www.hup.harvard.edu/catalog.php?isbn=9780674403413) was quite technical and dense.  On the other hand, [_The Handmaid's Tale_](https://en.wikipedia.org/wiki/The_Handmaid%27s_Tale) and [_The Song of the Lark_](https://en.wikipedia.org/wiki/The_Song_of_the_Lark) were both quite enjoyable, but my time reading them coincided with other notable life events.  I was reading _The Handmaid's Tale_ when certain unfortunate American political developments distracted me for several weeks in November 2016, and I was reading _The Song of the Lark_ when a family member passed away in March 2016.\n",
    "\n",
    "We modify the negative binomial regression model to include special factors for _The Handmaid's Tale_ and _The Song of the Lark_, in order to mitigate the influence of these unusual circumstances on our parameter estimates.\n",
    "\n",
    "We let\n",
    "\n",
    "$$\n",
    "x^{\\textrm{handmaid}}_i = \\begin{cases}\n",
    "    1 & \\textrm{if the } i\\textrm{-th book is }\\textit{The Handmaid's Tale} \\\\\n",
    "    0 & \\textrm{if the } i\\textrm{-th book is not }\\textit{The Handmaid's Tale}\n",
    "\\end{cases},\n",
    "$$\n",
    "\n",
    "and similarly for $x^{\\textrm{lark}}_i$.  We add the terms\n",
    "\n",
    "$$\n",
    "\\begin{align*}\n",
    "    \\beta^{\\textrm{handmaid}}, \\beta^{\\textrm{lark}}\n",
    "        & \\sim N(0, 5^2) \\\\\n",
    "    \\beta^{\\textrm{book}}_i\n",
    "        & = \\beta^{\\textrm{handmaid}} \\cdot x^{\\textrm{handmaid}}_i + \\beta^{\\textrm{lark}} \\cdot x^{\\textrm{lark}}_i \\\\\n",
    "    \\theta_i\n",
    "        & \\sim \\beta_0 + \\beta^{\\textrm{book}}_i + \\beta^{\\textrm{pages}} \\cdot x^{\\textrm{pages}}_i\n",
    "\\end{align*}\n",
    "$$\n",
    "\n",
    "to the model below."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [],
   "source": [
    "is_lark = (df['title']\n",
    "             .eq(\"The Song of the Lark\")\n",
    "             .mul(1.)\n",
    "             .values)\n",
    "is_lark_ = shared(is_lark)\n",
    "\n",
    "is_handmaid = (df['title']\n",
    "                 .eq(\"The Handmaid's Tale\")\n",
    "                 .mul(1.)\n",
    "                 .values)\n",
    "is_handmaid_ = shared(is_handmaid)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {},
   "outputs": [],
   "source": [
    "pages_.set_value(pages)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {},
   "outputs": [],
   "source": [
    "with pm.Model() as book_model:\n",
    "    β0 = pm.Normal('β0', 0., 5.)\n",
    "    \n",
    "    β_lark = pm.Normal('β_lark', 0., 5.)\n",
    "    β_handmaid = pm.Normal('β_handmaid', 0., 5.)\n",
    "    β_book = β_lark * is_lark_ + β_handmaid * is_handmaid_\n",
    "    \n",
    "    β_pages = pm.Normal('β_pages', 0., 5.)\n",
    "    \n",
    "    log_pages = tt.log(pages_)\n",
    "    log_pages_std = (log_pages - log_pages.mean()) / log_pages.std()\n",
    "    \n",
    "    θ = β0 + β_book + β_pages * log_pages_std\n",
    "    μ = tt.exp(θ)\n",
    "    \n",
    "    α = pm.Lognormal('α', 0., 5.)\n",
    "    \n",
    "    days_obs = pm.NegativeBinomial('days_obs', μ, α, observed=days - 1)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We now sample from the model's posterior distribution."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Auto-assigning NUTS sampler...\n",
      "Initializing NUTS using jitter+adapt_diag...\n",
      "Multiprocess sampling (3 chains in 3 jobs)\n",
      "NUTS: [α_log__, β_pages, β_handmaid, β_lark, β0]\n",
      "100%|██████████| 1000/1000 [00:12<00:00, 77.79it/s]\n"
     ]
    }
   ],
   "source": [
    "with book_model:\n",
    "    book_trace = pm.sample(**SAMPLE_KWARGS)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Again, the BFMI, energy plots and Gelman-Rubin statistics indicate convergence."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {},
   "outputs": [
    {
     "data": {
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64fzaCJ7w4Jw6/ERrzZrIBqC3d/hmfW9mhtl5sE1ejbTJEyLNSGCKBfXW3sj9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\nWIMEphBCCLEGCUwhhBBiDf8DM2GXswNTqU0AAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f10ecacba90>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "ax = pm.energyplot(book_trace)\n",
    "\n",
    "bfmi = pm.bfmi(book_trace)\n",
    "ax.set_title(f\"BFMI = {bfmi:.2f}\");"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1.0012914523533143"
      ]
     },
     "execution_count": 33,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "max(np.max(gr_stats) for gr_stats in pm.gelman_rubin(book_trace).values())"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We see that the special factors for _The Handmaid's Tale_ and _The Song of the Lark_ were indeed notable."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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2u+wuAwAAyxA+DLd27QbFx0fo0KHjdpcCAIAl2HYxXEhIiEJCQuwuAwAAy7DyYbgDBw7I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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f10eeab3da0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "pm.forestplot(\n",
    "    book_trace, varnames=['β_handmaid', 'β_lark'],\n",
    "    chain_spacing=0.025,\n",
    "    rhat=False\n",
    ");"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Again, we calculate the model's predictions in order to examine standardized residuals."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "100%|██████████| 500/500 [00:01<00:00, 463.09it/s]\n"
     ]
    }
   ],
   "source": [
    "with book_model:\n",
    "    book_pred_trace = pm.sample_ppc(book_trace)\n",
    "    \n",
    "book_pred_days = book_pred_trace['days_obs'].mean(axis=0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {},
   "outputs": [],
   "source": [
    "book_std_resid = (days - book_pred_days) / book_pred_trace['days_obs'].std(axis=0)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Both standardized residual plots show no cause for concern."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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o1TGlExdJCwryZT1ZiXVlHdaTdVhP1mNdWScoyHJj1xSTLfWtW7eaPfCpp56y6YI//fQT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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f10e395c630>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = plt.subplots(figsize=(8, 6))\n",
    "\n",
    "ax.scatter(book_pred_days, book_std_resid);\n",
    "\n",
    "ax.hlines(\n",
    "    sp.stats.norm.isf([0.975, 0.025]),\n",
    "    0, 120,\n",
    "    linestyles='--', label=\"95% confidence band\"\n",
    ");\n",
    "\n",
    "ax.set_xlim(0, 120);\n",
    "ax.set_xlabel(\"Predicted number of days to read\");\n",
    "\n",
    "ax.set_ylabel(\"Standardized residual\");"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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BQIoxhyf+pFg2Qz01NRXff/89kpKSsGzZMuvjHh4eGDRokCSFcxQuOlJxYp/Z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\nAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f10e36c8208>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = plt.subplots(figsize=(8, 6))\n",
    "\n",
    "ax.scatter(df['pages'], book_std_resid);\n",
    "\n",
    "ax.hlines(\n",
    "    sp.stats.norm.isf([0.975, 0.025]),\n",
    "    0, 900,\n",
    "    linestyles='--', label=\"95% confidence band\"\n",
    ");\n",
    "\n",
    "ax.set_xlim(0, 900);\n",
    "ax.set_xlabel(\"Number of pages\");\n",
    "\n",
    "ax.set_ylabel(\"Standardized residual\");"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Since we now have two models, we use [WAIC](http://www.jmlr.org/papers/volume14/watanabe13a/watanabe13a.pdf) to compare them."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "metadata": {},
   "outputs": [],
   "source": [
    "compare_df = (pm.compare(\n",
    "                    [nb_trace, book_trace],\n",
    "                    [nb_model, book_model]\n",
    "                )\n",
    "                .rename(index={0: 'NB', 1: 'Book'}))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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Kggc8aN26jekIAOCKJXoAACxEwQMeZGSsUEbGCtMxACAIS/SAB7m5X5uOAACu2IMHAMBC\nFDwAABai4AEAsBAFDwCAhTjJDvCgceMmpiMAgCsKHvDg/vv7mY4AAK5YogcAwEIUPODB1q2fauvW\nT03HAIAgFDzgwbZtn2rbNgoeQOVDwQMAYCEKHgAAC1HwAABYiIIHAMBCXAcPeBASwr+RAVROFDzg\nwcMP/8R0BABwxe4HAAAWouABD77++qi+/vqo6RgAEISCBzxYs2al1qxZaToGAASh4AEAsBAFDwCA\nhSh4AAAsRMEDAGAhCh4AAAvxRjeAB336xJmOAACuKHjAg0aNbjUdAQBcsUQPAICFKHjAgwULXteC\nBa+bjgEAQViiBzy4cOG86QgA4Io9eAAALETBAwBgIZboAVitoKBA6ekrdeBAttq3v0s9evRReHi4\n6VhAuTO6B3/o0CFFRkZq9+7dgW1Lly7V0qVLdf/99+uhhx6S3+/XkCFDtGDBAoNJAVRFmzdvUrdu\nHZSaukDnzhUqJSVFXbu21+bNm0xHA8qd8T34O++8Uy+99JJmzZoVdN+sWbNUq1YtnTlzRr1791ZS\nUpJCQ0MNpATctW3bwXQEXEFBQYFGjhyuadP+W/37D5AkRUTUUUrKQo0cOVxZWdvYk4fVjBd8mzZt\nVFBQoPXr1ysmJsb1a06dOqV69epR7lVU585tr3hfSIhPxcVOBaaxA3P7bvn5+TpzJl8TJ/5OEyf+\nTtJ/5nbq1El17BipWrVqGU5ZNfDzdvWuNLNNm3ZUWAbjBS9Jv/3tbzVu3DhFR0eX2P7oo4/K5/Np\n//79mjRp0nc+Tr16NVWtmtl/BERE1DH6/JVRSIjP0/1wx9xKV1R0QWFhYUFzCgnxKSwsTEVFF5jh\nVWBWV89tZhXZEZWi4Js1a6a77rpL6enpJbZfXKLPy8vT6NGj1bp1a7Vo0eKKj3PixJnyjlqqiIg6\nOnbstNEMlVFW1vYr3lfVZ7Z27buSpJ49e1fo81b1uVWEJUtSlZq6QIsWLQtsuzi35OTBSkoariFD\nkgwmrDr4ebt6V5rZ9Z5jaf9gqDSXyY0ZM0YzZ87UhQsXgu6rXbu2unXrpi1bthhIBlxZTs4B5eQc\nMB0DLgYMiNfOnZ8pI2NVie0ZGau0c+dnGjAg3lAyoGJUij14SWrQoIF69+6thQsXasSIESXucxxH\n27dvV+/eFbuXBKDqCg8PV0rKAo0cOVz/8z+z1aFDlHbt2q4tW7YqJWUBJ9jBepWm4CXpJz/5SYnL\n4R599FGFhobq7Nmzuvfee9WpUyeD6QBUNVFRnfXJJ1uVnr5SBw8e0MiRIzVrFtfB48ZgtOBvu+02\nvfDCC4HbtWrVUmZmpiQpISHBVCwAFqlRo0bgWDvHknEjqTTH4AEAwPVTqZbogaqmfv0fmI4AAK4o\neMCDAQMGm44AAK5YogcAwEIUPODB55/v0uef7zIdAwCCsEQPeLBhwzpJUsuWkYaTAEBJ7MEDAGAh\nCh4AAAtR8AAAWIiCBwDAQhQ8AAAW4ix6wIPExBHf/UUAYAAFD3jAp5IBqKxYogc8yMs7rbw8Pp0M\nQOVDwQMeLFu2SMuWLTIdAwCCUPAAAFiIggcAwEIUPAAAFqLgAQCwEAUPAICFuA4e8KB7956mIwCA\nKwoe8KB58ztNRwAAVyzRAwBgIQoe8GD58lQtX55qOgYABGGJHvDg9OlvTEcAAFfswQMAYCEKHgAA\nC1HwAABYiIIHAMBCnGQHeHDHHT80HQEAXFHwgAc/+tG9piMAgCuW6AEAsBAFD3jwySeZ+uSTTNMx\nACAIBQ94sGfPTu3Zs9N0DAAIQsEDAGAhCh4AAAtR8AAAWIiCBwDAQlwHD3hQo0YN0xEAwBUFD3gw\ndOjDpiMAgCuW6AEAsBAFD3iQk3NQOTkHTccAgCAUPODB2rXvaO3ad0zHAIAgFDwAABai4AEAsBAF\nDwCAhSh4AAAsRMEDAGAh3ugG8ODBBxNMRwAAVxQ84EG9evVNRwAAVyzRAx4UFRWpqKjIdAwACELB\nAx7Mnz9X8+fPNR0DAIJQ8AAAWIiCBwDAQhQ8AAAWouABALAQBQ8AgIW4Dh7woHPnbqYjAIArCh7w\n4K672puOAACuWKIHAMBCFDzgwdtvr9Lbb68yHQMAgrBED3hw9OhXpiMAgCv24AEAsBAFDwCAhSh4\nAAAsRMEDAGAhTrIDPLjllsamIwCAKwoe8KB37/6mIwCAK5boAQCwEAUPeLB9+xZt377FdAwACMIS\nPeDBli0bJUnt2nU0nAQASmIPHgAAC1HwAABYiIIHAMBCFDwAABai4AEAsJDPcRzHdAgAAHB9sQcP\nAICFKHgAACxEwQMAYCEKHgAAC1HwAABYiIIHAMBCFPxVOnv2rHr16qWlS5fqq6++0ujRozVixAiN\nHj1ax44dkyStWLFCQ4YMUWJiotLS0gwnrhwundvmzZs1fPhw+f1+PfLIIzp+/Lgk5ubm0rld9NFH\nH6lVq1aB28wt2KVze+6555SQkCC/3y+/36+1a9dKYm6Xu3Rm58+f1xNPPKGhQ4dq1KhROnXqlCRm\n5ubSuf3qV78K/JwNHDhQkyZNkiTNnj1bQ4cOVWJioj744IMKy8anyV2lV199VTfddJMk6c9//rOS\nkpIUFxenN998U3PnztXjjz+uGTNmKC0tTdWrV9ePf/xj9e7dO/A9N6pL5zZ37lxNmzZNTZo00fTp\n05WamqqRI0cyNxeXzk2SCgsLNXPmTEVEREiSzpw5w9xcXDq3M2fOaMqUKYqMjAzcz9yCXTqz1NRU\n1atXTy+99JIWLVqkjRs3KiYmhpm5uHRuL7/8cmD7+PHjlZiYqJycHKWnp2vhwoXKy8vTsGHD1L17\nd4WGhpZ7Nvbgr8L+/fu1b98+9ezZU5L0zDPPqF+/fpKkevXq6eTJk9q6davatWunOnXqKDw8XF26\ndNGnn35qMLV5l8/t5ZdfVpMmTeQ4jo4ePapGjRoxNxeXz02S/va3v+mhhx5SWFiYJDE3F5fPLT8/\nP+hrmFtJl8/s/fffV3x8vCQpOTlZvXr1YmYu3H5HJelf//qXTp8+rfbt22vDhg3q0aOHwsLCVL9+\nfTVu3Fj79u2rkHwU/FV48cUX9dRTTwVu16xZU6GhoSoqKtL8+fM1cOBA5ebmqn79+oGvadCgQWDp\n/kZ1+dwk6cMPP9QDDzyg3NxcxcfHMzcXl88tOztbu3fvVv/+/QPbmFuwy+eWn5+v6dOny+/368kn\nn9TJkyeZ22Uun9nhw4eVlZWlRx55RL/5zW+Y2RW4/d0mSSkpKRoxYoQks7+jFHwZLV++XB07dlST\nJk1KbC8qKtK4ceMUHR2tmJgYXf7Ov47jyOfzVWTUSuVKc4uNjdXq1at1xx13aObMmcztMm5zmzp1\nqsaPH1/i65hbSW5zGzZsmJ588knNmzdPLVq00CuvvMLcLuE2M8dxdMstt2jOnDn64Q9/qNdee42Z\nXeZKf7edO3dOmzZtUnR0tCSzv6Mcgy+jtWvXKicnR2vXrtWRI0cUFhamRo0aafny5WrWrJkef/xx\nSVLDhg0DJ/FI0tdff62OHTsaSm2e29xq1Kih/v37y+fzqV+/fnrllVcUFRXF3C5x+dyqVaumkJAQ\nPfnkk5K+nc+IESP0y1/+krldwu3n7dlnn1Xz5s0lSX369NHkyZPVt29f5vZ/3GbWoEEDdenSRZLU\nvXt3vfLKK+rZsyczu8SVOsFxHLVv3z7wdQ0bNlR2dnbg9tGjRwPn0JQ7B1ft5ZdfdpYsWeK89dZb\nzoQJE0rcV1BQ4PTu3ds5deqUk5eX5/Tt29f55ptvDCWtXC7ObeDAgc7OnTsdx3GclJQUZ8qUKcyt\nFBfndqn77rvPcRx+3kpzcW4/+9nPnMOHDzuO4zhvvPGGM3nyZOZ2BRdn9tprrzlpaWmO4zjO/Pnz\n+R39Dpf+jr766qtOSkpK4L7Dhw87Dz74oFNYWOgcOXLE6du3r1NUVFQhudiD92D+/PkqLCyU3++X\nJLVo0UKTJ0/WE088oUceeUQ+n09jxoxRnTp1DCetXKZMmaI//OEPCg0NVXh4uKZNm6bw8HDmdg2Y\n23e7uNJRs2ZN1ahRQ1OnTmVu38Hv9+vpp5/W8uXLFRYWphdffJGZldGxY8fUtGnTwO1bb71VSUlJ\nGjFihHw+nyZPnqyQkIo5Os7HxQIAYCFOsgMAwEIUPAAAFqLgAQCwEAUPAICFKHgAACxEwQMAYCEK\nHriBJSQkaOrUqSW25eTkqFWrVlqyZEmJ7WvWrFHbtm2Vl5cn6dtPZOvUqZPuv//+oLfjPHTokFq1\naqXPP/88sM1xHC1YsEAJCQmKiopS165dNXz4cKWnp5fTqwNubBQ8cAOLjY3VunXrSmxbt26datas\nqczMzBLbMzMz1alTJ9WuXVuStGrVKrVq1Urnzp3T+vXrv/O5JkyYoBkzZmjs2LHKysrS+++/ryFD\nhmjChAmaM2fO9XtRACRR8MANLTY2Vnv37tXRo0cD2zIzMzV48GBlZmaW2DPPzMxUbGxs4HZaWpoG\nDBig/v37Ky0trdTn2bBhg5YtW6ZZs2bp3nvvVbVq1VS7dm0NHTpUzz//vM6dO3f9Xxxwg6PggRtY\nhw4dVLdu3cBefHFxsTZs2KCkpCQVFxdrz549kr5dcv/iiy8CBb9371599tlniouL06BBg/TOO+/o\n5MmTV3yeNWvWqFOnToqMjAy6Ly4uTj//+c/L4dUBNzYKHriBhYaG6p577gkU/I4dOxQaGqpWrVrp\n7rvvDmzPzMxUo0aN1LJlS0lSamqqunfvrvr166tt27Zq2rSpVq5cecXn+eKLLwKf6AagYlDwwA0u\nNjY2sByfmZmpmJgY+Xw+RUdHB47DZ2ZmqkePHpK+/bzrFStWKD4+PvAYgwYN0uLFi0t9nuLi4vJ7\nEQCCUPDADa5Hjx46ceKEdu/erXXr1ikmJkaSFBMTo40bN6qwsFAff/xxYHn+7bff1smTJzVhwgRF\nRUUpKipK06dP1549e7R9+3bX52jevLn27t1bYa8JAAUP3PAiIiIUGRmpzMxMbdu2Tffcc4+kb0v5\npptuUlpamk6fPh3YvnjxYg0ePFhvvfWWli9fruXLl2vlypXq1q3bFU+2e+CBB7R9+3ZlZWUF3bd6\n9Wr5/f6gS+0AeEPBA1BsbKwWLlyoRo0a6dZbbw1sj4mJUUpKSuDyuJycHG3YsEEPP/ywmjVrVuK/\n5ORkrVq1SmfPng16/M6dOysxMVFjxoxRenq6zp07p7y8PC1evFjjx49XQkKCfD5fRb5kwHoUPAD1\n6NFDX3zxRWB5/qLo6GgdOHAgcPx98eLFatmypdq1axf0GH379lVoaKhWr17t+hzPPfecxo4dq5kz\nZ6pbt27q1auX0tPTNWPGDA0ePPj6vyjgBudzWBcDAMA67MEDAGAhCh4AAAtR8AAAWIiCBwDAQhQ8\nAAAWouABALAQBQ8AgIUoeAAALETBAwBgof8PghHtexrihpUAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f10ecf12a90>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = plt.subplots(figsize=(8, 6))\n",
    "\n",
    "pm.compareplot(\n",
    "    compare_df, \n",
    "    insample_dev=False, dse=False,\n",
    "    ax=ax\n",
    ");\n",
    "\n",
    "ax.set_xlabel(\"WAIC\");\n",
    "ax.set_ylabel(\"Model\");"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Since lower WAIC is better, we prefer the model with book effects, although not conclusively.\n",
    "\n",
    "Again, we examine this model's predictions directly by sampling from the posterior predictive distribution."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "100%|██████████| 5000/5000 [00:07<00:00, 640.09it/s]\n"
     ]
    }
   ],
   "source": [
    "pages_.set_value(PP_PAGES)\n",
    "is_handmaid_.set_value(np.zeros_like(PP_PAGES))\n",
    "is_lark_.set_value(np.zeros_like(PP_PAGES))\n",
    "\n",
    "with book_model:\n",
    "    pp_book_trace = pm.sample_ppc(book_trace, samples=5000)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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0E90w0A2DBOuhvlzd9q2KGi9Or0pighVVC54n2oYEbSGE6OI03UAzDD7fXoGF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\ngg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f110a89b320>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = plt.subplots(figsize=(8, 6))\n",
    "\n",
    "low, high = np.percentile(\n",
    "    pp_book_trace['days_obs'],\n",
    "    [100 * ALPHA / 2, 100 * (1 - ALPHA / 2)],\n",
    "    axis=0\n",
    ")\n",
    "\n",
    "ax.fill_between(\n",
    "    PP_PAGES, low, high,\n",
    "    alpha=0.35,\n",
    "    label=f\"{1 - ALPHA:.0%} credible interval\"\n",
    ");\n",
    "ax.plot(\n",
    "    PP_PAGES, pp_book_trace['days_obs'].mean(axis=0),\n",
    "    label=\"Posterior expected value\"\n",
    ");\n",
    "\n",
    "df.plot(\n",
    "    'pages', 'days',\n",
    "    s=40, c='k',\n",
    "    kind='scatter',\n",
    "    label=\"Observed\",\n",
    "    ax=ax\n",
    ");\n",
    "\n",
    "ax.set_xlabel(\"Number of pages\");\n",
    "ax.set_ylabel(\"Number of days to read\");\n",
    "\n",
    "ax.legend(loc=2);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The predictions are visually similar to those of the previous model.  The plot below compares the two model's predictions directly."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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55zaZhw8fFm0yBUG4YUaTiS83JXDgTB6bDmYCMHZIOGOHRBAT4c5dHbx57qF2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\nYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f10ffce5278>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = plt.subplots(figsize=(8, 6))\n",
    "\n",
    "ax.plot(\n",
    "    PP_PAGES, pp_nb_trace['days_obs'].mean(axis=0),\n",
    "    label=\"Negative binomial model\"\n",
    ");\n",
    "ax.plot(\n",
    "    PP_PAGES, pp_book_trace['days_obs'].mean(axis=0),\n",
    "    label=\"Book effect model\"\n",
    ");\n",
    "\n",
    "ax.set_xlabel(\"Number of pages\");\n",
    "ax.set_ylabel(\"Number of days to read\");\n",
    "\n",
    "ax.legend(title=\"Posterior expected value\", loc=2);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The predictions are quite similar, with the book effect model predicting slightly shorter durations, which makes sense as that model explicitly accounts for two books that it took me an unusually long amount of time to read."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Timeseries model\n",
    "\n",
    "We now turn to the goal of this post, quantifying how my reading habits have changed over time.  For computational simplicity, we operate on a time scale of weeks.  Therefore, for each book, we calculate the number of weeks from the beginning of the observation period to when I started reading it."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "metadata": {},
   "outputs": [],
   "source": [
    "t_week = (df['start_date'] \n",
    "            .sub(df['start_date'].min())\n",
    "            .dt.days\n",
    "            .floordiv(7)\n",
    "            .values)\n",
    "t_week_ = shared(t_week)\n",
    "\n",
    "n_week = t_week.max() + 1"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We let the intercept $\\beta^0$ and the (log standardized) pages coefficient $\\beta^{\\textrm{pages}}$ vary over time.  We give these time-varying coefficient Gaussian random walk priors,\n",
    "\n",
    "$$\n",
    "\\begin{align*}\n",
    "    \\beta^0_t \\sim N(\\beta^0_{t - 1}, 10^{-2}), \\\\\n",
    "    \\beta^{\\textrm{pages}}_t \\sim N(\\beta^{\\textrm{pages}}_{t - 1}, 10^{-2}).\n",
    "\\end{align*}\n",
    "$$\n",
    "\n",
    "The small drift scale of $10^{-1}$ is justified by the intuition that reading habits should change gradually."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "metadata": {},
   "outputs": [],
   "source": [
    "pages_.set_value(pages)\n",
    "\n",
    "is_handmaid_.set_value(is_handmaid)\n",
    "is_lark_.set_value(is_lark)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 46,
   "metadata": {},
   "outputs": [],
   "source": [
    "with pm.Model() as time_model:\n",
    "    β0 = pm.GaussianRandomWalk(\n",
    "        'β0', sd=0.1, shape=n_week\n",
    "    )\n",
    "    \n",
    "    β_lark = pm.Normal('β_lark', 0., 5.)\n",
    "    β_handmaid = pm.Normal('β_handmaid', 0., 5.)\n",
    "    β_book = β_lark * is_lark_ + β_handmaid * is_handmaid_\n",
    "    \n",
    "    β_pages = pm.GaussianRandomWalk(\n",
    "        'β_pages', sd=0.1, shape=n_week\n",
    "    )\n",
    "    \n",
    "    log_pages = tt.log(pages_)\n",
    "    log_pages_std = (log_pages - log_pages.mean()) / log_pages.std()\n",
    "    \n",
    "    θ = β0[t_week_] + β_book + β_pages[t_week_] * log_pages_std\n",
    "    μ = tt.exp(θ)\n",
    "    \n",
    "    α = pm.Lognormal('α', 0., 5.)\n",
    "    \n",
    "    days_obs = pm.NegativeBinomial('days_obs', μ, α, observed=days - 1)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Again, we sample from the model's posterior distribution."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 47,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Auto-assigning NUTS sampler...\n",
      "Initializing NUTS using jitter+adapt_diag...\n",
      "Multiprocess sampling (3 chains in 3 jobs)\n",
      "NUTS: [α_log__, β_pages, β_handmaid, β_lark, β0]\n",
      "100%|██████████| 1000/1000 [03:26<00:00,  4.85it/s]\n"
     ]
    }
   ],
   "source": [
    "with time_model:\n",
    "    time_trace = pm.sample(**SAMPLE_KWARGS)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Again, the BFMI, energy plots, and Gelman-Rubin statistics indicate convergence."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 48,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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mCHseX4Ci8k5irCa61WpAIXEez738IBwOhYQEaGnz09Q6/SpzVcJyAN5rlKO/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\ngg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f10e3979518>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "ax = pm.energyplot(time_trace)\n",
    "\n",
    "bfmi = pm.bfmi(time_trace)\n",
    "ax.set_title(f\"BFMI = {bfmi:.2f}\");"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 49,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1.0038733152191415"
      ]
     },
     "execution_count": 49,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "max(np.max(gr_stats) for gr_stats in pm.gelman_rubin(time_trace).values())"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Once more, we examime the model's standardized residuals."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 50,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "100%|██████████| 500/500 [00:00<00:00, 913.23it/s]\n"
     ]
    }
   ],
   "source": [
    "with time_model:\n",
    "    time_pred_trace = pm.sample_ppc(time_trace)\n",
    "    \n",
    "time_pred_days = time_pred_trace['days_obs'].mean(axis=0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 51,
   "metadata": {},
   "outputs": [],
   "source": [
    "time_std_resid = (days - time_pred_days) / time_pred_trace['days_obs'].std(axis=0)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In general, the standardized residuals are now smaller and fewer are outside of the 95% confidence band."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 52,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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PnsasWdM1Hm/v3kNo3doHRUVF8PfvpHGbmTNnY/z4IABAcHAQrly5rLZNt27+2LhxKwBg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\nSUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f10ddbac780>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = plt.subplots(figsize=(8, 6))\n",
    "\n",
    "ax.scatter(time_pred_days, time_std_resid);\n",
    "\n",
    "ax.hlines(\n",
    "    sp.stats.norm.isf([0.975, 0.025]),\n",
    "    0, 120,\n",
    "    linestyles='--', label=\"95% confidence band\"\n",
    ");\n",
    "\n",
    "ax.set_xlim(0, 120);\n",
    "ax.set_xlabel(\"Predicted number of days to read\");\n",
    "\n",
    "ax.set_ylabel(\"Standardized residual\");\n",
    "\n",
    "ax.legend(loc=1);"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 53,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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Akye/yYoVn+TZJiwsjI0btwGwffs3DBv2st3jLVu2hgYNIsnMzKRVq2Z2txk6dDh9+vQF\nYMCAvuzduyfPNvfc04rZs+cDsHDhPFv5brZ372EAfvrpR/761x52z1GzZs2lVavWALRt25rk5Mt5\ntunV61mGDRsBwJgxr7Fx44Y829SrV58VKz4DYP36zxg3LsZumTZs+JqIiAguXLjAww+3s7vNuHET\n6dz5CQC6dXuCX345Znsv9zvVqdPDTJp0rfd0+vQpLF36UZ79lC9fgW++2QnArl07GTx4oN3jLVmy\nnMaN7wCgefM77W7j7HM54LJz+fVceS7ftOkru9sVhttD/cqVK0yZMoXFixdTsWJFdx9eRETEtNx+\nT3358uXMnDmTunXr2l6bPHky1atXz/czZuhK8fY6gOphJGaoA5ijHmaoA6geRuJV3e/du3ene/fu\n7j6siIiI6WlFOREREZNQqIuIiJiEQl1ERMQkFOoiIiImoVAXERExCYW6iIiISSjURURETEKhLiIi\nYhIKdREREZNQqIuIiJiEQl1ERMQkFOoiIiImoVAXERExCYW6iIiISSjURURETEKhLuJlMrIsnE1I\nJSPL4umiiIjBlPF0AUSkcCw5OSz/+hj74+K5eCWDyqGBREWG071dffx8dX0uIgp1Ea+x/OtjbNlz\nyvZzYnKG7eeeHSI9VSwRMRBd3ot4gYwsC/vj4u2+tz8uQV3xIgIo1EW8wuWUDC4mZ9h9L+nKVS6n\n2H9PREoXhbqIG2RkWbiQlFbsFnWFkEAqlw+0+16l0CAqhNh/T0RKF91TF3GhGwa3JWdQuXzxBrcF\n+vsRFRl+wz31XFGRYQT6+zmz2CLipRTqIi7kzMFt3dvVB67dQ0+6cpVKoUFERYbZXhcRUaiLuIij\nwW1dousVqYXt5+tLzw6RdImuh1+AP5bMLLXQReQGuqcu4iKuGtwW6O/HLWHlFOgikodCXcRFNLhN\nRNwt3+73kydPFvjBWrVqOb0wImaiwW0i4m75hvpf//pXfHx8sFqted7z8fFh69atLi2YiBlocJuI\nuFO+of7111/n+6G9e/e6pDAiZnP94LbLKRlUCAlUC11EXMbh6PeUlBTWrl1LUlISAFlZWaxevZpv\nv/3W5YUTcbeMLItLwjfQ34+ISsFO25+IiD0OQ33o0KFUr16db7/9lk6dOrFz507GjRvnhqKJuI+z\nFokREfEkh2erjIwM/vnPf1KjRg1GjhzJRx99xIYNG9xRNhG3yV0kJjE5Ayt/LBKz/Otjni6aiEih\nOQz1rKws0tLSyMnJISkpiYoVKzocGS/iTfQENBExC4fd748//jgrVqyga9euPPLII5QrV44GDRq4\no2wiblGYRWJ0P1xEvIHDUH/mmWds/27VqhWJiYk0btzYpYUScafcRWIS7QS7FokREW/iMNTfe++9\nPK9t3ryZIUOGuKRAIu6mRWJExCwchrqf3x8ntKysLH744Qe11MV0tEiMiJiBw1AfPHjwDT9bLBZe\nfvlllxVIxBO0SIyImEGRH71qsVg4ceKEK8oi4nFaJEZEvJnDUI+OjsbHxwcAq9VKcnIyTz75pMsL\nJiIiIkXjMNQ//vhj2799fHwICQmhfPnyLi2UiIiIFF2+of7ZZ58V+MEnnnjC6YURERGR4ss31Hfu\n3AlAUlISR44coWnTplgsFg4ePEhUVJRCXURExGDyDfWpU6cCMHz4cDZv3kzZsmWBa09ti4mJcU/p\nREREpNAcrv1+4sQJW6ADhISEcObMGZcWSkRERIrO4UC5evXq0aNHD6KiovD19eXAgQPUrl3bHWUT\nERGRInAY6m+99RY7d+4kLi4Oq9VK//79adOmjTvKJiIiIkWQb/f7Tz/9BMCuXbvw9fWlUaNG3H77\n7QQEBBAbG+u2AoqIiEjh5NtSX7t2LY0bN2b27Nl53vPx8aFVq1YuLZiIiIgUTb6hPnr0aACWLFly\nw+s5OTn4+jocX1eguLg4Bg0aRN++fendu3eJ9iUiIiLXOEznNWvWsHTpUiwWC8888wzt27e/YZW5\nokpLS2PChAlq6YuIiDiZw1Bfvnw5Xbt2ZfPmzTRo0ICtW7eyYcOGYh8wICCA+fPnExERUex9iIiI\nSF4OQz0wMJCAgAC2b9/Oww8/XOKu9zJlyhAUFFSifYgUV0aWhbMJqWRkWUq0jwtJaSXah4iIKxTq\n0avjx49n3759TJw4kf3795OZmenqct0gPDzUrcdzBTPUAby3HhZLDovW/8juw2eJv5ROeMWy3Hvn\nLfTrfAd+foW7UHXGPpzJW/8WNzNDPcxQB1A9zMBhqE+bNo0vv/ySZ599Fj8/P06fPs348ePdUTab\n+Pgrbj2es4WHh3p9HcC76/Hxlji27Dll+/lCUjrrdvxKWnomPTtEum0fzuLNf4vrmaEeZqgDqB5G\nUpKLEofNi4iICOrUqWN7wMtdd91Fw4YNi31AEXfLyLKwPy7e7nv74xIK1Y3ujH2IiLiaw1CfOnUq\nq1evZs2aNQCsX7+eiRMnFvuAhw8fpk+fPnz66ad89NFH9OnTh0uXLhV7fyKOXE7J4GJyht33kq5c\n5XKK/fecvQ8REVdz2P1+6NAhW/gCvPTSS/To0aPYB7zzzjvzzH0XcaUKIYFULh9Iop1QrhQaRIWQ\nQLfsozTKyLJwOSWDCiGBBPr7ebo4IqbnMNStVitwbRU5AIvFgsWirkZxn5IGQ6C/H1GR4TfcD88V\nFRlWqH06Yx+liSUnh+VfH2N/XDwXkzOoXD6QqMhwurerj18JZ9CISP4chnqzZs0YPXo0Fy5c4IMP\nPmDz5s20bNnSHWWTUs6ZwdC9XX3g2v3vpCtXqRQaRFRkmO11d+2jtFj+9bEbLoASkzNsP7t7UKFI\naeJjzW2KF+Crr74iNjaWgIAAmjdvTseOHd1RNhszjGT09jqA++tx82jzXB1a1Cx2MGRkWfAL8MeS\nmVXs1rURupSN/J3KyLIQM3+33VsVVcoHMbH/Pbbfm5HrUVhmqAOoHkZSktHvDlvq8+bNY8CAATz0\n0EPFPohIUTkabd4lul6xu+LDw8qV6D99oL8fEZWCi/15syvMoEL9/kRcw2EfZlxcHL///rs7yiJi\no9Hm3it3UKE9GlQo4loOW+r//e9/efTRR6lQoQL+/v5YrVZ8fHzYtm2bG4onpZVGm3svDSoU8RyH\noT5nzhx3lEPkBgoG76ZBhSKe4TDUa9So4Y5yiOShYPBefr6+9OwQSZfoeh4fVChSmhTqgS4inuCq\nYLiamc2FpDQFjRtoUKGIeynUxfCcFQy5894P/pJIfFK6FkQREdPJN9Q/++yzAj/4xBNPOL0wIq6k\nBVFExOzyDfXcp7IlJSVx5MgRmjZtisVi4eDBg0RFRSnUxatcSctkz5ELdt8rybx3EREjyTfUp06d\nCsDw4cPZvHkzZcuWBSAlJYWYmBj3lE6khHK73PceiedSSqbdbbQgioiYhcN76idOnLAFOkBISAhn\nzpxxaaFEnOXmLnd7NO9dRMzCYajXq1ePHj16EBUVha+vLwcOHKBOnTruKJtIiRS01Oz1NO9dRMzC\nYai/9dZb7Ny5k7i4OKxWK/3796dNmzbuKJtIiRS01CxAxZAAWjSK0Lx3ETGNQk1py8rKwt/fn969\ne3PixAnbs9VFjKzApWZDAhnX725CgwM8UDIREddwODl36tSprFq1ijVr1gCwfv16Jk6c6PKCiZRU\n7lKz9jRvFK5AFxHTcRjqhw4dYtasWZQrVw6Al156iR9//NHlBRNxhu7t6tOhRU2qlA/C1+fa87z/\n0uY2dbmLiCk57H63Wq0Ati53i8WCxWJxbalEnMTeUrM1q1cs0fPURUSMymGoN2vWjNGjR3PhwgU+\n+OADNm/eTMuWLd1RNhGn0RrkIlIaOAz1V199la+++oqgoCDOnTtH37596dixozvKJmKTkWUp9kNd\nSvJZERFv4jDUDx48yEMPPcRDDz1ke23Dhg08/PDDLi2YCPyxItz+uHguJmcU6SEs+X12cLcoN5Ve\nRMS9HA6U69mzJyNGjCAj449pQZ988olLCyXmk5Fl4UJSGhlZRRuPkbsiXGJyBlb+eAjL8q+PFfuz\ni9aXjoGexf2di4j3cthSj4qKomnTpvTq1Yt3332XWrVq2QbPiThSkpZ2QSvCOXoIS0Gf3X34LA+3\nrOUVXfHFuXVQkt+5iHg3h6Hu4+NDr169aNy4MYMGDWL48OFafEYKrSSPOy1oRbiLV67y6+nL3Faj\ngt2wK+izCZfSDf8Al5IEsx4xK1J6Obxsz22VR0VF8cEHH7BgwQLNU5dCcdTSdtQtnLsinD0+wNRl\n/yFm/m4+3hKHJSen0J8Nq1jW8A9wKe5th5L+zkXEuzkM9SlTptj+HRYWxuLFi5kwYYJLCyXmUFBr\nOfdxpwUpaEW4nP/dAcov7Ar67L133mLorveSBHNJf+ci4t3y7X6fO3cuAwcOZPr06Xa72x955BGX\nFky8X0iwP4EBflzNzBtChX3cae7Kb/vjErh45So+/BHo17N3j/36zyZduUql0CCiIsPo1/kOLl5M\nLV6l3KAwwVwzn88WuN69HjErYnr5hnrjxo0BuO+++9xWGDGXz3YctxvoUPjHnV6/Ityvpy8zddl/\n7G6XG3bX3ye3t5pcoL8ffn7GHixWkmDO7aGw9wx5dz5iVmsDiHhGvqFer149zpw5wz333OPO8ohJ\nFNSFHBTgxxNtbivS/gL9/bitRgWqFCPsvG01uZIGc349FO5Y714j70U8K99Qf+aZZ/Dx8cFqtXLh\nwgVCQ0PJzs4mPT2dWrVqsWnTJneW09TM2KopqAs5M8tCSlomwYGFevKvjVFaoe5QkmDOr4fCHTTy\nXsSz8j2rbt++HYC3336bv/zlL7bu+AMHDrB+/Xr3lM7JjBaeZm7VuOreridboe7kjGB2dw9FSdYV\nEBHncNhU+u9//2sLdICmTZvy7rvvurRQzmbU8MyvVWPJsdLp7lqGufgoDle1qj3ZCvUEb7p1UJgB\nft5SFxFv5TDUs7Ozeeedd2jevDk+Pj7s37//hiVjvYERuwQLatVs33+ab/adpooLLz7c0Wvhyla1\nN4VdaaGR9yKe5zDUZ8yYwUcffcSyZcuAawPoZsyY4fKCOYtRuwQLatXcPAcbnHfx4c5ei9LWqi7t\nStOYBxGjchjq27dv59VXX3VHWVzCqF2CBbVqbubMiw9P9FqoVV16mGXMg9HG34gUlsNQ37RpEw8+\n+CChoaHuKI/TGbVLsKBWzc2cdfFh1F4LMQ9v750x6vgbkcJyGOoZGRm0a9eOunXr4u/vb3t96dKl\nLi2Ysxi5S7Cwq6U56+LDqL0WYj7e2jtjxPE3IkXhMNRffPHFPK9521PajNoleHOrZuP3J/hm/5k8\n2znr4sOovRYiRqCeLDEDh6HesmVLUlNTuXz5MgCZmZkMHz6cVatWubxwzmL0LsHcVk3PByPx8/N1\n2cWHkXstnE33RKWo1JMlZuAw1OfPn8/cuXPJzMwkODiYjIwMOnfu7I6yOZ3RuwTdcfFh1F4LZ9E9\nUSku9WSJK7i7geEw1Ddu3Mh3333H888/z5IlS9i6dStnzuTtIhbnyb34yMiycCEpzalfBqP3WpSU\n7olKcZWmnixxPU81MByGerly5QgICCArKwuA9u3b07dvX/r06eOyQpV27vgyOLvXwgjd3bonKiVl\n9p4scR9PNTAchnqFChVYt24dkZGRjB49mpo1a3LhwgWXFUi8q7VppO5u3ROVkjJ7T5a4hycbGA7P\nupMnT6ZZs2aMHj2aOnXqkJSUxPTp011SGHH8ZcjIsv98ck/JvQBJTM7Ayh8XIMu/Pub2suTeE7VH\n90SlKHJ7shToUhyFaWC4Sr4t9evvm/v6+pKUlMRf/vIXlxVErvGm1qbRurt1T1REjMCTgy4L/Tz1\nkJAQLBaLnqfuYt40AteIFyC6JyoFcTT2wwhjQ8T7ebKBUaqep+4NvKm1acQLEN0TFXscjf0w0tgQ\nMQdPNTBKxfPUvY07vgzOaJEY+QLE6GsSiHs5GnzqTYNTxTt4qoHh9uepT5o0iQMHDuDj48OYMWO4\n6667ir0vs3Lll8HZLRJ1d4vRORr70fm+Ww01NkTMxd0NDLc+T/3777/n999/Z/ny5Rw7dozRo0ez\ncuXKYu0Fn2/CAAAfp0lEQVSrNHDFl8HZLRJ1d4vRORr7cepCiuHGhogUl8NQr1KlCq+++ipWqxWr\n1c4jxIpg165ddOjQAYD69euTnJxMSkoKISEhJdqvFI4rR6uXpu5uDabyLo7GftSMCDHc2BCR4nIY\n6gsWLGDOnDmkpqYCYLVa8fHx4eeffy7ywRISErjjjjtsP1epUoX4+HiHoR4e7p3Pcr+eEepwNiGV\ni1fyb5H4BfgTHlauwH0YoR7OUJx6WCw5LFr/I7sPnyX+UjrhFcty75230K/zHfj5uX8wVWn+WxRV\n66Y1WLfjVzuvV+e2OlUKfL9m9YoO96+/hbGYpR7F4TDUV69ezbp166hevXqJD3ZzSz/3AsGR+Pgr\nJT62J4WHhxqiDpYsC5VD82+RWDKzCiynUepRUsWtx8db4m64dXEhKZ11O34lLT3T7YOpSvvfoqg6\nt6pNWnpmnrEfnVvVJj7+isP3jVAHV1M9jKMkFyUOQ71OnTpOCXSAqlWrkpCQYPv5woULhIWFOWXf\n3sjd3bhGHq1udEZbaEeKxtHYD40NEbNwGOoNGzbk73//Oy1btsTP748v+dNPP13kg7Vu3ZqZM2fS\no0cPfvrpJyIiIkrl/XRPzonVaPXiKclCO7oHbxyOxn6UprEhYk4OQ/3ChQsEBATwn//854bXixPq\nzZo144477qBHjx74+PgwduzYIu/DDDw5J1YtEriamV3kR9oWZ6EdLWgiIu7mMNTfeuutPK999NFH\nxT7g8OHDi/1ZMzBKN25hWyTXtzK9XW7IHvwlkfik9CKFbHFuXWhBExFxN4eh/vPPPzNnzhySkpIA\nyMzM5Ny5czz77LMuL5wZGXG9dHvstTJbN61B51a1vbaVWdKQLcqtC3dcvKlbX0Ru5jDUx48fT58+\nfZg3bx6vvvoqX331FcOGDXNH2UzJiOul22MvAD010tsZnBGyRbl14cqLN0tODvM/O8TOA6fVrS8i\nN3B4BggKCuLRRx+lfPnyPPDAA0yaNImFCxe6o2ymlNuNa49RRqB72zPdC8OZzzcuzLO2Xfls9+Vf\nH2Pdjl8N8Qx7ETEWh6GekZFBXFwcAQEBfP/995w/f57Tp0+7o2ym1b1dfTq0qEmV8kH4+kCV8kF0\naFHTMCPQnRmARuHKkLXHVRdvZrzgEhHncdj9Pnz4cE6cOMErr7zCiBEjSExMpH///u4om2kZfQS6\nt9wiKApPzNF3xfTBknbr6z68iLkV6iltueu1b9y4EYAtW7a4tlSlRH4j0D194jXrIjW5YXrwl0QS\nLqW7fI6+Ky7einvBpel14iqePl/JjfIN9VOnTnHy5EkmT57MqFGjbEu8ZmRk8Oabb9qCXpzHSCde\ne63M1k2r07lVbbeWw5lyQ3Zgl7L88luiW1fyc9aMhuJecGl6XV4Ko5Ix0vlK/pBvqMfHx/Pll19y\n+vRp3n//fdvrvr6+PPPMM24pXGljpBOvvVZmzeoVvXpN5dyTeGiFsoaYNlhc3dvVJ7hsADsPnClU\nt75R1kYwCktODh9vOcp/4hK4lKIwKi4jna/kD/mGelRUFFFRUURHR6tV7gZGPfGaYdnMm1sU4ZXK\ncle9Kl57Evfz9aX/E014uGWtfFua17dCvWVtBHew5OTwz8V7OHkhxfaawqjojHq+kgJCPSUlhVWr\nVtG3b18Ali1bxieffEKdOnV44403SvWDWFxBJ17XublFcSEp3RQncXsXXPa6RO+qV8V0Ax+L6+PN\ncTcE+vUURoWn85Vx5dtMeeONN0hMTATg+PHjTJ8+nZEjR9KqVSvefPNNtxWwtHD3lKvSorRNAcu9\ngLl+Dvs3+88QHORvd3tvHvjoSEaWhQtJaba/cUaWhf1HE/Ld/qKXTtf0BJ2vjCvflvrJkyeZPn06\ncG3U+0MPPcR9993Hfffdx5dffum2ApYWZh1x7mmlqUVR0AVManoWbZvV4OCxRNM/nS+/AVxto2pw\nKSUz389VLBeoMCokna+MK99QDw7+40T3ww8/0KVLF9vPPj4+ri1VKaXHojqfGefc56egC5hLKRl0\nursW3drWN/2I7/wGcFlyrFTJ57sA8CeFUZGUxvOVN8yYyDfULRYLiYmJpKamsm/fPlurPTU1lfT0\ndLcVsDQx+qI03qg0tSgKcwFjhoGPBSmot+LgsUTuqleFb/afyfNerYgQenZo4OrimUppOl950/S9\nfEO9f//+PPLII1y9epWXXnqJChUqcPXqVXr27Em3bt3cWcZSx1UnXm+4ynSFm1sUYRX/GP1uJqXp\nAiY/jm63dGhRCz8/X/bHJXAx+SoVQgKIahBGzwcjDXdy9hZmv1AE75q+l2+oR0dH8+2335KRkUFI\nSAhw7eEur732Gvfff7/bCigl501Xma5wc4ui3q1VuHLZnL1NpbFL9HqOeisqlw8qNa1LcQ5vm75X\n4DKx/v7++PvfOGpWge59vOkq05VyWxRBAWXw3iV0ClaaukTtKWxvRWloXYpzeNtgW/M300q50jal\nS64pzONhzcroT0EU7+Jt0/ccPtBFvJclJ4clG/+b72hfI15lOltpHUfgLN74+yvtvRXiXN42VkWh\nbmLLvz7Gd4fP5fu+Ea8ynaWgcQTimBnGYaiLXZzFm8aqKNRNqqBu91xGvMp0loLGEQx5prnbyuGN\nLV3QOAyR63lT749C3aQKGtwB0PrOaoa8ynQGR+MIrmZmu7wM3tzS9bbRviLu4g29P8Y+u0ixFTS4\no3JoIL07NTR8uBSXo9GqSQVc7DiLvTXYt+w5xfKvj7n82CVVmNG+ImJM5jyri21whz3NGoabuqXl\naLRqpXzecxZvn3HgbaN9ReQPCnUTK61Tewq6oImKDCMowLV3nYrS0r35SWJG4Oj3Z+YLQhFvp3vq\nJuZNgzuczZOjVQuzBrsR7rkXNIjPm0b7isgfFOqlgDcM7nA2T17QOJrXCrD4yyPsvG66oTtHlxfm\ngqI0XxCKeDOFupiapy5o7LV0/9SgCjlWK6/P28XFK/af6+2O0eVFma5m1AtCb50qKObn6e+mQl3E\nBey1dFdv/4Wtdlrv13P1Kn/ePl3NCLctROwxyndToS7iQrkt3cIsBgSuH13ubQ+nuJkWxRGjMsp3\nU5e2Im7gaDGgXK4eXe7N09W8faqgmJeRvpsKdTEsI073Kq6CwhSgSvlAt0w39ObpakZeFMdM31Up\nOiN9N9X9LoZjlHtTzlTQiPj77qxGn04N3Rao3jpdrTBTBd3NkpPD/M8OsfPAadN8V6XojPTdVKiL\n4Rjl3pSzFRSm7gwAb52uZsRHYJr1uypFY6TvpkJdDMVTo7PdMQ3FaGFq1OlqBTFSL4O3zyQQ5zLK\nd1OhLobi7tHZnujq98YwNQojXRh5+0wCcS6jfDd100cMxd2js735aWqlWe6FkSdbwt48k0Bcx9Pf\nTYW6GIo7R2cbaRqKeB9vnkkg5qXudzEcd92bUveplFT3dvUJLhvAzgNnPH6PXwQU6mJA7ro3ZaRp\nKOKd/Hx96f9EEx5uWcvj9/hFQN3vYmCuvjel7lPn0MIrnr+PKpJLLXUp1YwyDcUbmXGRIBFvp1CX\nUs0o01C8kRZeETEeXU6LoO7TotLMARFjUqiLW+n+qzkY6QEWIvIHdb+LW+j+q7lo5oCIMelsKm6h\nldvMRTMHRIxJoS5Od3MXu+6/Goczb390b1efDi1qUqV8EL4+UKV8kFueCS8i+VP3uzhNfl3sbaNq\naOU2D3PF7Q/NHBAxHre31L///ntatWrFN9984+5Di4vl18W+Ze8pPfjCw1x5+0MzB0SMw62hfuLE\nCT744AOaN2/uzsOKGxTUxX7wWCJ31ati9z3df3U93f4QKT3cGurh4eHMmjWLkJAQdx5W3MDRFKcO\nLWrp/quHaPqZSOnh1nvqZcuWdefhxI0cTXGqXD5I9189RNPPREoPl4X6ypUrWbly5Q2vvfzyy7Rp\n06bI+woPD3VWsTzGDHWAguvRumkN1u341c7r1alZvaLt55ouKVnRmOHvUZQ6FPZv4wml7W9hZKqH\n93NZqHft2pWuXbs6ZV/x8Vecsh9PCQ8P9fo6gON6dG5Vm7T0zDwPR+ncqrah6u/pv0dGlqXEvRVF\nrYNR/zae/ls4gxnqAKqHkZTkokRT2sRpNMWpYJ5cVU9/G5HSwa2hvm3bNhYuXMivv/7Kjz/+yJIl\nS1i0aJE7iyBukDvFSW5khKea6W8jYm5uDfUHHniABx54wJ2HFDEER9PKukTXU8tZREpMy8SKuIGm\nlYmIOyjURdwgd1qZPZpWJiLOolAXcQM91UxE3EGj30XcJHf1vJunlWlVPRFxFoW6iJtoWpmIuJpC\nXcTNNK1MRFxF99RFRERMQqEuIiJiEgp1ERERk1Coi4iImIRCXURExCQU6iIiIiahUBcRETEJhbqI\niIhJKNRFRERMQqEuIiJiEgp1ERERk1Coi4iImIRCXURExCQU6iIiIiahUBcRETEJhbqIiIhJKNRF\nRERMQqEuIiJiEgp1ERERk1Coi4iImIRCXURExCQU6iIiIiahUBcRETEJhbqIiIhJKNRFRERMQqEu\nIiJiEgp1ERERk1Coi4iImIRCXURExCQU6iIiIiahUBcRETEJhbqIiIhJKNRFRERMQqEuIiJiEgp1\nERERk1Coi4iImIRCXURExCQU6iIiIiahUBcRETEJhbqIiIhJKNRFRERMQqEuIiJiEgp1ERERk1Co\ni4iImEQZdx4sOzub119/nZMnT5Kdnc2IESNo0aJFgZ+59dZbycmx5nl90KBXeP75Af/7d39iY3fl\n2aZ58xbMm7cYgCVLFjNjxjS7x9i1ax8BAQEcPRpHjx5P2d1m+vSZREe3BaBTpwdISEjIs023bs8w\ncuTrAIwd+zqff74WAF9fH1sdateuw6effgHAhg1fEBMz0u7x1q/fSPXqNbh0KYn27dvY3WbMmDfo\n0qUbAL16deXIkZ/zbNO2bQemTZsBwMyZM1i8eEGebYKDg9mx43sA9uz5noED+9k93qefrqF27UgA\n7rnnT2RnZ+fZZsCAFxk48CUAhg59iR07tufZpkmTpixevBSAZcuWMnXqW3aPt337bkJCQvjtt+N0\n6dLZ7jZTpkynffuOADz2WEfOnj2TZ5snn3yamJhxAEycOI61a1fn+U7dckt1Pv98EwBbt25ixIhh\ndo+3evV6br21LikpKURH32t3m9deG02PHr0A6Nu3F4cOHcizTZs20cyY8T4Ac+e+z7x5/y/PNmXK\nlCE29j8AHDiwn379+tjeu/47NXfuIlq0aPm//bYkLS0tz7769n2Bl18eCsDw4UP55pstebZp1Oh2\nli5d+b96rmDSpH/ard/WrTuoWLESZ86cpnPnTna3mThxMg8//CgATz75KCdO/J5nm8cee5zZs/8F\nwOTJb7JixSd5tgkLC2Pjxm0AbN/+DcOGvWz3eMuWraFBg0gyMzNp1aqZ3W2GDh1Onz59ARgwoC97\n9+7Js80997Ri9uz5ACxcOM9Wvpvt3XsYgJ9++pG//rWH3XPUrFlzadWqNQBt27YmOflynm169XqW\nYcNGADBmzGts3Lghzzb16tVnxYrPAFi//jPGjYuxW6YNG74mIiKCCxcu8PDD7exuM27cRDp3fgKA\nbt2e4Jdfjtney/1Oder0MJMmTQVg+vQpLF36UZ79lC9fgW++2QnArl07GTx4oN3jLVmynMaN7wCg\nefM77W7j7HM54LJz+fVceS7ftOkru9sVhltDfe3atZQtW5aPP/6Yo0ePMnr0aFatWuXOIoiIiJiW\nj9VqzXuJ6SJZWVnk5OQQGBhIYmIi3bt3Z8uWvC2Gm8XHX3FD6VwnPDzU6+sAqoeRmKEOYI56mKEO\noHoYSXh4aLE/69ZQv9706dPx9fVl6NChnji8iIiI6bis+33lypWsXLnyhtdefvll2rRpw9KlS/nx\nxx+ZM2dOofZlhqsub68DqB5GYoY6gDnqYYY6gOphJCVpqbss1Lt27UrXrl3zvL5y5Uq+/vprZs+e\njb+/v6sOLyIiUuq4daDcyZMnWbZsGf/3f/9HYGCgOw8tIiJiem4N9ZUrV3Lp0iUGDBhge23hwoUE\nBAS4sxgiIiKm5NZQHzZsGMOG2Z//KyIiIiWjFeVERERMQqEuIiJiEgp1ERERk1Coi4iImIRCXURE\nxCQU6iIiIiahUBcRETEJjz3QRURERJxLLXURERGTUKiLiIiYhEJdRETEJBTqIiIiJqFQFxERMQmF\nuoiIiEm49dGrRTFp0iQOHDiAj48PY8aM4a677vJ0kRyKi4tj0KBB9O3bl969e3P27FlGjBiBxWIh\nPDycqVOnEhAQwLp16/jwww/x9fWle/fuPP30054uus2UKVPYu3cv2dnZDBw4kCZNmnhVHdLT0xk1\nahSJiYlkZGQwaNAgGjVq5FV1uN7Vq1d59NFHeemll2jVqpXX1ePw4cMMGjSIOnXqABAZGckLL7zg\ndfVYt24dCxYsoEyZMgwZMoTIyEivq8PKlStZt26d7efDhw/zySefMG7cOAAaNmzI+PHjAViwYAFf\nffUVPj4+DB48mOjoaE8UOY/U1FRGjhzJ5cuXycrK4qWXXiI8PNyr6gCQk5PD2LFjOXr0KP7+/owb\nN47g4GDnfKesBhQbG2sdMGCA1Wq1Wo8ePWp9+umnPVwix1JTU629e/e2xsTEWJcsWWK1Wq3WUaNG\nWb/88kur1Wq1Tp482bp06VJramqqtWPHjtbk5GRrenq6tVOnTtakpCRPFt1m165d1hdeeMFqtVqt\nFy9etEZHR3tdHb744gvrvHnzrFar1Xrq1Clrx44dva4O15s+fbr1qaeesq5evdor6xEbG2udOHHi\nDa95Wz0uXrxo7dixo/XKlSvW8+fPW2NiYryuDjeLjY21jhs3ztq7d2/rgQMHrFar1frKK69Yt23b\nZj1x4oT1ySeftGZkZFgTExOtDz74oDU7O9vDJb5myZIl1mnTplmtVqv13Llz1k6dOnldHaxWq3XT\npk3WIUOGWK1Wq/X333+3DhgwwGnfKUN2v+/atYsOHToAUL9+fZKTk0lJSfFwqQoWEBDA/PnziYiI\nsL0WGxtL+/btAWjfvj27du3iwIEDNGnShNDQUIKCgmjRogX79u3zVLFvcPfdd/Pee+8BUKFCBdLT\n072uDo888gj9+/cH4OzZs1StWtXr6pDrl19+4dixYzzwwAOA932f4FrL6mbeVo9du3bRqlUrQkJC\niIiIYMKECV5Xh5u9//779O/fn9OnT9t6QXPrERsbS5s2bQgICKBy5crUqFGDY8eOebjE11SqVIlL\nly4BkJycTMWKFb2uDgC//fabrcy1a9fmzJkzTvtOGTLUExISqFSpku3nKlWqEB8f78ESOVamTBmC\ngoJueC09PZ2AgAAAwsPDiY+PJyEhgcqVK9u2CQsLM0zd/Pz8CA4OBq511f35z3/2ujrk6tGjB8OH\nD2fMmDFeW4fJkyczatQo28/eWI+0tDT27t3LCy+8QK9evdi9e7fX1ePUqVNYrVaGDh1Kz5492bVr\nl9fV4XoHDx7klltuwc/Pj/Lly9te94Z6PProo5w5c4YHH3yQ3r17M2LECK+rA1y7DfXtt99isVj4\n9ddfOXnyJKdPn3bKd8qQ99StN61ca7Va8fHx8VBpiu/6MufWyRvqtmXLFlatWsWiRYvo1KmT7XVv\nqsOyZcv4+eefee2117zy7/DZZ5/xpz/9iVq1atle88Z6NGrUiJdeeon27dtz/PhxnnvuObKzs23v\ne0s9zp8/z6xZszhz5gzPPvusV/4tcq1atYonn3wyz+veUI+1a9dSvXp1Fi5cyJEjR3jllVdsDRHw\njjoAREdHs2/fPnr16kXDhg257bbbiIuLs71fknoYsqVetWpVEhISbD9fuHCBsLAwD5aoeMqWLcvV\nq1eBayeFiIgIu3ULDw/3VBHz2LFjB3PmzGH+/PmEhoZ6XR0OHz7M2bNnAbj99tuxWCxeVweAbdu2\nsXXrVrp168bKlSuZPXu2V9ajXr16ti7FunXrEhYWRnJyslfVo0qVKkRFRVGmTBlq165NuXLlvPJv\nkSs2NpaoqCgqV65s68qG/Otx/vx5w9Rj37593H///cC1C8a0tLQ8ZTV6HXK9+uqrLFu2jPHjx5Oc\nnEzVqlWd8p0yZKi3bt2ajRs3AvDTTz8RERFBSEiIh0tVdPfdd5+tHps2baJNmzY0bdqUQ4cOkZyc\nTGpqKvv27aNFixYeLuk1V65cYcqUKcydO5eKFSsC3leHPXv2sGjRIuDabZy0tDSvqwPAjBkzWL16\nNStWrKBr164MGjTIK+uxatUqPvroIwDi4+NJTEzkqaee8qp63H///ezevZucnBwuXrzotd8puBYW\n5cqVIyAgAH9/f2677Tb27NkD/FGPe++9l23btpGZmcn58+e5cOEC9evX93DJr6lTpw4HDhwA4PTp\n05QrV47IyEivqgPAkSNHGD16NAD//ve/ady4sdO+U4Z9Stu0adPYs2cPPj4+jB07lkaNGnm6SAU6\nfPgwkydP5vTp05QpU4aqVasybdo0Ro0aRUZGBtWrV+ett97C39+fr776ioULF+Lj40Pv3r35y1/+\n4uniA7B8+XJmzpxJ3bp1ba+9/fbbxMTEeE0drl69yuuvv87Zs2e5evUqgwcP5s4772TkyJFeU4eb\nzZw5kxo1anD//fd7XT0uX77M8OHDSUtLIzMzk8GDB3P77bd7XT2WLVvGF198QXp6Oi+++CJNmjTx\nujrAtfPUjBkzWLBgAQDHjh3jjTfeICcnh6ZNm9qCZsmSJaxfvx4fHx+GDh1Kq1atPFlsm9TUVMaM\nGUNiYiLZ2dkMGTKE8PBwr6oDXJvSNmbMGI4fP05oaCiTJ0/GYrE45Ttl2FAXERGRojFk97uIiIgU\nnUJdRETEJBTqIiIiJqFQFxERMQmFuoiIiEko1EXc7NSpUzRs2PCGJ2YBtGvXzin7b9iw4Q2rtrnC\nxo0bad++PStXrnTpcUSkaBTqIh5w66238v777xv+QUX52b59O88//zxdu3b1dFFE5DqGXPtdxOwi\nIiK4//77mT17NiNGjLjhvTVr1vDdd98xbdo0APr06cOLL76In58fc+bMoVq1ahw6dIimTZvSsGFD\nNm/ezKVLl5g/fz7VqlUDYN68eezdu5eLFy8yefJkIiMjOXLkCJMnT8ZqtZKTk8OoUaNo3Lgxffr0\noVGjRvz88898+OGH+Pn52cqybds23n//fYKCgihbtiwTJkxg//79bN++nb179+Ln50f37t1t2/fp\n04fGjRtz9OhR4uPjGThwII899hi//PILY8eOxc/Pj5SUFIYOHUqbNm1ISkri73//O2lpaURGRnLy\n5En69+/Pfffdx5IlS9iwYQNlypShRo0ajB07FovFwt///neSk5PJzs6mbdu2vPjii274i4l4B7XU\nRTzkueeeY/v27fz666+F/szBgwcZOXIkq1atYv369ZQvX54lS5Zwxx132JaYhGvrrC9cuJCePXsy\na9YsAF577TXGjx/P4sWLGTNmDDExMbbtg4OD+b//+78bAj09PZ2YmBhmzpzJkiVL+POf/8yMGTN4\n6KGHaNOmDS+88MINgZ4rOzubRYsWMWvWLCZNmkROTg4JCQkMGTKEDz/8kJiYGN59910AFi9eTIMG\nDVi2bBm9e/fmhx9+sNVz8+bNLF26lI8++ojQ0FBWrlzJd999R3Z2Nh9//DHLli0jODiYnJycov3i\nRUxMLXURDwkICGDEiBG8+eabLFy4sFCfqVevnm1d/ooVKxIVFQVcewjSlStXbNu1bt0agGbNmrFo\n0SISExM5fvw4r7/+um2blJQUWyA2a9Ysz7F+++03qlSpYmv9t2zZkmXLljksY+4DN+rUqYOPjw+J\niYmEh4czZcoU3n33XbKysmwPEjly5IjtwiAyMtK2RHFsbCwnTpzg2WefBa49wrVMmTI88sgj/Otf\n/2LIkCFER0fTtWtXfH3VNhHJpVAX8aDo6Gg++eQTNm/ebHvt5kcrZmVl2f59fUv65p+vX/E5N+hy\nH9UYGBiIv78/S5YssVsOf39/h2Ut7OMrr285535mwoQJPProozz99NPExcXxt7/9zbbt9fvMLXdA\nQADt2rXjjTfeyLP/tWvXsn//frZu3UqXLl349NNPCQoKclgukdJAl7giHjZmzBjeeecdMjMzAQgJ\nCeHcuXMAJCYmcvTo0SLvc9euXcC1R1VGRkYSEhJCzZo12b59OwDHjx+3dcvnp27duiQmJnLmzBnb\nPps2berw2Lt377Ydw9fXl8qVK5OQkEDt2rUB+PLLL211ve2229i/fz9w7eEiubcimjVrxr///W9S\nU1MBWLp0Kfv37+fbb79l27ZtNG/enBEjRlCuXDkSExOL9LsRMTO11EU8rHbt2nTq1Ik5c+YA17rO\nFy5cSLdu3ahXr56ti72w/Pz8OHr0KMuWLSMpKYmpU6cCMHnyZCZOnMi8efPIzs5m1KhRBe4nKCiI\nN998k1dffZWAgACCg4N58803HR4/OzubF198kVOnTvGPf/wDX19f+vXrxz/+8Q9q1qxJ37592bRp\nE2+//TbPPfccr7zyCj179qR+/frccccd+Pn50aRJE3r16kWfPn0IDAwkIiKCp556iosXLzJq1CgW\nLFiAn58frVu3pkaNGkX6/YiYmZ7SJiJOkztS/7777ivU9r/++isnT54kOjqaq1ev0qFDB1atWmW7\njy8iRaOWuoh4TGhoKIsXL2b27NlkZ2czYMAABbpICailLiIiYhIaKCciImISCnURERGTUKiLiIiY\nhEJdRETEJBTqIiIiJqFQFxERMYn/DxfszUm85X76AAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f10ddbbb320>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = plt.subplots(figsize=(8, 6))\n",
    "\n",
    "ax.scatter(df['pages'], time_std_resid);\n",
    "\n",
    "ax.hlines(\n",
    "    sp.stats.norm.isf([0.975, 0.025]),\n",
    "    0, 900,\n",
    "    linestyles='--', label=\"95% confidence band\"\n",
    ");\n",
    "\n",
    "ax.set_xlim(0, 900);\n",
    "ax.set_xlabel(\"Number of pages\");\n",
    "ax.set_ylabel(\"Standardized residual\");\n",
    "\n",
    "ax.legend(loc=1);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Again, we use WAIC to compare the three models."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 54,
   "metadata": {
    "scrolled": false
   },
   "outputs": [],
   "source": [
    "compare_df = (pm.compare(\n",
    "                    [nb_trace, book_trace, time_trace],\n",
    "                    [nb_model, book_model, time_model]\n",
    "                )\n",
    "                .rename(index={0: 'NB', 1: 'Book', 2: 'Time'}))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 55,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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7dqtBg9uvynXwlX1upjC3K8PcSq8iLNFf1hF8QUGBCgoKVKVKFUnSiRMndOrUqauTDqjE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\nAAALUfAAAFiIggcAwEIUPAAAFvp/b+v6abyOAUcAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f10f70c0198>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = plt.subplots(figsize=(8, 6))\n",
    "\n",
    "pm.compareplot(\n",
    "    compare_df, \n",
    "    insample_dev=False, dse=False,\n",
    "    ax=ax\n",
    ");\n",
    "\n",
    "ax.set_xlabel(\"WAIC\");\n",
    "ax.set_ylabel(\"Model\");"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The timeseries model performs marginally worse than the previous model.  We proceed since only the timeseries model answers our original question.\n",
    "\n",
    "We now use the timeseries model to show how the amount of time it takes me to read a book has changed over time, conditioned on the length of the book."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 56,
   "metadata": {},
   "outputs": [],
   "source": [
    "t_grid = np.linspace(\n",
    "    mdates.date2num(df['start_date'].min()),\n",
    "    mdates.date2num(df['start_date'].max()),\n",
    "    n_week\n",
    ")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 57,
   "metadata": {},
   "outputs": [],
   "source": [
    "PP_TIME_PAGES = np.array([100, 200, 300, 400, 500])\n",
    "\n",
    "pp_df = (pd.DataFrame(\n",
    "                list(product(\n",
    "                    np.arange(n_week),\n",
    "                    PP_TIME_PAGES\n",
    "                )),\n",
    "                columns=['t_week', 'pages']\n",
    "           )\n",
    "           .assign(\n",
    "               is_handmaid=0,\n",
    "               is_lark=0\n",
    "           ))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 58,
   "metadata": {},
   "outputs": [],
   "source": [
    "is_handmaid_.set_value(pp_df['is_handmaid'].values)\n",
    "is_lark_.set_value(pp_df['is_lark'].values)\n",
    "\n",
    "t_week_.set_value(pp_df['t_week'].values)\n",
    "pages_.set_value(pp_df['pages'].values)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 59,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "100%|██████████| 10000/10000 [00:12<00:00, 791.11it/s]\n"
     ]
    }
   ],
   "source": [
    "with time_model:\n",
    "    pp_time_trace = pm.sample_ppc(time_trace, samples=10000)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 60,
   "metadata": {},
   "outputs": [],
   "source": [
    "pp_df['pp_days'] = pp_time_trace['days_obs'].mean(axis=0)\n",
    "pp_df['t_plot'] = np.repeat(t_grid, 5)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 61,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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Kyjp84sOHD1NRUcH06dMB2LJlCzNnzgTalgtu3rz54iIXQgja9mCPBGqx2AeR\n3W82xhSsvd6T6U1ZmG1lhH0nCAfq1Q7nokQCTsL+GswZZSlf2bHDa/7f+973+NOf/kR+fj4rVqzg\n0ksv5dZbb+3wiZ988kkWL17M8uXLAQgEAhiNRgAcDgdOp7PD58jKSkOvl7P3M3E4bGqHkDSkrTov\nGduqat9qAIoGTCUzgfEnY1t1F4NyOYd3HCbm242jeOAptyVTO504sB6AotLJZKkQdyLbqsPk/+ab\nb3LXXXdx1113dfpJly9fzpgxY+jX77MJExqNpv3/iqJ06nlaWvydfs3exOGw4XR61A4jKUhbdV4y\ntlU8Fqap5mN0BhthpU/C4k/GtupOCv3atk6u3o4p6wq0upMdveRpJ0WJ4azehlZnIaLpl/C4P99W\niTgJ6DD5r169mlmzZmGzdT6YdevWcfz4cdatW0ddXR1GoxGLxUIwGMRsNlNfX09engzNCSEujt+1\nDyUeJj1vYkovy+rpNBot6TljcddtwO/aizVnrNohnbeAu4J41IfVcRkabadq3iW1Dt9hKBRixowZ\n9O/fH4Phs2Uzf/3rX8/6mF/84hft///Vr35Fnz59+OSTT1i1ahVz5sxh9erVTJs27SJDF0L0dt6m\njwGSMtmkGmvOWNx17+Nt3J6Un4evaQcA1uwxKkeSGB0m///3//5fl7zQV7/6VR555BGWLVtGUVER\nt9xyS5c8rxCi94nHwgQ9hwn7TmC2laE3ZqodUq+nN9oxZwwk6D5EJNiEwZyjdkidFov4CLQewmAp\nwJiWurv6fV6Hyf+yyy67qBf46le/2v7/P/7xjxf1XEKI3i0adtNY+SphXzXQNnfI6hivblCiXZp9\nMEH3IYKew0mV/H3Nu4B4+7LF3iD1L2wIIVKGp+FDwr4TGNOKMFlLMNsGYMnoeOmxSAzzp59FwH0Y\nm+PiOo6JoihxPI1b0Wj0pGWPUjuchJHkL4RICooSx9+yB63OTP6ghWi0sgy4p9EbM9Gbcgl5K5Om\nzK/ftZ9Y2IU1dzw6fZra4SRMp5L/tm3b2L17NxqNhtGjRzN2bPJN5hBCJLeQt5JY1Is1Z5wk/h7M\nklGGx7mFkO84kKV2OOekKAqe+k0A2PImqRxNYnW4NuaZZ55hyZIlNDQ0UF9fz+OPP86LL76YiNiE\nEKKdr3kPQK8amk1GZtsAoG3ov6cLeasIB2qx2IdiMGWrHU5Cddjz37JlCy+//HL7fv7RaJTbbruN\ne++9t9ulirxaAAAgAElEQVSDE0IIACUexe/aj86QgSm9WO1wxDmYbKWg0X26R37P5m5o22Y+I3+y\nypEkXoc9/3g8fkohH71ef8pufUII0d0CrQdR4iHSs0fJ908Pp9UaMFuLiQTqiYTcaodzVpGAk6D7\nEKb0filfvvdMOuz5jxgxgvvuu48pU6YAsGnTJkaOHNntgQkhxEm+lt0ApGXJkH8yMNvKCHqO4m46\nCIYhaodzRp7GrQDY8npfrx86kfwfffRRVq5cyc6dOwG4+eabuf7667s9MCGEAIhFAwTchzCY86Vi\nX5IwZ5RBzbu4Gw9iLex5yT8eC+Nr3o3OYMNiH6x2OKroMPn/7Gc/48EHH+SGG25oP/boo4/yxBNP\ndGtgQggB4G3cCkqc9JxL1A5FdJLBnIfOYMPddJD0gniPq7vQVhMi1KtrQpw1+b/zzjusXr2azZs3\n09DQ0H48GAzyySefJCQ4IUTvFo+F8DR8iFZnwZpzqdrhiE7SaDRY7EPxNm4l6D6MxT5I7ZBO4W3c\nDoA1p3fs438mZ03+06ZNIzs7mz179jB58mfXRDQaDQ888EBCghNC9G4e50fEY0HshVe1l4kVySE9\nexTexq34Wnb3qOQfDtQT9ldjzhjYq2tCnDX5m81mLr30UpYvX47JZEpkTEII8blevzlptooVnzGm\n9cGUlkvAVU48FkKr6xl5xNvUNnJtzRmnciTq6vBihyR+IYQaPM6txGMBbHmTekziEJ2n0WjILhyH\norTt0aAWRYnjrt+Eu34j3qad+Jp3odNbe9RohBpkb38hRI8Tj0fwOD9EI73+pJZTOI7aw6vxNe9S\n7fq6r3k3rpp3TzmWnn85Gk3v3iK6U8nf6/VitVppbGyksrKScePGnbLxjxBCdCV/y17iUT8Z+Zej\n1ZnVDkdcIFNaDqb0foS8lUTDbvTGjITH4G3cCmjIKbkFJR4hHg/1+iF/6MSw/2OPPcbKlStxuVzM\nnz+fP//5z/zgBz9IQGhCiN7K2/QxINdlU0FadtsSTf+nGzUlUshXTdhfg8U+mPTsUVhzx5GRN1ku\nI9GJ5L9v3z7mzZvHypUr+cIXvsAzzzxDVVVVImITQvRC4UADYd8JzLYy9KbeOxs7VaRnDgeNjta6\nD3DXb0poqV+P89Nd/HInJOw1k0WHyV9RFADWrVvHjBkzAAiHw90blRCi12rv9efKuv5UoNVbyO53\nI2g0uGrepWb/cwmp+BeL+PC79qI35WCy9e/210s2HSb/0tJSrr/+enw+H8OGDWP58uXY7fZExCaE\n6GXi8Qi+5l1oZTZ2SrHmjKZo+Fex5U0mFvHSePTvRELN3fqa3qaPQYlhc0yQYlBn0OGEv0ceeYS6\nujrKysoAGDhwIEuWLOn2wIQQvU/AtR8lFsQms7FTjk5vIavPLIyWApqq/kFT5evkD17YLZ+zosTx\nNm5HozWSnj26y58/FXTY87/pppv4/e9/z8cftw3FjRw5koyMxM/YFEKkvs+2XR2rciSiu6RnjyIt\naxRhfw2tteu65TUCrQeIRdykZ18ik/vOosPk/95773HDDTfw+uuvM3fuXF544YVT9voXQoiuEI14\nCPmOY7KWojdlqR2O6EbZ/a5Hb8zCXb8Rf+uBLn9+mejXsQ6Tv8Fg4KqrrmLJkiU8/fTTbNiwgVmz\nZvHggw/S3Ny912yEEL1H8NNJYL21xGpvotWZyCn9Ami0NB5ZRsuJVcTjkS557kjASchbiclaisHi\n6JLnTEUdXvMPBoP861//4h//+Acej4d58+bxm9/8hvfff5+vfe1r/OUvf0lEnEKIFBd0VwBgyRio\nciQiEUzpfckffCdNlcvxOLcQcFdgSu8HgFZnJiN/KjpD+nk/r6fx016/7Ax5Th0m/5kzZzJ9+nS+\n9a1vcckln9XTnj17NitXruzW4IQQvYOixAl4jqAz2tGbctQORySIKa2IgqH34KpZg9f5EdFQU/tt\nkVAjjgH/cV4z9eOxIL7mnegMGT1yBCkWixMORbGkGU85tvfjGhrrPDTUe/C0Bvnu/9zQ7bF0mPxX\nrVqF1Wo95diTTz7JI488wi9/+ctuC0wI0XuEfdUosSCWzBGyLKuX0WoNZPe9Dnv+5cTjbXvItBx/\nm6C7Al/TJ1hzO7/Lo695F0o8gjX/cjSanrUFfSwW55+v7KLmmIuyoXmMm1xMJBJj/b8O0uz0AWA0\n6cjMTktIPB0m/507d/Kzn/0Ml8sFtG3wY7fbeeSRR7o9OCFE7xDwtA35m2XIv9fSGaycXPSXXXwz\nteW/pqV6NWZb/3NOAI1FPPhbDxL21xJoLQeNrsdtC60oCh+8c4jqKhdGk46K/Q1U7P9s4vzwMYVc\ne/NIAqFwwk5+O0z+v/jFL1i8eDE//vGPeeKJJ3j77bcZP358ImITQvQSbZP9tJhtpWqHInoAvTGD\n7L6zaapaTtOxN8gb+J9nTIrxWIi6A78jFvG0HdDosBdceUFzBbrT3o9r2Lejlpy8dG65dSy1x1vZ\nseUY8bjCpOkDKOyXic1uJujsmkmPndFh8rdarYwZMwaDwcCgQYP4+te/zt13383UqVMTEZ8QIsXF\nIj7C/hpM1hJZky3apWWNwu8qJ9BajrfpY2xn2O65te59YhEP1pxxWHPHY7A4eszmULFYnPpqN8eO\nNrPjw2NY0gzM/rdRGE16SgbmUDJQ3bktHSb/aDTKtm3byMjI4B//+Af9+vXjxIkTiYhNCNELBD1H\nAJnlL06l0WjI7jebGs8RWmvWkpY5HJ3e0n57JNiEx/khOqOdzL7XotUaVIz2VFWHm3h3xT7CoRgA\nBqOOa+eOxGbvOeWpO0z+P/zhD2lsbOThhx/mscceo7Gxkfvuuy8RsQkheoGAW673izPTGWzYC67A\nVfMurbXvkd3v+vbbWqpXgRInq881PSrxez0h1ry5n1hMYdSlfehTmkWf4kyMpg7TbUJ1GM2AAQMY\nMGAAAH/4wx+6PSAhRO+hKHGC7gp0eisGc57a4YgeyOaYiLfpE7yN27HmjMNgycffsoeguwKTtRSL\nfajaIbaLxxXWvLmfUDDKtGsGMXJcH7VDOquzJv8ZM2acc9bhmjVruiUgIUTvEfJWEY8FsOaOlyV+\n4ow0Wh1Zfa/DefivOI8sQ1EixKN+QENW32t71O/Nzo+OU3PMRenAHEaMLVI7nHM6a/JfunQpAMuW\nLcPhcDBp0iRisRgbN27E7/cnKj4hRArzu8oBSOtBvTfR81gyyrBkDiPg2o9ObyU9ewzpOaMxWvLV\nDq1dU4OXjzYcJc1qZPr1Q3rUScmZnDX5FxcXA3DkyBEeeuih9uMjRoyQa/5CiIumKAqB1nK0OjMm\nW4na4YgeLrfkC0QLZ6A3ZffIxLp53RHicYXp1w05ZQe/nqrDLZCqq6v54IMP8Pv9BINBNm/eTHV1\ndSJiE0KksLC/mljEg8U+pMcsz0olx482s+z3W2lyetUOpUtotHoM5pwemfirq1o4fqSZouJMisuy\n1Q6nUzo12//JJ5/k4MGDAAwcOJDFixd3e2BCiNR2csjfkilD/l1NURS2rD9Ks9PHupUH+MJt49Bq\ne17STAWKovDh+rblqpOmD+iRJydn0mHyHzt2LC+//HIiYhFC9BInh/w1WgNm2wC1w0k5tSdacdZ5\n0Go1NNR42PtxNaPG91U7rJRUeaiRhhoPA4bkkl+UoXY4ndazKh8IIXqFSLCBaKgZS8agHrVGO1Xs\n+qhtI7arbx6Oyaxny4ajeN1BlaNKPfF42wiLRgOXXdFf7XDOiyR/IUTC+V37ARny7w6tLQGOHmrE\nUWBjwJBcpswoIxKOsWH1IRRFUTu8lFJV0UhLk58howrIyulZ9QQ6ctbk/9prrwHw97//PWHBiJ4t\nGnbjbdqBr3kX/pZ9eBq303TsLerKf0tDxV/wuw6gKHG1wxQ9XCzixdu4DY1GjyVjkNrhpJzd29p6\n/aMv64tGo2HIqAKKijOpqmjiX6/tIRhIXPGYVLf3kxoALpmQfJdUznrN/9e//jWRSIT//d//PeME\nhi9+8YvdGpjoWfytB2iueoN47AxDhxodKDGCniPojVlk9plFmvToxBkoikLTsRXEo34y+1wjhXy6\nUDyu4KzzsH9XLek2EwOGOIC2PfJnzRnOuyv2UVnRxN//uI1J0wegxBX8vgiOAit9Ss5eMlecmdsV\n4PjRFgr62slxWNUO57ydNfk//PDDrF+/Ho/Hw/bt20+7XZJ/76AoMVw1a/E0bEaj0WMvvAqdPh1F\niaLRGjBaCjFYHJ8W2diCr3kXjUdfJW/grZhtyXUNTHQ/b+M2gu4KzLYB2BwT1Q4n6bQ0+jCY9Fht\nn500tbb42bL+KMePthAORQG4bFpfdLrPBnbT0o3c+O+j+XhzFds+qOTdFftPed7r542ipEzdKnPJ\nZt+Otl7/iDGFKkdyYc6a/K+55hquueYaVq1axbXXXpvImMQFiEY8+Jt342veTTweJH/QQvTGi5t5\nGg27aap8jZDvOHpTNrmlX8SYVnDG+xoteeQU30R69iU0VPwZ59G/UzD4Tgzm3IuKQaSOSMCJq/od\ntDoL2SVzkmZJVE9Qc8zFto2VVFe50Oo0jBzXh3GTi6nY38CH644QjcSx2c2UDXXQr39We6//87Ra\nDeOnltK3NIvqKhdmiwGtVsP77xzi3RX7mHvHuKS7bq2WWDTO/l11mMx6Bgw9va2TQYdL/caMGcN3\nv/tddu/ejUajYcyYMTzwwANkZyfHRga9gb9lH42VrwEKoAEUmqqWkzfwNjSaU6d1KEqclhOrMJhz\nsOZOOOsXcMB9mKaqfxCP+knLHE528U2dGqI1W0vI7ncTzcfewHnkZfIH34lOn3bxb1IkvZbqVShK\nlJziuegNNrXDSQqxWJx33tjH0YONAPQpycTtCrJr6wn2bK8mHlcwmfVcdf1QBg7rXGGkgj52CvrY\n23/W6bWseXM/K1/bw7/dMQ6TWVZfdOTIQSdBf4TRl/VFr0/ODao6TP7f//73mTZtGgsXLkRRFDZt\n2sR3v/tdXnjhhUTEJzrB3bAZgKy+s0nLGkHzsTcJtB7AXb8Je8Hlp9637n28jVsBiIZayOxzzSkn\nANFwK6216/E17wCNlqy+s8+76Io1ZzTRUCPu+o00Hv07eWW3odEm5x+I6Bphfy1BzxFM1lKZD9JJ\niqKw7u0DHD3YSEGfDCbPKKOgj51YNM6eT6r5ZPMx8vtkcOW1g0mzXvjcicEj8mlq8LJjy3GW/3UH\nl04pYcCQXLRaWQx2Nvs+neg3fEzPLt5zLh0m/0AgwK233tr+8+DBg1m7dm23BiU6LxbxEPZXY7KW\nYHNMACC7+CbqymtorV2H2dYfU3pbWcmQ7wStdRvQGTLQ6kx4nFuIRQPYHOOJhl2EfdV4GreBEsNg\nziO7+Kb2x54ve+EMIqFmAq79NB//J9nFN8kwby/mrt8IQEb+VJUjSR5b1h/l4N568gpt3PjvozEY\n206gdXotoyf045Lxfbvsb2rilQMIBiKU76rjnTf2YbObmXbNIJkHcAYtjT5qjrfSpySTzOzkHdXs\nVPJvaGggL69tSKmuro5wONzhEwcCAb797W/T1NREKBRi0aJFDB06lIcffphYLIbD4eCpp57CaOz5\nBRB6Mn/rAeDUqmg6fRo5JXNoqPgLziMvk5E3hfTskTRV/gNQyCm5BYMlD+fhv+Fv2YW/ZddnjzVk\nYC+cTnr2JaddMjgfGo2GnJJbaAi58DXvwGDOkS/+XioSbMLv2ofBUii7+XVAUdpm7B/YXc+ej6ux\nZ1m4ft6o9sT/eV15Mq3Varjq+qGMm1zMzq0nKN9Zy7sr9jH/7stIt8mKjM/be3KiXw8v2duRDpP/\nokWLmDt3Lg6HA0VRaG5u5oknnujwid977z1GjhzJPffcQ3V1NXfeeSfjxo1jwYIFzJ49myVLlvDq\nq6+yYMGCLnkjvVWgfX/0IaccN9sGkNXnWly1a3HVvIOr5l1AwZY3BbOtFIC8gbfjrv8AJR5Fb8pE\nb8zEZOvfZTuuabUGcsvmU3/g97hq1qA355JmH9LxA0VKOXlZyp4/VUZ/zqKl0cf+XbVU7G/A52nr\nXKXbjNz475cktEKcPSuNK64ZTI7DyoZVB9mw+iDXzR0pn9unIpEYB3bXk5ZupHRQck9m7jD5T58+\nnXfffZfKykoA+vfvj8nU8Zng9ddf3/7/2tpa8vPz2bJlCz/84Q8BmDlzJkuXLpXkfxHi0SBBTyUG\nSyF6Y+Zpt9vyJpKWfQnexq14nB+1rcEvvKr9dq3OSGbRjG6NUW+w4Rgwn/qDf6C56g2MQ+9Fb7R3\n/ECREqIRD77mnehN2bKb3xk46zx88O4h6k64ATCZ9QwemU//Qbn06599xh5/IgwfU0jF/gYqDzVx\nuNzZ6cmEqe7w/gbCoSgjLy0+ZSllMuow+QOYzWaGDr2wP9z58+dTV1fHCy+8wMKFC9uH+R0OB06n\n85yPzcpKS9qZlN3N4bDRVHsIiOPocwkOx9lmT9ug8AYUZTbARQ3lXzgbRt0cju17DXf1CgaPvzeh\nEwDP3jbi/+rqtjpx8H1QYhSVXYUjL7VO+i62rZqcXt7++278/jADBjsYN6mYwSPye8x33txbx/HC\nT9excU0Fo8f1veBJhan097dizw7QwOVXDeqW6/2JbKtOJf+L8fLLL7N//34eeuihU4aOOrPHdEuL\nvztDS1oOhw2n04Pz+A4A4vr+OJ0elaM6N8U4HEvmPryu/RzesxJ74ZUJed2TbSU61tVtFY9HcB7/\nEK0+DcUwJKU+h/Npq3hc4eCeOg7sqaegTwaXTOhLPK7wjz9/gt8X5srrBrfPGu9p33mXTevPprWH\n+efru5k++/wv2aXS35+zzkP1MRclZdlEYrEuf1+fb6tEnAR0mPwVRbmg6z179uwhJyeHwsJChg0b\nRiwWw2KxEAwGMZvN1NfXt08iFOcvHo8QdFegN2VjMPf8TSY0Gg05/W6k1ldDa92GtlUI1mK1wxLd\nyN+8m3gsQEb+5Wi03d7P6HEC/jDVVW2b87Q0tiX1mmMudm09gSXNgMcdYsK00h69XGzU+L7s31VL\n+a5aRk/oS1Zu790E6OSOfsOTfKLfSR3+Rd5xxx38+c9/Pu8n3rZtG9XV1Tz66KM0Njbi9/uZNm0a\nq1atYs6cOaxevZpp06ZdUNACgq2HUOIRLPYhSTMZR6u3kFP6BRoOLaXp2JsUDr23VyaF3kBRFDzO\njwAN1tzxaofTbULBtuVxez+pwe8Lk5ZuJC3diNcTwtPaVgdDo4FhowsZM7Efx482s2PLcTzuECPG\nFXHplBKV38G5abUaJl45gH+9toctG45y3dyRaoekimgkxqF9DVgzTBQPSI3ljx1+8w4bNoxnnnmG\nsWPHYjB8Ngt88uTJ53zc/PnzefTRR1mwYAHBYJDvfe97jBw5kkceeYRly5ZRVFTELbfccvHvoBeK\nhLy0nPgXoCU9+xK1wzkvZmsxVsdleJ0f0Vr3PplFV3X8IJF0Qt4qIsEG0jJHXPQ20z1BPK7Q0uij\nvsZNS6MfRVFwNfupPdFKNBJHp9eSmWXB7wvT2hLAbNFTPCAbR6GNQcPz2rfNzcxOY/iYIpoavDgK\nbElx4l46MIeCvhkcPdhIXXXrKbsD9hbHjjQTCccYOa4PWm3P/8w6o8Pkv39/WwGIbdu2tR/TaDQd\nJn+z2czTTz992vE//vGP5xuj+BxFUajc+wqxqJfMoqsxWvLVDum8ZRZeRcBVjrt+I2lZw5PyPYhz\na+v1g81xmcqRXJzGei+7tp3gyAEnkXDstNutGSZGTu3DsNGFmC1tnaN4PI5GozlrYtfptOQVJs8J\nkUajYdKVA1j+1x18+N4R5tw6JilOWrrS4fIGAMqSdB//M+kw+Z8c8r/Qa/+ia3kaNuNuLMdsK8OW\nd+4TsJ5KqzOR3e8GnEf+RvOxN8kffKdKqxBEd4iGXARaD2C0FGJMT74659BWrvW9tw9Qc8wF0F40\nJ78og5w8K337ZeEPhNEbtKd9L6bitriF/TIpGZhDVUUTVYebKB2Y3Gvcz0ckEqOyogl7loXc/OQr\n3Xs2Hf6WlpeXM3fuXGbPblsq9txzz7Fz585uD0ycLuyvw1WzFoMpg5ySW5L6ZMxiH0Ra1kjC/hrq\nD/6BSLBR7ZBEF/E0bgUUrI7LkvJ3NBKO8varu6k55qJPSSbXf3EUt943kauuH8rwMUXkF2WQmZ2G\nwahLyvd3oSZdOQCNBjavPUwsFlc7nIQ5driJaCRO2TBHSn3eHSb///mf/+HHP/4xDkfbcMf111/P\nT37yk24PTJxKURRaqt8B4pSMmIfOkPyzbrP73UBa1ijC/hrqyn/TPlQsklc8HsHX9AlafTrpWSPU\nDue8KYrCupUHaGn0M3JcH27+jzGUDMxJqS/9C5XtSGf4mCJczQH2flrYpjeo2N+2H83Aoam1Oq3D\n5K/Vak/Z4Kd///7o9TJDO9GCnsOEvEc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YUEeSJOyNm4Eo1sK7UWrS4y3SNeN2BWis7eLD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\nAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f10e39eecc0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = plt.subplots(figsize=(8, 6))\n",
    "\n",
    "for grp_pages, grp_df in pp_df.groupby('pages'):\n",
    "    grp_df.plot(\n",
    "        't_plot', 'pp_days',\n",
    "        label=f\"{grp_pages} pages\",\n",
    "        ax=ax\n",
    "    );\n",
    "    \n",
    "ax.set_xlim(t_grid.min(), t_grid.max());\n",
    "ax.xaxis.set_major_formatter(mdates.DateFormatter('%b %Y'));\n",
    "ax.xaxis.set_major_locator(mdates.MonthLocator(interval=6));\n",
    "ax.xaxis.label.set_visible(False);\n",
    "\n",
    "ax.set_ylabel(\"Predicted number of days to read\");"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The plot above exhibits a fascinating pattern; according to the timeseries model, I now read shorter books (fewer than approximately 300 pages) slightly faster than I did in 2015, but it takes me twice as long as before to read longer books.  The trend for longer books is easier to explain; in the last 12-18 months, I have been doing much more public speaking and blogging than before, which naturally takes time away from reading.  The trend for shorter books is a bit harder to explain, but upon some thought, I tend to read more purposefully as I approach the end of a book, looking forward to starting a new one.  This effect occurs much earlier in shorter books than in longer ones, so it is a plausible explanation for the trend in shorter books.\n",
    "\n",
    "This post is available as a Jupyter notebook [here](http://nbviewer.jupyter.org/gist/AustinRochford/722d4a98ba45f577b7e415e2b73cda0d)."
   ]
  }
 ],
 "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": "3.6.3"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}