{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Preface"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import pandas as pd\n",
    "import seaborn as sns\n",
    "import torch\n",
    "\n",
    "import pyro\n",
    "import pyro.distributions as dist\n",
    "\n",
    "from rethinking import LM, coef"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Code 0.1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2017-12-07T01:31:33.358577Z",
     "start_time": "2017-12-07T01:31:33.356029Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "All models are wrong, but some are useful.\n"
     ]
    }
   ],
   "source": [
    "print(\"All models are wrong, but some are useful.\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Code 0.2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2017-12-07T01:31:33.433222Z",
     "start_time": "2017-12-07T01:31:33.359596Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "tensor(200.0000)"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x = torch.arange(1., 3)\n",
    "x = x * 10\n",
    "x = x.log()\n",
    "x = x.sum()\n",
    "x = x.exp()\n",
    "x"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Code 0.3"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "tensor(-inf)\n",
      "tensor(-921.0341)\n"
     ]
    }
   ],
   "source": [
    "print(torch.tensor(0.01).pow(200).log())\n",
    "print(200 * torch.tensor(0.01).log())"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Code 0.4"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2017-12-07T01:31:33.798552Z",
     "start_time": "2017-12-07T01:31:33.508571Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "{'Intercept': tensor(-17.4259), 'speed': tensor(3.9238), 'sigma': tensor(15.0173)}\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 576x432 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Load the data:\n",
    "# car braking distances in feet paired with speeds in km/h\n",
    "# see cars.info() for details\n",
    "cars = pd.read_csv(\"../data/cars.csv\")\n",
    "\n",
    "# fit a linear regression of distance on speed\n",
    "m = LM(\"dist ~ speed\", data=cars).run()\n",
    "\n",
    "# estimated coefficients from the model\n",
    "print(coef(m))\n",
    "\n",
    "# plot residuals against speed\n",
    "y = coef(m)[\"Intercept\"].item() + coef(m)[\"speed\"].item() * cars[\"speed\"]\n",
    "resid = cars[\"dist\"] - y\n",
    "ax = sns.scatterplot(cars[\"speed\"], resid)\n",
    "ax.set(xlabel=\"speed\", ylabel=\"residual\");"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2017-12-07T01:31:33.798552Z",
     "start_time": "2017-12-07T01:31:33.508571Z"
    }
   },
   "source": [
    "### Code 0.5"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2017-12-07T01:31:33.798552Z",
     "start_time": "2017-12-07T01:31:33.508571Z"
    }
   },
   "source": [
    "```sh\n",
    "pip install jupyter pandas pyro-ppl seaborn torch\n",
    "```"
   ]
  }
 ],
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