2_BayesPractice.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Pyladies Meetup Week Two: Bayes in Practice"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Meant for an \"after work\" live presentation\n",
    "This notebook is meant for a live presentation and may be confusing to follow without direct explanation. It also is a very quick treatment of Bayes Theorem for the mean for the \"after work exhausted professional\".\n",
    "\n",
    "If you're interested after this tutorial I would suggest reading\n",
    "\n",
    "* Bayesian Analysis with Python - Osvaldo Martin\n",
    "* Statistical Rethinking - Richard McElreath"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "WARNING (theano.configdefaults): install mkl with `conda install mkl-service`: No module named 'mkl'\n"
     ]
    }
   ],
   "source": [
    "import pymc3 as pm\n",
    "import numpy as np\n",
    "import arviz as az\n",
    "import matplotlib.pyplot as plt\n",
    "from scipy import stats"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Agenda\n",
    "1. Bayes Refresher from last week\n",
    "2. A case of a little data and a lot of data\n",
    "3. Linear Regression\n",
    "    * Least Squares Method\n",
    "    * Bayesian Method\n",
    "5. Real world example\n",
    "6. Why's this useful?"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Refresher\n",
    "Bayesian methods let us \n",
    "* Define our own model of how data is generated\n",
    "* Incorporate prior beliefs\n",
    "* Estimate uncertainty in our beliefs given data/observations\n",
    "\n",
    "Last week this is how we did it with our cards data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Number of Red Observations 2, Total Number of Observations 5\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Auto-assigning NUTS sampler...\n",
      "Initializing NUTS using jitter+adapt_diag...\n",
      "Multiprocess sampling (2 chains in 2 jobs)\n",
      "NUTS: [p_red]\n",
      "Sampling 2 chains: 100%|██████████| 11000/11000 [00:06<00:00, 1712.42draws/s]\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "observations = [0, 0, 0, 1, 1]\n",
    "red_observations = sum(observations)\n",
    "total_observations = len(observations)\n",
    "print(f\"Number of Red Observations {red_observations}, Total Number of Observations {total_observations}\")\n",
    "\n",
    "with pm.Model() as five_obs_model:\n",
    "    # Prior\n",
    "    p_red = pm.Uniform(\"p_red\", 0, 1)\n",
    "    \n",
    "    # Likelihood\n",
    "    num_red = pm.Binomial(\"number_observed_red\", p=p_red, n=total_observations, observed=red_observations)\n",
    "    trace_binomial = pm.sample(draws=5000)\n",
    "    \n",
    "az.plot_posterior(trace_binomial);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Linear Regression: The next obligatory statistics example\n",
    "Let's simulate some linear data. We'll simulate some noise/error that always occurs in real life as well."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(array([32, 35, 41, 20, 23, 47, 23, 27, 29, 39]),\n",
       " array([ 71.47182784,  85.90977334,  95.79835559,  48.48237038,\n",
       "         63.63560234, 107.24243574,  57.45293646,  65.73742144,\n",
       "         67.45525228,  92.23061389]))"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.random.seed(0)\n",
    "sample_size = 10\n",
    "\n",
    "# Generate random values between 1 and 50\n",
    "x = np.random.randint(20, 50, sample_size)\n",
    "\n",
    "intercept = 10\n",
    "slope = 2\n",
    "\n",
    "# Generate y values using out slope and intercept\n",
    "y= x*slope + intercept\n",
    "\n",
    "# Add some noise in using a zero centered Gaussian/Normal Distribution\n",
    "noise = 3\n",
    "noisy_y = y + stats.norm(0, noise).rvs(sample_size)\n",
    "\n",
    "x[:10], noisy_y[:10]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(2.098083473268639,\n",
       " 9.24222117477855,\n",
       " 0.9859735912820652,\n",
       " 1.6650805641793438e-07,\n",
       " 0.12556611746463195)"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "slope, intercept, r_value, p_value, std_err = stats.linregress(x, noisy_y)\n",
    "slope, intercept, r_value, p_value, std_err"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Standard Linear Regression"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x1c21a78f28>]"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAXoAAAD8CAYAAAB5Pm/hAAAABHNCSVQICAgIfAhkiAAAAAlwSFlzAAALEgAACxIB0t1+/AAAADl0RVh0U29mdHdhcmUAbWF0cGxvdGxpYiB2ZXJzaW9uIDMuMC4yLCBodHRwOi8vbWF0cGxvdGxpYi5vcmcvOIA7rQAAHtRJREFUeJzt3Xl4VOX5xvHvA0QIokQWEYJpEDEoUEAjCqhslrC0Qq1YrVK0tNiK1vZXEbC2uKGpqNXWVkvdaOtGLYIVFJRF1AoIskTBVAQEEmQRgygBQvL+/shkmgkTCDkzObPcn+viSt4nZzLP8ejN8T1n3mPOOUREJHHV87sBERGJLgW9iEiCU9CLiCQ4Bb2ISIJT0IuIJDgFvYhIglPQi4gkOAW9iEiCO2rQm9mTZrbDzD6oVBthZh+aWZmZZVfZfqKZrTezfDPLiUbTIiJScw1qsM3TwCPA3yrVPgAuBf5SeUMzOwu4AugEtAHeMLMznHOlR3qDFi1auMzMzJp3LSIirFixYpdzruXRtjtq0DvnFptZZpXaOgAzq7r5MOB559wBYKOZrQd6AO8e6T0yMzNZvnz50VoREZFKzOzTmmwX6Tn6dGBLpfHWQE1ERHwS6aA/7BQfCLtqmpmNMbPlZrZ8586dEW5DREQqRDrotwKnVhq3BQrDbeicm+qcy3bOZbdsedQpJhERqaVIB/3LwBVm1tDM2gEdgGURfg8RETkGR70Ya2bPAX2BFma2FZgE7Ab+CLQEZpvZKudcjnPuQzObDqwFDgFjj3bHjYiIRFdN7rq5spofvVTN9pOByV6aEhGRyNEnY0VEElxNPjAlIiIR9o8ln3Lnv9dysLSM9LRUxuVkMbx7dO5GV9CLiNSxqx9fytvrdwXHBUXFTJyRBxCVsNfUjYhIHVm1pYjMCbNDQr5CcUkpU+bmR+V9dUYvIhJlBw+VcfGDb7J5974jbldYVByV99cZvYhIFD2z9FPOuO3VYMj/fXQP0tNSw27bppq6VzqjFxGJgsKiYnrlLgiOh3Q5hT/94GzMjHE5WUyckUdxyf8+ZpSaUp9xOVlR6UVBLyISQc45bnhuJbPXbAvW3pnQP+QsvuKC65S5+RQWFdNGd92IiMSHd9bv4qrHlwbHdw3rxMiemWG3Hd49PWrBXpWCXkTEo30HD3He5PnsPXAIgLYnpTL/V31o2KC+z52VU9CLiHjwp4XrQ26LnHF9L87OOMnHjg6noBcRqYUNO7+i/wNvBsc/OC+De77bxceOqqegFxE5BmVljh88voQlG3YHa8tvu5gWTRr62NWRKehFRGrotQ8+46f/WBEcP3xFN4Z1i/2npSroRUSOYs++ErreOS847tq2Kf/6WS8a1I+Pz5wq6EVEjmDy7LX89a2NwfHcX1xE1ikn+NjRsVPQi4iE8WHhHob+4e3geGy/9ozL6ehjR7WnoBcRqaSktIxv/+Ft8rfvBaCewapJAzmxUYrPndWegl5EJOCfy7cw7sU1wfGT12TTv2MrHzuKDAW9iCS9HXv302Py/OC4X1ZLnrzmXMzMx64iR0EvIknt5n+u5sUVW4PjxeP6kdG8sY8dRZ6CXkSS0rKNu7n8L+8Gx7cNPZMfX3iajx1Fj4JeRJLK/pJSLrxvITv3HgCgRZOGvD2+H41SYmMBsmhQ0ItI0nj8rQ3cPXtdcDz9up70aNfMx47qhoJeRBLelt37uPC+hcHxpWen88CIrglzsfVojhr0ZvYk8G1gh3Ouc6DWDHgByAQ2AZc7576w8n9qDwNDgH3ANc6596PTuojIkTnn+NHT77Ewf2ewtvTWAbQ6sZGPXdW9mizU8DQwqEptAjDfOdcBmB8YAwwGOgT+jAEejUybIiLHZuFHO2g3cU4w5O/73jfZlDs06UIeanBG75xbbGaZVcrDgL6B76cBi4DxgfrfnHMOWGJmaWbW2jm3DRGROrB3fwld75hHmSsfn9GqCbN/fiEpcbIAWTTUdo6+VUV4O+e2mdnJgXo6sKXSdlsDtcOC3szGUH7WT0ZGRi3bEBH5nwfn5fOHBeuD41duvIDO6U197Cg2RPpibLgrGy7chs65qcBUgOzs7LDbiIjUxH+372Xg7xcHx6MvaMdvvn2Wjx3FltoG/faKKRkzaw3sCNS3AqdW2q4tUOilQRGR6pSWOS599D+s3lIUrK367bdIa3ycj13FntpOWr0MjAp8PwqYVan+Qyt3PrBH8/MiEg0vry6k/a1zgiH/2NVnsyl3qEI+jJrcXvkc5RdeW5jZVmASkAtMN7PRwGZgRGDzOZTfWrme8tsrr41CzyKSxD7/6gDn3P1GcHz+ac149sfnU69ectwTXxs1uevmymp+NCDMtg4Y67UpEZFwbpuZxz+WbA6O5/+qD+1bNvGxo/igT8aKSMxbufkLvvvn/wTHNw88gxv6d/Cxo/iioBeRmHXgUCnfenAxm3fvA6BJwwYsvXUAxzdUdB0L/dMSkZj09yWf8puZHwTH/xh9Hhd0aOFjR/FLQS8iMaWwqJheuQuC46FdWvPID7onzQJk0aCgF5GY4Jxj7LPvMyfvs2DtPxP60yYt1ceuEoOCXkTqxMyVBUyZm09hUTFt0lIZl5PF8O7pALyzfhdXPb40uO1dwzoxsmemT50mHgW9iETdzJUFTJyRR3FJKQAFRcVMnJHHgUOl3PnvtXx9sLx+arNU3vi/PjRskLhPe/KDgl5Eom7K3PxgyFcoLill/L/yguOXru9F94yT6rq1pKCgF5GoKywqrvZnV52XweTvdqnDbpJP8i7QLCJ1proLqqec2EghXwcU9CISdW3SDn+qU2pKfSYM7uhDN8lHUzciEjWbP9/HRVMWHlZPr3LXjUSXgl5EoiJzwuyQ8R+v7M53urbxqZvkpqAXkYiavnwLt7y4JqS2KXeoT90IKOhFJEL2l5TS8TevhdTendif1k31yVa/KehFxLPv/+Vdlm7cHRz/sOc3uHNYZx87ksoU9CJSax8U7OHbf3w7pLbhniF62lOMUdCLSIgjrUlTwTlHu4lzQmrP/vg8ep2uZYRjkYJeRIKqW5MGCIb9nxauZ8rc/OBr0tNSeWdC/7pvVmpMQS8iQdWtSTNlbj79sk6m653zQn62+rcDado4pS5blFpQ0ItIUHVr0hQUFYeE/LicLMb2O72u2hKPFPQiEtQmLZWCIyxABrDx3iF62lOc0Vo3IhI0LieL1JTwa8G/cuMFbModqpCPQwp6EQka3j2djOaNQ2rtWx7PptyhdE5v6lNX4pWnqRszuwn4CWDAX51zD5lZM+AFIBPYBFzunPvCY58iEmWffv41faYsCql9dNcgGlVzhi/xo9ZBb2adKQ/5HsBB4DUzmx2ozXfO5ZrZBGACMD4SzYpIdFRdgOzmgWdwQ/8OPnUjkebljP5MYIlzbh+Amb0JfBcYBvQNbDMNWISCXiQmTfvPJia9/GFITQuQJR4vQf8BMNnMmgPFwBBgOdDKObcNwDm3zcxO9t6miERSuAXI5v3yIs5odYJPHUk01TronXPrzOx3wOvAV8Bq4FBNX29mY4AxABkZGbVtQ0SO0UX3LWTz7n3Bcde2TZl1wwU+diTR5ulirHPuCeAJADO7B9gKbDez1oGz+dbAjmpeOxWYCpCdne289CEiR7dmaxGXPPJOSO3jyYNJqa+b7xKd17tuTnbO7TCzDOBSoCfQDhgF5Aa+zvLcpYh4UvVi6wMjuvK9c9r61I3UNa+fjP1XYI6+BBjrnPvCzHKB6WY2GtgMjPDapIjUTu6rH/HYm5+E1HSxNfl4nbq5MEztc2CAl98rIt7sKS6h6x2hC5AtmTiAU5o28qkj8ZPWuhFJMFWnaS7p2oY/XNndp24kFijoRRLEovwdXPPUeyE1LUAmoKAXiXvhnvY07Uc96HNGS586klijoBeJY2OffZ/Za7aF1HSxVapS0IvEoW17iul574KQ2upJA2maqqc9yeEU9CJRUpOHbNdG1YutP+vbnvGDOnr+vZK4FPQiUVCTh2wfqxdXbOXmf64OqWmaRmpCQS8SBUd6yPaxBn1JaRkdfv1qSO3lG3rzzbZpnvuU5KCgF4mC6h6yXV29Ot/549vkFewJjjOaNWbxLf089SbJR0EvEgXVPWS7TVpqjV6f/9lech5aHFq7exANG+hpT3LsFPQiUTAuJytkjh4gNaU+43Kyjvraqhdb7xzWiR/2zIx0i5JEFPQiUVAxD38sd908suBj7p/335CaLrZKJCjoRaJkePf0Gl14/frAITpNmhtSWzyuHxnNG0erNUkyCnoRH3WeNJevDvzvwWx9s1ry9LU9fOxIEpGCXsQHSzd8zvenLgmpbbhnCPXqaQEyiTwFvUgdCrcA2WNXn8Ogzqf41JEkAwW9SB2ZOGMNzy3bElLTxVapCwp6kSjbufcA505+I6S24raLad6koU8dSbJR0ItEUdV74q8+P4O7h3fxqRtJVgp6kSiYk7eN6595P6SmaRrxi4JeJIJKyxztbw292PrPn/bk3MxmPnUkoqAXiZirH1/K2+t3BccnNGpA3u05PnYkUk5BL+LRpl1f0/f+RSG1tXfm0Pg4/eclsUH/Jop4UPVi6y2Dsri+7+k+dSMSnqegN7NfAj8GHJAHXAu0Bp4HmgHvAyOdcwc99ikSU556ZyN3/HttSE0XWyVW1TrozSwd+DlwlnOu2MymA1cAQ4DfO+eeN7PHgNHAoxHpVsRn+0tK6fib10Jqr//yIjq0OsGnjkSOzuvUTQMg1cxKgMbANqA/8IPAz6cBt6OglwTQO3dByMNEup2axsyxvX3sSKRmah30zrkCM7sf2AwUA/OAFUCRc65iOb6tgPfH3ov4aPWWIob96Z2Q2vrJg2lQv55PHYkcGy9TNycBw4B2QBHwT2BwmE1dNa8fA4wByMjIqG0bIlFV9WLrg5d35dKz2/rUjUjteJm6uRjY6JzbCWBmM4BeQJqZNQic1bcFCsO92Dk3FZgKkJ2dHfYvAxG/3DNnHVMXbwip6WKrxCsvQb8ZON/MGlM+dTMAWA4sBC6j/M6bUcAsr02K1JU9+0roeue8kNqSiQM4pWkjnzoS8c7LHP1SM3uR8lsoDwErKT9Dnw08b2Z3B2pPRKJRkWirOk0zrFsbHr6iu0/diESOp7tunHOTgElVyhsAPQtN4sbC/B1c+9R7IbWN9w7BTE97ksSgT8ZK0gr3tKe//agHF53R0qeORKJDQS9J6fpnVjAn77OQmi62SqJS0EtSKSwqplfugpDamtsHcmKjFJ86Eok+Bb0kjaoXW6/v255bBnX0qRuRuqOgl4Q3/b0t3PKvNSE1TdNIMlHQS8IqKS2jw69fDam9cuMFdE5v6lNHIv5Q0EtCunLqEt7d8Hlw3K7F8Sy8ua9/DYn4SEEvCSXc057y7x5Ewwb1/WlIJAYo6CVhVL3Y+uerzmZIl9Y+dSMSOxT0EveeX7aZCTPyQmq62CryPwp6iVvFB0s587ehT3vSAmQih1PQS1y67NH/sPzTL4Lja3plcvslnXzsSCR2KeglruRt3cN3Hnk7pLbhniHUq6cFyESqo6CXuBBuAbJnf3Ievdq38KkjkfihoJeY98f5H/PA6/8NjtPTUnlnQn8fOxKJLwp6iVlF+w7S7c7XQ2qrJw2kaaoWIBM5Fgp6iUk9Jr/Bjr0HguPxgzrys77tfexIJH4p6CWmvPXxTkY+sSykpnviRbxR0EtMKCtznHZr6MXW2T+/gE5ttACZiFcKevHdrS/l8ezSzcFxr/bNefYn5/vYkUhiUdCLb8I97emjuwbRKMX7AmQzVxYwZW4+hUXFtElLZVxOFsO7p3v+vSLxSEEvvqi6ANn9I7py2TltI/K7Z64sYOKMPIpLSgEoKCpmYmAtHIW9JKN6fjcgyWXWqoLDQn5T7tCIhTzAlLn5wZCvUFxSypS5+RF7D5F4ojN6qRMHDpWSdVvoAmRv3dKPU5s1jvh7FRYVH1NdJNEp6CXqrn1qGQvzdwbHl53TlvtHdI3a+7VJS6UgTKi3SUuN2nuKxLJaB72ZZQEvVCqdBvwW+FugnglsAi53zn1R9fWS+PI/20vOQ4tDap/cM4T6UV6AbFxOVsgcPUBqSn3G5WRF9X1FYlWtg945lw90AzCz+kAB8BIwAZjvnMs1swmB8fgI9CpxpOo8/FPXnEu/jifXyXtXXHDVXTci5SI1dTMA+MQ596mZDQP6BurTgEUo6JPGE29v5K5X1gbHJzRqQN7tOXXex/Du6Qp2kYBIBf0VwHOB71s557YBOOe2mVnY0zgzGwOMAcjIyIhQG+KXvftL6HL7vJDaitsupnmThj51JCIVPAe9mR0HXAJMPJbXOeemAlMBsrOzndc+xD/fevBNPt7xVXB8Q7/TuVnz4SIxIxJn9IOB951z2wPj7WbWOnA23xrYEYH3kBj03qbdjHjs3ZDaxnuHYKanPYnEkkgE/ZX8b9oG4GVgFJAb+DorAu8hMSTc055mXN+LszNO8qkjETkST0FvZo2BbwHXVSrnAtPNbDSwGRjh5T0kttw7Zx1/WbwhOO6cfiKv3Hihjx2JyNF4Cnrn3D6geZXa55TfhSMJZMfe/fSYPD+k9uEdORzfUJ+5E4l1+q9UjuqMX7/KwdKy4PiuYZ0Y2TMz7LZaNVIk9ijopVrzPvyMMX9fEVI70tOetGqkSGxS0MthDpWWcfqvXw2pzf9VH9q3bHLE1x1p1UgFvYh/FPQS4sbnVvLv1YXB8aBOp/DYyHNq9FqtGikSmxT0AsDGXV/T7/5FIbWPJw8mpX7NH1mgVSNFYpOCPglVvWBaNZz/fNXZDOnS+ph/r1aNFIlNCvokE+6CaWVHuth6NFo1UiQ2KeiTTLgLpgCnnNiIJbd6//iDVo0UiT16ZmySCTeHDrD9y/113ImI1BUFfZJYs7XosIeBVKYLpiKJS1M3CS7cAmTH1a8X8klXXTAVSWw6o09gf5j/cUjIZzRrzKbcodx32TdJT0vFgPS0VO69tIvm1UUSmM7oPYrFtV2++Pog3e96PaS2etJAmqamALpgKpJsFPQexOLaLtl3v8Gurw4ExxMHd+S6Pu196UVEYoOC3oNYWtvlrY93MvKJZSE1L/fEi0jiUNB7EAtru5SWOdrfGnqx9dWbLuTM1ifWWQ8iEtsU9B74vbbLxBl5PLdsc3Dc+/TmPPPj8+vkvUUkfijoPfBrbZeComJ65y4IqX101yAapdSP6vuKSHxS0Hvgx9ouVT/09MCIrnzvnLZRez8RiX8Keo/q6lbFmSsL+MULq0JqutgqIjWhoI9xBw6VknXbayG1t27px6nNGvvUkYjEGwV9DBv15DLe/O/O4Pjy7Lbcd1lXHzsSkXikoI9B+Z/tJeehxSG1T+4ZQv165lNHIhLPFPQxpurF1qeuPZd+WSf71I2IJAJPQW9macDjQGfAAT8C8oEXgExgE3C5c+4LT10mgcff2sDds9cFx01TU1g9aaCPHYlIovB6Rv8w8Jpz7jIzOw5oDNwKzHfO5ZrZBGACMN7j+ySsvftL6HL7vJDaitsupnmThj51JCKJptZBb2YnAhcB1wA45w4CB81sGNA3sNk0YBEK+rAGPLCIT3Z+HRz/vP/p/N9ArQsvIpHl5Yz+NGAn8JSZdQVWADcBrZxz2wCcc9vMTBPMVby3aTcjHns3pLbx3iGY6WKriESel6BvAJwN3OicW2pmD1M+TVMjZjYGGAOQkZHhoY34Ee5pTzPH9qbbqWk+dSQiycDLE6a2Aludc0sD4xcpD/7tZtYaIPB1R7gXO+emOueynXPZLVu29NBGfLhnzrqQkO+S3pRNuUMV8iISdbU+o3fOfWZmW8wsyzmXDwwA1gb+jAJyA19nRaTTOLXjy/30uGd+SG3tnTk0Pk53topI3fCaNjcCzwTuuNkAXEv5/yVMN7PRwGZghMf3iFun3zqHQ2UuOL5reGdGnv8NHzsSkWTkKeidc6uA7DA/GuDl98a7uR9+xnV/XxFS0wJkIuIXzR94VPnh4K2bNqJwz/6Qn8//VR/at2ziU3ciIgp6T6o+HLxyyA/pcgp/vuocv1oTEQnyctdN0gv3cHCANk0bKeRFJGYo6D0I97xYgG1Vpm9ERPykoK+FvK17DltlsrK6eji4iEhNaI7+GBw8VMaghxezIbA+TYN6RoN6xv5DZcFt6uLh4CIix0JBX0PPL9vMhBl5wfHT155L36yTQ+66qYuHg4uIHCsF/VFs/3I/51X6ZOu3zmrF1JHnBBcgq6uHg4uI1JaCvhrOOX7xwipmrSoM1vRQbhGJRwr6MJZs+Jwrpi4Jjid95yyu7d3Ox45ERGpPQV9J8cFSeubOp2hfCQCtmzZi4c19aZRS3+fORERqT0Ef8Jc3P+HeVz8Kjl/8aU+yM5v52JGISGQkfdBv2vU1fe9fFBx/P/tUfnfZN/1rSEQkwpI26MvKHKOeWsZbH+8K1t779cW0PEEP5RaRxJKUQf/62u385G/Lg+MHL+/KpWe39bEjEZHoSaqg31NcQtc75gXHndqcyKyxvWlQXytBiEjiSpqgz331Ix5785Pg+NWbLuTM1if62JGISN1I+KBft+1LBj/8VnB8XZ/TmDj4TB87EhGpWwkb9IdKy7jkkXdYu+3LYG31pIE0TU3xsSsRkbqXkEE/4/2t/N/01cHx1JHnMLDTKT52JCLin4QK+p17D3Du5DeC4ws7tGDatT2oV8987EpExF8JE/TjX1zDC8u3BMeLbu5LZovjfexIRCQ2xH3Qr/h0N9979N3geMLgjvy0T3sfOxIRiS1xHfSff3UgGPJpjVN4d8IAUo/TAmQiIpV5Cnoz2wTsBUqBQ865bDNrBrwAZAKbgMudc194azO8pqkpXHfRafTJakmv9i2i8RYiInEvEh8J7eec6+acyw6MJwDznXMdgPmBcVQ0qF+PiUPOVMiLiBxBND77PwyYFvh+GjA8Cu8hIiI15DXoHTDPzFaY2ZhArZVzbhtA4OvJHt9DREQ88HoxtrdzrtDMTgZeN7OPjvqKgMBfDGMAMjIyPLYhIiLV8XRG75wrDHzdAbwE9AC2m1lrgMDXHdW8dqpzLts5l92yZUsvbYiIyBHUOujN7HgzO6Hie2Ag8AHwMjAqsNkoYJbXJqszc2UBvXMX0G7CbHrnLmDmyoJovZWISNzyMnXTCnjJzCp+z7POudfM7D1gupmNBjYDI7y3ebiZKwuYOCOP4pJSAAqKipk4Iw+A4d3To/GWIiJxqdZB75zbAHQNU/8cGOClqZqYMjc/GPIViktKmTI3X0EvIlJJ3D5aqbCo+JjqIiLJKm6Dvk1a6jHVRUSSVdwG/bicLFJTQte1SU2pz7icLJ86EhGJTXG7qFnFPPyUufkUFhXTJi2VcTlZmp8XEakiboMeysNewS4icmRxO3UjIiI1o6AXEUlwCnoRkQSnoBcRSXAKehGRBGfOOb97wMx2Ap96+BUtgF0RaicWaf/iW6LvHyT+Psbq/n3DOXfU5X9jIui9MrPllR5lmHC0f/Et0fcPEn8f433/NHUjIpLgFPQiIgkuUYJ+qt8NRJn2L74l+v5B4u9jXO9fQszRi4hI9RLljF5ERKoRV0FvZqea2UIzW2dmH5rZTYF6MzN73cw+Dnw9ye9ea+MI+3e7mRWY2arAnyF+91pbZtbIzJaZ2erAPt4RqLczs6WBY/iCmR3nd6+1cYT9e9rMNlY6ht387tULM6tvZivN7JXAOCGOX4Uw+xfXxy+ugh44BPzKOXcmcD4w1szOAiYA851zHYD5gXE8qm7/AH7vnOsW+DPHvxY9OwD0d851BboBg8zsfOB3lO9jB+ALYLSPPXpR3f4BjKt0DFf512JE3ASsqzROlONXoer+QRwfv7gKeufcNufc+4Hv91J+INKBYcC0wGbTgOH+dOjNEfYvYbhyXwWGKYE/DugPvBiox/MxrG7/EoaZtQWGAo8HxkaCHD84fP8SQVwFfWVmlgl0B5YCrZxz26A8LIGT/essMqrsH8ANZrbGzJ6M16mpCoH/LV4F7ABeBz4BipxzhwKbbCWO/4Krun/OuYpjODlwDH9vZg19bNGrh4BbgLLAuDkJdPw4fP8qxO3xi8ugN7MmwL+AXzjnvvS7n0gLs3+PAu0pnwrYBjzgY3ueOedKnXPdgLZAD+DMcJvVbVeRU3X/zKwzMBHoCJwLNAPG+9hirZnZt4EdzrkVlcthNo3L41fN/kGcH7+4C3ozS6E8BJ9xzs0IlLebWevAz1tTfiYVl8Ltn3NueyA8yoC/Uh6Occ85VwQsovx6RJqZVTzxrC1Q6FdfkVJp/wYFpuWcc+4A8BTxewx7A5eY2SbgecqnbB4icY7fYftnZv+I9+MXV0EfmAt8AljnnHuw0o9eBkYFvh8FzKrr3iKhuv2r+Ess4LvAB3XdW6SYWUszSwt8nwpcTPm1iIXAZYHN4vkYhtu/jyqdiBjl89dxeQydcxOdc22dc5nAFcAC59xVJMjxq2b/ro734xdvz4ztDYwE8gJzoAC3ArnAdDMbDWwGRvjUn1fV7d+Vgdu5HLAJuM6f9iKiNTDNzOpTfqIx3Tn3ipmtBZ43s7uBlZT/hRePqtu/BWbWkvJpjlXAT/1sMgrGkxjHrzrPxPPx0ydjRUQSXFxN3YiIyLFT0IuIJDgFvYhIglPQi4gkOAW9iEiCU9CLiCQ4Bb2ISIJT0IuIJLj/B3gyGMjdhzaKAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = plt.subplots()\n",
    "\n",
    "# Plot Dots\n",
    "ax.scatter(x, noisy_y)\n",
    "\n",
    "# Plot Best Fit Line\n",
    "_x = np.linspace(0, 20, 1000)\n",
    "ax.plot(x, x*slope+intercept)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Does a linear regression answer?\n",
    "1. How noisy the data is?\n",
    "2. What future data will look like?"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Bayes Linear Regression"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Auto-assigning NUTS sampler...\n",
      "Initializing NUTS using jitter+adapt_diag...\n",
      "Multiprocess sampling (2 chains in 2 jobs)\n",
      "NUTS: [noise_estimate, intercept_estimate, slope_estimate]\n",
      "Sampling 2 chains: 100%|██████████| 11000/11000 [00:10<00:00, 1039.37draws/s]\n",
      "The acceptance probability does not match the target. It is 0.8897258193640742, but should be close to 0.8. Try to increase the number of tuning steps.\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "(<Figure size 432x475.2 with 1 Axes>,\n",
       " array([<matplotlib.axes._subplots.AxesSubplot object at 0x1c227838d0>],\n",
       "       dtype=object))"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x475.2 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "with pm.Model() as linear_model:\n",
    "    \n",
    "    slope_estimate = pm.Normal(\"slope_estimate\", 0, 1)\n",
    "    intercept_estimate = pm.Normal(\"intercept_estimate\", 0, 1)\n",
    "    \n",
    "    # Noise is its own parameter\n",
    "    noise_estimate = pm.HalfNormal(\"noise_estimate\", 5)\n",
    "    \n",
    "    # The data follows a mean of y with a known noise\n",
    "    y_estimate = pm.Normal(\"y_estimate\",\n",
    "                           # This is what we typically get from an OLS regression\n",
    "                           mu=slope_estimate*x + intercept_estimate, \n",
    "                           \n",
    "                           # This is the characterization of the noisea\n",
    "                           sd=noise_estimate, observed=noisy_y)\n",
    "    trace_linear_regression = pm.sample(draws=5000)\n",
    "    \n",
    "\n",
    "az.plot_forest(trace_linear_regression)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(<Figure size 432x302.4 with 1 Axes>,\n",
       " array([<matplotlib.axes._subplots.AxesSubplot object at 0x1c227eb4a8>],\n",
       "       dtype=object))"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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7jr+oWze/2+/N3fSlJAuGbRNJmmnGDbgks4HPAxcBTwCeApwI3DGg7O7AZ4D/BzweeAu1W+81fUXfAPwYeBLwduCYJIu7fQT4EjAfeA6wG3Ah8LUk84ao7+OBc4EvdPVdDDwR+Nchzudi4AhgDTCvm94zxuGOAL7dncengY8DZwJf7o55IXB6kpG/JzILWA4cDDwWOBp4K/DSbv17uv2c13P8i5NsBVwArAP2BhYC1wLndeskSf1KKWNOwHbUP7my94B1i7p123fzZwBf6yuzBLimZ34Z8NW+Mh8BLur+vS+wGtiyr8yVwJuHqO8ngI/2LXtiV88dxjqfruxhwOoBy78OnNR3Hv/WM791t9//27Nsp27ZHmPU9zjgvJ7504Av9pV5GbCU7s8bdcs2A24EDh6nTSSpNeNmVyll/Du4Up89nQac03WLvSHJjqMUfyzwX33LLgLm93YRApf0lbkEeFz3792BrYDru26+1d2gj12BR4xX3277l/RtO1KnR0zwfMbz/ZF/lFJWU+/8ftCzfkX3c4eRBUkOT3JZkuu7ur0eeOgQ57QzsKrnnH4HbMtwbSJJM85Qg0xKKS9N8j5gf+B5wLuSHAjc2lc0jP4HNof9w5uzqMHwjAHrbhly+48AJwxYtxxGP59SyjlD1nHEbX3zpW/ZyDmPPGM7BHgfcCS1O/QW4NXAX4xznFnUO9gXDVjn4BdJGmDoUZSllO8B3wPeneRs6mCIU/uK/QjYs2/ZntQuylU9y57aV+ap1GdyAFcAc4E7Sym/GLZ+Pa4Adiml/HysQqOczznAH6jdf1NhT+DSUkrvYJX+O7BBx78C+EvghlLKyimqmyQ1ZZhBJjsnOa4bmfiwJPsAf0INs37HA3t3oyQfleTFwBuBf+4r99QkRyVZkOR/A3/N3Xdc51G7FD+f5IDu+AuT/GOSQXd1/d4NPDnJh5LsluSRSZ6T5JQhz2cZsEWS/ZJsP8mDOH4GPKk7rwVJ3kYdNNJrGbBrkkd3x9+c+mxzBbVN9u7OYa8kxzuSUpIGG+ZrAmuAR1FHR/6MOlLwDGqQ3EMp5QrghcBBwA+pAyiOA/p/A8h7qaHyXeCdwD+UUv6j20cBngV8Dfgw8FPqyMJHA78Zr7KllO8De1EHeHyDepd2LHc/DxvzfEopFwMfAv4NuB5483jHnIBTqOdyJvCdro7H95X5MPVu9rLu+E8vpazpzukXXb1/0tV7W+DmSayfJDUjNU824gGTZdTRiGMNv9fk2bgvsCRNvYxfxF/VJUlq1H0u4JKc3fsVgL7prdNdP0nSpmGjd1FuqCTzgS1HWX1T8XdG9rtvvcCSNL6huijvcwGnCfMFltQan8FJkmYuA06S1CQDTpLUJANO0ga7btU6Lr/6Zq5btW66qyLdxb/oLWmDfO67y1ly1lU8bLutuPqmNSx57i4cuNv86a6W5CjKGWC9X+BDTun/q0aaKtfcvIblK++bdz9bzJ7FWa/dkwVzt2HpilU89/0Xse72O6e7WkOZP2cLHrKtfzN4Y/n3Vy6crF05ilLS1Js3Z0sWzN0GgAVzt2HenNG+piptXHZRalST+GlL4zjhqz/jxPOXTnc11su1K9eydMWqu+7grl25drqrNLQX7L4jr9/vUdNdDU0Ruyjb5wusKeUzOE0Df5OJAANOG8F1q9bx65vWsuN2W7LDNltMd3XUPgNOgAEnqT0OMpEkzVwGnCSpSQacJKlJBpwkqUkGnCSpSQacJKlJBpwkqUkGnCSpSQacJKlJBpwkqUkGnCSpSQacJKlJBpwkqUkGnCSpSQacJKlJBpwkqUkGnCSpSQacJKlJBpwkqUkGnCSpSQacJKlJBpwkqUkGnCSpSQacJKlJBpwkqUkGnCSpSQacJKlJBpwkqUkGnCSpSQacJKlJBpwkqUkGnCSpSQacJKlJBpwkqUkGnCSpSQacJKlJBpwkqUkGnCSpSQacJKlJBpwkqUkGnCSpSQacJKlJBpwkqUkGnCSpSQacJKlJBpwkqUkGnCSpSQacJKlJBpwkqUkGnCSpSQacJKlJBpwkqUkGnCSpSQacJKlJBpwkqUkGnCSpSQacJKlJBpwkqUkGnCSpSQacJKlJBpwkqUkGnCSpSQacJKlJBpwkqUkGnCSpSQacJKlJBpwkqUkGnCSpSQacJKlJBpwkqUkGnCSpSQacJKlJBpwkqUkGnCSpSQacJKlJBpwkqUkGnCSpSQacJKlJBpwkqUkGnCSpSQacJKlJBpwkqUkGnCSpSQacJKlJBpwkqUkGnCSpSQacJKlJBpwkqUkGnCSpSQacJKlJBpwkqUkGnCSpSQacJKlJBpwkqUkGnCSpSQacJKlJBpwkqUkGnCSpSQacJKlJBpwkqUkGnCSpSQacJKlJBpwkqUkGnCSpSQacJKlJBpwkqUkppUx3HTSFknwF2H6U1dsDN2zE6txX2C6D2S6D2S6DTWW73FBK2X+8QgbcDJbkslLKHtNdj02N7TKY7TKY7TLYptAudlFKkppkwEmSmmTAzWynTncFNlG2y2C2y2C2y2DT3i4+g5MkNck7OElSkww4SVKTDDhJUpMMuAYkOSrJd5LckuT6JGcl2XWcbRYl+XySa5OsSfL9JC8bUKYMmB4ztWc0OdazXR6X5IIkK5KsS/KLJMckuV9fub2TXN5T5vCpPZvJM1XtMhOvl77tFyRZlWT1gHUz6nrp235gu2yM68WAa8Mi4IPA04B9gduB85JsN8Y2TwN+ALwA2BU4GTg1yV8NKLsLMK9nWjppNZ9ai5h4u/wB+DjwZ8CjgSOAlwPvHCmQZGfgy8DFwG7AscD7kxw0+acwJRYxBe3SYyZdLwB0Qf8p4MIB62bi9QKM3S49pux6cRRlg5JsDfwOOLCUctYEtvs0sFkp5aBufhFwAfDgUsp9/lcRbUC7vBdYWEpZ2M2/G1hcSlnQU+YjwC4jZe5LJrFdFjFDr5ckJwBzgG8AJ5VStu5ZN2Ovl3HaZRFTfL14B9embaiv7c0T3O6Bo2xzWdeVeX6SfTa4dtNnwu2S5JHA/tT/oCMWAuf2FT0H2CPJ5htayWkwWe0yYkZdL0meDTwH+LtRiszI62WIdhkxZdeLAdemE4ErgUuG3SDJc4A/5Z5fzrwW+FvgIGAx8FPg/CR7TV5VN6qh2yXJxUnWUbtLLgLe2rP6j4EVfZusAGYz+i+23pRNVrvMuOslyTzgw8ChpZRVoxSbcdfLkO0y5dfL7MnakTYNXbfRnsCepZQ7htzm6cCZwN+VUr49sryU8lPqRTfikiQ7AUcydp/6Jmc92uUQ6ifVJwD/Avwf6rOTEf19+xll+SZtMttlhl4vpwMnl1K+Nc4uZ9r1Mm67bJTrpZTi1MgEnED9VPSYCWyzJ3ALcMSQ5d8O/Hi6z3Wq26Vv+5cA64DZ3fyFwAf6yrwQuA3YfLrPd7raZSZeL9SAur1nuqNn2d/M1OtlmHbZGNeLd3CNSHIi8CJgUSnlJ0NusxfwJWBJKeV9Qx7qidSL/D5hfdplgFnU3o7NqP9BLwEO7CuzH3BZKeW29a3rxjRF7TJI69fL4/vmnw8cDTwZWN4tm4nXyzDtMsjkXi/T/anAacMn4APUu7B9qf39I9PWPWWOBc7vmV8E/J7azdS7zYN7yhxB/Y+5gDqU91jqp7DF033OU9guh1I/XT8GeDhwMPU/5Kd6yuzctd37gMcCr6AOoz9ous95mttlxl0vA/ZxGLC6b9mMu16GbJcpv16mvfGcJuFFrBfFoGlJT5nTgGV984O26S3zZuDnwFrgJuCbwLOm+3ynuF3+ErgCWAWsBq6iDqTYsm/fe3flbgV+CRw+3ec73e0yE6+XAfu41xv5TLxehmmXjXG9+D04SVKT/JqAJKlJBpwkqUkGnCSpSQacJKlJBpwkqUkGnCSpSQacJKlJBpwkqUn/H1B9USO06cobAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<Figure size 432x302.4 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "az.plot_forest(trace_linear_regression, var_names = [\"slope_estimate\"])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Simulating Draws through Posterior Predictive sampling\n",
    "Bayes Models are generative meaning you're able to generate what new "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "100%|██████████| 2000/2000 [00:02<00:00, 801.62it/s]\n"
     ]
    }
   ],
   "source": [
    "ppc = pm.sample_posterior_predictive(trace_linear_regression, samples=2000, model=linear_model)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(2000, 10)"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "ppc[\"y_estimate\"].shape"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Plot uncertainty with data\n",
    "Uncertainty estimates give us range estimates that can characterize either  the underlying noise, or the uncertainty due to a low number of observations.\n",
    "Note: In making this tutorial I ran into a possible bug in ArviZ. Hopefully we don't hit it in the tutorial."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x1c22b34668>]"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1440x720 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = plt.subplots(figsize=(20,10))\n",
    "\n",
    "az.plot_hpd(x, ppc['y_estimate'], credible_interval=0.5, color='gray', ax=ax)\n",
    "az.plot_hpd(x, ppc['y_estimate'], credible_interval=0.94, color='gray', ax=ax)\n",
    "plt.plot(x, noisy_y, 'b.', markersize=20)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Are there real world examples?\n",
    "\n",
    "Let's just jump to the best [public example I've seen](https://render.githubusercontent.com/view/ipynb?commit=bde6534c5543ca4af56fd19e845c4d6193b064ec&enc_url=68747470733a2f2f7261772e67697468756275736572636f6e74656e742e636f6d2f43616d4461766964736f6e50696c6f6e2f50726f626162696c69737469632d50726f6772616d6d696e672d616e642d426179657369616e2d4d6574686f64732d666f722d4861636b6572732f626465363533346335353433636134616635366664313965383435633464363139336230363465632f43686170746572315f496e74726f64756374696f6e2f4368315f496e74726f64756374696f6e5f50794d43332e6970796e62&nwo=CamDavidsonPilon%2FProbabilistic-Programming-and-Bayesian-Methods-for-Hackers&path=Chapter1_Introduction%2FCh1_Introduction_PyMC3.ipynb&repository_id=7607075&repository_type=Repository#Introducing-our-first-hammer:-PyMC3) in Bayesian Method for Hackers written by Cam Davidson Pilon"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Benefits of Bayesian Modeling (From this lecture)\n",
    "1. Uncertainty estimates help statistician further decide how much can be inferred from data\n",
    "2. Generative modeling allows simulation of what the future will look like with past data\n",
    "3. Ability to create models for different situations (or data generating methods) flexibly"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Modeling heteroskedastic data\n",
    "This one's a more challenging exercise. Using your Bayesian skills"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(array([6, 1, 4, 4, 8, 4, 6, 3, 5, 8]),\n",
       " array([23.01355124, 12.18172848, 18.78593725, 17.0552393 , 26.14391008,\n",
       "        17.43500406, 22.06267001, 15.19505251, 21.38294233, 26.61906054]))"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.random.seed(0)\n",
    "sample_size = 300\n",
    "\n",
    "# Generate random values between 1 and 50\n",
    "x = np.random.randint(1, 10, sample_size)\n",
    "\n",
    "intercept = 10\n",
    "slope = 2\n",
    "\n",
    "# Generate y values using out slope and intercept\n",
    "y= x * slope + intercept\n",
    "\n",
    "# Add some noise in using a zero centered Gaussian/Normal Distribution\n",
    "noise = .2\n",
    "noisy_y = y + stats.norm(0, noise).rvs(sample_size)*x\n",
    "\n",
    "x[:10], noisy_y[:10]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x1c22f77ba8>]"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = plt.subplots()\n",
    "\n",
    "# Plot Dots\n",
    "ax.scatter(x, noisy_y)\n",
    "\n",
    "# Plot Best Fit Line\n",
    "_x = np.linspace(0, 20, 1000)\n",
    "ax.plot(x, x * slope + intercept)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Fill in model here\n",
    "Fit a bayes model to recover the noise coefficient to understand how our process variability increases over time. Use posterior plots to check if you're able to get the value from above.\n",
    "Hint:\n",
    "* Think about what is different here from constant varying noise linear model\n",
    "* How would you express the difference to a Bayes Model\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Insert model!"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Additional Advanced Topics\n",
    "\n",
    "### Hierachial Regressions\n",
    "Bayesian Methods allow for a concept of hierarchial pooling, where multiple subgroups can share inforation from a pooled group. This is a great way to make the most of sparse datasets. A good example of this is Radon Levels in basements, where many counties only have a couple measurements, but overall there are a couple hundred measurements. \n",
    "\n",
    "### Other Bayesian Model Types\n",
    "* Gaussian Processes\n",
    "* Mixture Modeling\n",
    "* Bayesian Ordinary Differential Equations\n",
    "* Bayesian Survival Analysis\n",
    "* Bayesian Neural Networks\n",
    "* Others I'm sure I'm missing\n",
    "\n",
    "### Decision Analysis\n",
    "The generative model part becomes really great with decision analysis, which lets you optimize future choices. An example [optimizing the best place to buy material from](http://canyon289.github.io/BayesianDecisionMaking.html#BayesianDecisionMaking)\n",
    "\n",
    "### You get to work with an amazing group of people making cool open source software to freely share knowledge with the world!!!!\n",
    "Ok sure this one doesn't look like the others, but really the people I've worked interacted with in the Bayesian community are fantastic. If you're looking to join an open source community I've found no better. Feel free to reach out to me or check out the contributing guide on the repos. Or show up to PyDataLA where we are running open source sprints!"
   ]
  }
 ],
 "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": "3.6.8"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 4
}