Blog Post 1 final.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Frequentist vs Bayesian Statistics: a Practical Introduction to Parameter Estimation with Python\n",
    "\n",
    "### Parameter estimation is a critical component of statistical inference, data science, and machine learning workflows. Though this topic can be complex, we offer an introduction to the process comparing two approaches with some theory and some code."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "%%capture\n",
    "#Install Plotly\n",
    "# !pip install plotly"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "A parameter is a variable that governs the relationship between an input variable (sometimes also called a predictor or an independent variable) and an output variable (also know as an outcome or a dependent variable). We rarely have complete information, and thus we are forced to come up with ways in which we can understand the relationship between the information we do have access to (our predictor variables) and the information we are trying to predict (our outcome variable).\n",
    "\n",
    "$Y = f_\\theta(X) $\n",
    "\n",
    "Although the true value of the parameter is inherently unknowable, we can work with their approximations and in this blog post, we're going to look at two different approaches to doing so. We'll start with the Frequentist -  or Classical approach- using Maximum Likelihood Estimation (MLE) before moving on to the Bayesian framework for parameter estimation. Our intention is not to argue in favor of one approach or another, but rather to explain the difference in workflows and begin a more general discussion around statistical inference and what we are trying to accomplish as statistical practitioners.\n",
    "\n",
    "## The Binominal Distribution\n",
    "We'll center this discussion around the example of a coin-flip (as is mandatory of any statistics text). Specifically, we are interested in accurately predicting how often a coin will come up heads, or the probability that a coin will come up heads in a given flip. In this case, the outcome of our coin-flip is our random variable and it can take on the value of 0 (Tails) or 1 (Heads).\n",
    "The outcome of a single coin-flip then can be modeled as a Bernoulli process where Y  is the outcome of an individual coin flip with two potential values, heads or tails. Formally, we have:\n",
    "\n",
    "$Y\\sim Bernoulli(p)$\n",
    "\n",
    "In this context, p is the probability of the coin coming up heads, and this is our parameter of interest. Our task will be to estimate p as precisely as possible.\n",
    "As such, we have:\n",
    "\n",
    "$P(\\text{Y = 1 or Heads}) = p$\n",
    "\n",
    "$P(\\text{Y=0 or Tails}) = 1-p$\n",
    "\n",
    "So, given a coin, how would we estimate p? \n",
    "\n",
    "For now, we aren't going to give you any additional information about this coin, and we'll discuss later on why this is important. For now though, we'll want to come up with ways in which we can get more information about p, we need to observe some data! In this case, we'll obtain data by, well, flipping the coin. \n",
    "We could just flip the coin once but this wouldn't be very informative. Imagine that the truth is that p=0.5 and after one flip we observe a head. \n",
    "\n",
    "If we only relied on that one flip for our information, we might conclude that p=1, so that the probability of flipping heads is 100%, and we'd flip heads all the time! In fact this is the answer that the Frequentist approach would give us, but more on that later.\n",
    "What we'll want to do instead is observe a lot of flips. Suppose that we conduct n independent coin-flips, where each coin-flip is of course a Bernoulli random variable. Of those n flips, the total number of heads, X, is a binomial random variable with parameters n and p (the number of trials, or coin flips and the probability of success, or the probability of tossing heads).\n",
    "Formally, we have:\n",
    "\n",
    "$Y\\sim Binomial(n, p)$\n",
    "\n",
    "$P(Y) = {n \\choose y} p^y(1-p)^{n-y} $\n",
    "\n",
    "By flipping the coin over and over again, we'll be able to gain more and more information about our parameter of interest, p. \n",
    "\n",
    "## Simulating Data\n",
    "Let's assume we have a biased coin that has a 60% probability of flipping heads, and we want to estimate that probability. We can use the scipy.stats library to draw outcomes from the Binomial distribution.\n",
    "Simulations are very useful because we can hard-code the \"true\" parameters, which then allows us compare how different frameworks compare in approximating the parameter.\n",
    "\n",
    "Let's simulate 10000 coin flips and observe some results."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "data": {
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\n",
      "text/plain": "<Figure size 432x288 with 1 Axes>"
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "import numpy as np\n",
    "import scipy.stats as stats\n",
    "from matplotlib import pyplot as plt\n",
    "np.random.seed(42) # set seed for reproducibility\n",
    "# Set the probability of heads = 0.6\n",
    "p = 0.6\n",
    "# Flip the Coin 10000 times and observe the results\n",
    "n_trials = 10000\n",
    "data = stats.bernoulli.rvs(p, size = n_trials)\n",
    "# plot results\n",
    "plt.hist(data);"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": "6108"
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sum(data)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "As expected, the split between heads and tails is close to 60/40, and that's simply because we've coded the parameter that way! \n",
    "\n",
    "Now that we have our data, let's compare how the Frequentist and Bayesian approaches obtain the parameter of interest: _p_.\n",
    "\n",
    "## The Frequentist Approach\n",
    "\n",
    "Frequentist statistics uses MLE. While a full treatment of MLE is outside the scope of this blog post, its working is in its name: it fits a model that maximizes the likelihood of having observed the observed data.\n",
    "\n",
    "For the Binomial distribution, the MLE is the sample proportion of success.[1]\n",
    "\n",
    "$\\text{MLE} = \\frac{\\text{Number of successes}}{\\text{Number of trials}}$\n",
    "\n",
    "As such the standard error is simply the standard deviation scaled by $\\sqrt{N}$. \n",
    "\n",
    "So S.E. =  $\\sqrt{\\frac{p*(1-p)}{N}}$\n",
    "\n",
    "We can find our 95% confidence intervals simply by multiplying the standard error with the 95% Z-stat, which is equal to 1.96.\n",
    "\n",
    "$\\text{S.D.} = \\sqrt{p*(1-p)}$\n",
    "\n",
    "$\\text{S.E.} =  \\sqrt{\\frac{p*(1-p)}{N}}$\n",
    "\n",
    "$\\text{C.I Bounds} = \\text{MLE} \\pm 1.96*\\text{S.E.}$\n",
    "\n",
    "Let's look at what happens when we toss 10 coins. Since we've already simulated 10000 coin flips above, we can directly use the first 10 flips from the results."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "i = 10\n",
    "results = {}\n",
    "sample = data[:i]\n",
    "p_estimated = np.mean(sample)\n",
    "q_estimated = 1 - p_estimated\n",
    "standard_error = np.sqrt(p_estimated*q_estimated)/np.sqrt(i)\n",
    "ci = 1.96*standard_error \n",
    "# store results in a dict\n",
    "results['number_of_heads'] = sample.sum()\n",
    "results['p_estimated'] = p_estimated\n",
    "results['q_estimated'] = q_estimated\n",
    "results['standard_error'] = standard_error\n",
    "results['low'] = p_estimated - ci\n",
    "results['high'] = p_estimated + ci"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": "<Figure size 432x432 with 1 Axes>"
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "import matplotlib.lines as mlines\n",
    "\n",
    "fig, axs = plt.subplots(figsize = (6,6))\n",
    "\n",
    "axs.axvline(results['p_estimated'], color = 'red', linestyle = \"dashed\")\n",
    "axs.axvline(0.6, color = 'green', linestyle = \"solid\")\n",
    "axs.axvline(results['low'], color = 'blue', linestyle='dotted')\n",
    "axs.axvline(results['high'], color = 'blue', linestyle='dotted')\n",
    "axs.get_yaxis().set_visible(False)\n",
    "axs.title.set_text(\"$ n = $\" + str(i) + \", $heads = $\" + str(results['number_of_heads']))\n",
    "axs.text(results['p_estimated'] - 0.1, 0.5, 'MLE = ' + str(np.round(results['p_estimated'], 2)), \n",
    "         horizontalalignment='center', verticalalignment='center', transform=axs.transAxes)\n",
    "\n",
    "blue_line = mlines.Line2D([], [], color='blue',\n",
    "                          markersize=15, label='Confidence Interval')\n",
    "red_line = mlines.Line2D([], [], color='red',\n",
    "                          markersize=15, label='MLE')\n",
    "green_line = mlines.Line2D([], [], color='green',\n",
    "                          markersize=15, label='True p')\n",
    "\n",
    "axs.legend(handles = [red_line, blue_line, green_line], loc=2);"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "fig.savefig('mle1')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Because we have observed 5 heads, the MLE is 0.5 (recall that the true value of p is 0.6). \n",
    "\n",
    "The uncertainty is captured by the confidence intervals, which indicate that the true value of p has a 95% probability of being between ~ 0.2 and ~ 0.8. \n",
    "\n",
    "Since the confidence intervals are proportional to the sample size, we can expect them to shrink as the number of coin flips increases - the more data we have the more confident we are about our predictions. \n",
    "\n",
    "To illustrate that, let's see what happens when we flip increasingly large amounts of coins."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": "<Figure size 1080x1080 with 10 Axes>"
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "full_results = []\n",
    "steps = [1, 10, 25, 50, 100, 500, 1000, 5000, 7500, 10000]\n",
    "\n",
    "for i in steps:\n",
    "    results = {}\n",
    "    sample = data[:i]\n",
    "    p_estimated = np.mean(sample)\n",
    "    q_estimated = 1 - p_estimated\n",
    "    standard_error = np.sqrt(p_estimated*q_estimated)/np.sqrt(i)\n",
    "    ci = 1.96*standard_error\n",
    "    \n",
    "    results['size'] = i\n",
    "    results['number_of_heads'] = sample.sum()\n",
    "    results['p_estimated'] = p_estimated\n",
    "    results['q_estimated'] = q_estimated\n",
    "    results['standard_error'] = standard_error\n",
    "    results['low'] = p_estimated - ci\n",
    "    results['high'] = p_estimated + ci\n",
    "    full_results.append(results)\n",
    "    \n",
    "# plot figure\n",
    "figs,axs = plt.subplots(5, 2, figsize=(15,15))\n",
    "\n",
    "axes = [(0,0),(0,1), (1,0), (1,1), (2,0), (2,1), (3,0), (3,1), (4,0), (4,1)]\n",
    "\n",
    "for i,sample in enumerate(full_results):\n",
    "    axs[axes[i]].axvline(sample['p_estimated'], color = 'red', linestyle ='dotted')\n",
    "    axs[axes[i]].axvline(0.6, color = 'green', linestyle = 'solid')\n",
    "    axs[axes[i]].axvline(sample['low'], color = 'blue', linestyle='dashed')\n",
    "    axs[axes[i]].axvline(sample['high'], color = 'blue', linestyle='dashed')\n",
    "    axs[axes[i]].get_yaxis().set_visible(False)\n",
    "    axs[axes[i]].title.set_text(\"$ n = $\" + str(sample['size']) + \", $heads = $\" + str(sample['number_of_heads']))\n",
    "    axs[axes[i]].text(sample['p_estimated'] - 0.22, 0.5, 'MLE = ' + str(np.round(sample['p_estimated'], 2)), \n",
    "    horizontalalignment='center', verticalalignment='center', transform=axs[axes[i]].transAxes)\n",
    "\n",
    "blue_line = mlines.Line2D([], [], color='blue',\n",
    "                          markersize=15, label='Confidence Interval')\n",
    "red_line = mlines.Line2D([], [], color='red',\n",
    "                          markersize=15, label='MLE')\n",
    "green_line = mlines.Line2D([], [], color='green',\n",
    "                          markersize=15, label='True p')\n",
    "\n",
    "figs.legend(handles = [red_line, blue_line, green_line], loc=2)\n",
    "figs.tight_layout();"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In the plots above, we take snapshots of our results after 1 flip, 10 flips, 25 flips, and so on up to 10,000 flips. Within each snapshot, we plot our Maximum Likelihood Estimate using our data up until that point, that is the red line each plot (note that this is always simply the proportion of heads to total number of flips). In addition to the MLE, we've also plotted our 95% confidence interval for our estimate, this is represented by the two dotted blue lines. These plots give us an idea of how our estimates, and our confidence in those estimates, change as we flip the coin a repeated number of times.\n",
    "\n",
    "As we continue to flip the coin over and over again, we gain more and more information about that coin's behavior. As a result, we should expect our estimates to become more and more precise, as well as more accurate. When we've only flipped the coin a couple of times (say 1 to 100 times), we can see that our confidence interval is quite wide. This is because we simply haven't seen enough information to rule out the likelihood that the true probability of heads lies somewhere to the sides of our current MLE. However, as we continue the flip the coin and observe more and more evidence about our parameter of interest, we see our confidence interval starting to narrow and hug the MLE. By the time we've flipped the coin 10,000 times, our confidence interval is only slightly to the side of our MLE. \n",
    "\n",
    "Let's think about this intuitively: as we begin to gain more evidence, we should become increasingly confident in our estimates. Additionally, and most important, we should expect our estimate to get closer and closer to the truth! This is the law of large numbers: as the size of a sample increase, its parameter estimand gets closer to the true value of the whole population. This is confirmed by the knowledge that we set the true probability of heads to 0.6, and indeed our MLE estimate after just 1,000 flips is 0.61 and it does not waver after this (only the confidence interval narrows).\n",
    "\n",
    "## The Bayesian Approach\n",
    "\n",
    "The material in this section - especially the simulation code is heavily indebted to https://tinyheero.github.io/2017/03/08/how-to-bayesian-infer-101.html [2].\n",
    "\n",
    "As a refresher, recall that Bayes' Theorem estimates model parameters by establishing them as a distribution conditional on the data we have observed.\n",
    "\n",
    "$P(\\theta|X) = \\frac{P(X|\\theta)P(\\theta)}{P(X)} = \\frac{P(X , \\theta)}{P(X)}$\n",
    "\n",
    "- P(θ) is the prior distribution of our model parameters, which represents our opinions about the relationship between our outcome and predictor variables before we've seen any data. \n",
    "\n",
    "- P(X|θ) is the likelihood term, indicating how well the prior fits the observed data. \n",
    "\n",
    "- P(X) is the marginal distribution of the predictor variables. In other words, it represents the probability of having observed the data given all the possible values for θ. When dealing with discrete distributions, P(X) can be obtained by summing over all values of θ; in the continuous case it is obtained by integrating over θ.\n",
    "\n",
    "## The Prior\n",
    "\n",
    "The first step of the Bayesian workflow is specifying what our prior beliefs are about the outcome variable. For this example, this means encoding our beliefs about the probability that a coin flip comes up heads: that's right - we're putting a probability on a probability."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": "<div>\n<style scoped>\n    .dataframe tbody tr th:only-of-type {\n        vertical-align: middle;\n    }\n\n    .dataframe tbody tr th {\n        vertical-align: top;\n    }\n\n    .dataframe thead th {\n        text-align: right;\n    }\n</style>\n<table border=\"1\" class=\"dataframe\">\n  <thead>\n    <tr style=\"text-align: right;\">\n      <th></th>\n      <th>Theta</th>\n      <th>Probability</th>\n    </tr>\n  </thead>\n  <tbody>\n    <tr>\n      <th>0</th>\n      <td>0.0</td>\n      <td>0.00</td>\n    </tr>\n    <tr>\n      <th>1</th>\n      <td>0.1</td>\n      <td>0.04</td>\n    </tr>\n    <tr>\n      <th>2</th>\n      <td>0.2</td>\n      <td>0.08</td>\n    </tr>\n    <tr>\n      <th>3</th>\n      <td>0.3</td>\n      <td>0.12</td>\n    </tr>\n    <tr>\n      <th>4</th>\n      <td>0.4</td>\n      <td>0.16</td>\n    </tr>\n    <tr>\n      <th>5</th>\n      <td>0.5</td>\n      <td>0.20</td>\n    </tr>\n    <tr>\n      <th>6</th>\n      <td>0.6</td>\n      <td>0.16</td>\n    </tr>\n    <tr>\n      <th>7</th>\n      <td>0.7</td>\n      <td>0.12</td>\n    </tr>\n    <tr>\n      <th>8</th>\n      <td>0.8</td>\n      <td>0.08</td>\n    </tr>\n    <tr>\n      <th>9</th>\n      <td>0.9</td>\n      <td>0.04</td>\n    </tr>\n    <tr>\n      <th>10</th>\n      <td>1.0</td>\n      <td>0.00</td>\n    </tr>\n  </tbody>\n</table>\n</div>",
      "text/plain": "    Theta  Probability\n0     0.0         0.00\n1     0.1         0.04\n2     0.2         0.08\n3     0.3         0.12\n4     0.4         0.16\n5     0.5         0.20\n6     0.6         0.16\n7     0.7         0.12\n8     0.8         0.08\n9     0.9         0.04\n10    1.0         0.00"
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "import pandas as pd\n",
    "# generate the prior values\n",
    "theta_values = list(np.linspace(0,1,11))\n",
    "vals_pmin = np.minimum(np.linspace(0,1,11), np.linspace(1,0,11))\n",
    "theta_probabilities = vals_pmin/sum(vals_pmin)\n",
    "prior_distribution_df = pd.DataFrame(list(zip(theta_values, theta_probabilities)), columns = (\"Theta\", \"Probability\"))\n",
    "\n",
    "prior_distribution_df"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [],
   "source": [
    "probabilities = [0, 0.04, 0.08, 0.12, 0.16, 0.2, 0.16, 0.12, 0.08, 0.04, 0]\n",
    "def generate_prior_df(theta_values = np.linspace(0,1,11), theta_probabilities = probabilities):\n",
    "    prior_distribution_df = pd.DataFrame(list(zip(theta_values, theta_probabilities)), columns = (\"Theta\", \"Probability\"))\n",
    "    return prior_distribution_df\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": "<div>\n<style scoped>\n    .dataframe tbody tr th:only-of-type {\n        vertical-align: middle;\n    }\n\n    .dataframe tbody tr th {\n        vertical-align: top;\n    }\n\n    .dataframe thead th {\n        text-align: right;\n    }\n</style>\n<table border=\"1\" class=\"dataframe\">\n  <thead>\n    <tr style=\"text-align: right;\">\n      <th></th>\n      <th>Theta</th>\n      <th>Probability</th>\n    </tr>\n  </thead>\n  <tbody>\n    <tr>\n      <th>0</th>\n      <td>0.0</td>\n      <td>0.00</td>\n    </tr>\n    <tr>\n      <th>1</th>\n      <td>0.1</td>\n      <td>0.04</td>\n    </tr>\n    <tr>\n      <th>2</th>\n      <td>0.2</td>\n      <td>0.08</td>\n    </tr>\n    <tr>\n      <th>3</th>\n      <td>0.3</td>\n      <td>0.12</td>\n    </tr>\n    <tr>\n      <th>4</th>\n      <td>0.4</td>\n      <td>0.16</td>\n    </tr>\n    <tr>\n      <th>5</th>\n      <td>0.5</td>\n      <td>0.20</td>\n    </tr>\n    <tr>\n      <th>6</th>\n      <td>0.6</td>\n      <td>0.16</td>\n    </tr>\n    <tr>\n      <th>7</th>\n      <td>0.7</td>\n      <td>0.12</td>\n    </tr>\n    <tr>\n      <th>8</th>\n      <td>0.8</td>\n      <td>0.08</td>\n    </tr>\n    <tr>\n      <th>9</th>\n      <td>0.9</td>\n      <td>0.04</td>\n    </tr>\n    <tr>\n      <th>10</th>\n      <td>1.0</td>\n      <td>0.00</td>\n    </tr>\n  </tbody>\n</table>\n</div>",
      "text/plain": "    Theta  Probability\n0     0.0         0.00\n1     0.1         0.04\n2     0.2         0.08\n3     0.3         0.12\n4     0.4         0.16\n5     0.5         0.20\n6     0.6         0.16\n7     0.7         0.12\n8     0.8         0.08\n9     0.9         0.04\n10    1.0         0.00"
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "generate_prior_df()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [
    {
     "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": [
    "def plot_distribution(df, title: str, likelihood = False):\n",
    "    \"\"\"\n",
    "    Simple helper functions to plot prior, likelihood and posterior distributions\n",
    "    \"\"\"\n",
    "    plt.scatter(df.iloc[:,0], df.iloc[:,1], color = 'blue')\n",
    "    for i in range(len(df)):       \n",
    "        plt.vlines(x = df.iloc[:i,0], color = 'blue', ymin = 0, ymax = df.iloc[:i,1])\n",
    "    \n",
    "    if likelihood:\n",
    "        plt.ylabel(\"Likelihood\")\n",
    "    else:\n",
    "        plt.ylabel(\"Probability\")\n",
    "    plt.xlabel(\"Probability of Flipping Heads\")\n",
    "    plt.title(title)\n",
    "\n",
    "plot_distribution(prior_distribution_df, title = \"Prior Distribution\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The prior distribution encapsulates our ideas around the probability of hitting heads without having seen any of the data. For the sake of simplicity, we are going to allow θ to only take on 10 values of 0.1 increments from 0 to 1. We're going to assume that we do not know that the coin is biased, and nothing indicates that it would be.\n",
    "\n",
    "Consequently, let's build a distribution that is peaked at 0.5, with a value of 0.2: we are saying that there is a 20% chance that the coin is fair. We are also entertaining the possibility that the coin might not be fair, and that is reflected in the probabilities for θ ranging from 0.1 to 0.9. The only scenarios we believe not to be possible are those where p is equal to 0 (no chance of NEVER flipping heads) or 1 (no chance of ALWAYS flipping heads).\n",
    "\n",
    "## The Likelihood\n",
    "Let's now look at the likelihood, which updates the prior with the observed data in our sample. The equation for the binomial likelihood is simply its Probability Mass Function (PMF) [3].\n",
    "\n",
    "$L(p|n, y) = {n \\choose y} p^y(1-p)^{n-y} $\n",
    "\n",
    "In the equation above, p is the probability of success (drawn from our prior distribution θ), n is the number of coin flips and y is the number of heads. For each value of theta in the parameter space, the likelihood function evaluates the probability of that theta value, given the data we've just observed. As an example, if we've observed 1 heads, then the likelihood of p= 0 must be 0 - since we've observed at least 1 heads, then the likelihood of NEVER flipping heads has to be 0.\n",
    "\n",
    "We'll keep the same first 10 data points from the previous example, so we have 5 heads out of 10 flips."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [
    {
     "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": [
    "def create_likelihood_df(n, heads, prior_df):\n",
    "    \"\"\"\n",
    "    Create a Binomial likelihood probability distribution dataframe \n",
    "    Parameters\n",
    "    ----------\n",
    "    n : The number of coin iid coin flips\n",
    "    heads : The number of heads in n flips\n",
    "    prior_df -  Dataframe containing a vector of theta values for the binomial distribution\n",
    "    \"\"\"\n",
    "    likelihood_vals = stats.binom.pmf(heads, n, prior_df.Theta)\n",
    "    likelihood_df = pd.DataFrame(list(zip(prior_df.Theta, likelihood_vals)), columns=('Theta', 'Likelihood'))\n",
    "\n",
    "    return likelihood_df\n",
    " \n",
    "likelihood_df = create_likelihood_df(10, 5, prior_distribution_df)\n",
    "plot_distribution(likelihood_df, title =  \"Likelihood Distribution\", likelihood = True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {},
   "outputs": [
    {
     "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": [
    "likelihood_df = create_likelihood_df(500, 293, prior_distribution_df)\n",
    "plot_distribution(likelihood_df, title =  \"Likelihood Distribution\", likelihood = True)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "You'll notice that the likelihood is peaked around 0.5, with values further away from it getting increasingly smaller. That makes sense: the likelihood has updated our prior beliefs about θ with the data, which have shown that for 5 out of 10 flips were heads - given the data we've observed, the most likely true value of theta is 0.5. Thus 0.5 will get the highest likelihood. Vice-versa, values such as 0.1 and 0.9 are very unlikely of being the true value, and we see that reflected in the chart accordingly. In turn, values at the extreme are not corroborated by the data, and are consequently given very small likelihood values.\n",
    "\n",
    "It is important to note however, that the likelihood is not a valid probability distribution. You can check that yourself by summing all of the probabilities for θ, the result does not add to 1! That's where the normalizing constant / denominator comes in: dividing each likelihood probabilities by the normalizing constant (which is a scalar) yields a valid probability distribution that we call the posterior."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## The Posterior Distribution\n",
    "Now that we've calculated our likelihood values, we obtain the numerator of Bayes' Theorem by multiplying them with the prior values, which yields the joint distribution of θ and X. In turn, the denominator is obtained by summing over the resulting vector (marginalizing out θ).\n",
    "You may have seen that the denominator is what often makes Bayesian Inference computationally intractable. Later blog posts will address why that is the case, but for this scenario we have the advantage of working with a parameter space that is discrete (summation is easier than integration) and that only takes on 10 values, so calculating the denominator is entirely feasible.\n",
    "\n",
    "In the next blog post, we'll deal with what happens when we work with continuous distributions. For now, note that our ability to derive the marginal distribution of X is possible because we are working with one variable, which in turn has very few (11) values. This makes summing over all of the values in the parameter space easy, which would not be the case if we were dealing with multiple predictors that can take on thousands (or an infinite! as in the continuous case) amount of values."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [
    {
     "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": [
    "def create_posterior_df(likelihood_df, prior_distribution_df):\n",
    "    \"\"\"\n",
    "    Creates a dataframe posterior probability distribution dataframe\n",
    "    Parameters\n",
    "    ----------\n",
    "    likelihood_df : Likelihood dsitribution dataframe from create_likelihood_df()\n",
    "    prior_distribution_df : Prior probability distribution dataframe from create_prior_df()\n",
    "    \"\"\"\n",
    "    # calculate denominator\n",
    "    marginal_likelihood_sum = (likelihood_df.Likelihood * prior_distribution_df.Probability).sum()\n",
    "    # divide joint distribution by denominator\n",
    "    posterior_prob = (likelihood_df.Likelihood * prior_distribution_df.Probability)/marginal_likelihood_sum\n",
    "\n",
    "    posterior_distribution_df = pd.DataFrame(list(zip(prior_distribution_df.Theta, posterior_prob )), \n",
    "                                             columns=('Theta', 'Posterior' ))\n",
    "    return posterior_distribution_df\n",
    "\n",
    "posterior_distribution_df = create_posterior_df(likelihood_df, prior_distribution_df)\n",
    "plot_distribution(posterior_distribution_df, title = \"Posterior Distribution\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "So what is the posterior distribution? It is a reflection of our beliefs about our parameter of interest, having incorporated all of the information we have access to. It is the product of two components: our prior beliefs about theta, and the likelihood, or the evidence, which reflects the information we gained from the observed data. In combining these two pieces, we obtain a probability distribution for our parameter of interest. This is key piece separating the Bayesian and Frequentist approach. In the frequentist methodology, our answer is expressed in the form of a point estimate (with a confidence interval). In the Bayesian methodology however, our answer is expressed in the form of a probability distribution, allowing us to place a value on the probability of each potential value of p being correct. \n",
    "\n",
    "In the case above, after having observed 10 flips and 5 heads, our prior distribution has been squeezed by the likelihood towards theta = 0.5, as seems to increasingly be the most likely answer. However, we haven't seen enough information to rule out the possibility that theta lies somewhere to the side of 0.5, so we will continue to observe more data. Similar to how we did in the frequentist discussion, let's see how our bayesian conclusion changes as we see more and more data.\n",
    "\n",
    "## Putting It All Together\n",
    "Let's now look at what happens as the number of coin flips increases under a Bayesian framework. \n",
    "\n",
    "The plot below overlays the posterior distributions (in blue and with values on the left Y-axis) and the likelihoods (in red and with values on the right Y-axis)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": "<Figure size 1080x1080 with 20 Axes>"
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "steps = [1, 10, 25, 50, 100, 500, 1000, 5000, 7500, 10000]\n",
    "\n",
    "fig, ax = plt.subplots(5,2, figsize = (15,15))\n",
    "axes = [(0,0),(0,1), (1,0), (1,1), (2,0), (2,1), (3,0), (3,1), (4,0), (4,1)]\n",
    "\n",
    "for i in range(len(steps)): \n",
    "    trials = steps[i]\n",
    "    num_heads = sum(data[:steps[i]])\n",
    "    likelihood_df = create_likelihood_df(trials, num_heads, prior_distribution_df)\n",
    "    posterior_distribution_df = create_posterior_df(likelihood_df, prior_distribution_df)\n",
    "    # figs.append(plot_single_df(create_posterior_df(likelihood_df, prior_distribution_df), title = \"Posterior Distribution\"))\n",
    "    ax[axes[i]].scatter(posterior_distribution_df.iloc[:,0], posterior_distribution_df.iloc[:,1], color = 'blue')\n",
    "\n",
    "    ax2 = ax[axes[i]].twinx()\n",
    "    ax2.set_ylabel(\"Likelihood\", color = \"red\")\n",
    "    ax2.scatter(likelihood_df.iloc[:,0], likelihood_df.iloc[:,1], color = 'red', s = 2.5)\n",
    "    ax[axes[i]].title.set_text(\"$ n = $\" + str(trials) + \", $heads = $\" + str(num_heads))\n",
    "    ax[axes[i]].set_ylabel(\"Probability\", color = \"blue\")\n",
    "    for j in range(len(posterior_distribution_df)+1): \n",
    "        # print(posterior_distribution_df.iloc[:j,0])\n",
    "        ax2.vlines(x = likelihood_df.iloc[:j,0], color = 'red', ymin = 0, ymax = likelihood_df.iloc[:j,1], linewidth = 0.5)\n",
    "        ax[axes[i]].vlines(x = posterior_distribution_df.iloc[:j,0], color = 'blue', ymin = 0, ymax = posterior_distribution_df.iloc[:j,1])\n",
    "    \n",
    "fig.tight_layout()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 46,
   "metadata": {},
   "outputs": [],
   "source": [
    "fig.savefig('posteriors_and_likelihoods.png')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's start off by analyzing the situation in which we've flipped the coin a single time and observed heads. In the frequentist approach, we saw that, in this scenario, our estimate of p = 1, an obviously incorrect conclusion, and yet we had no other way to answer the question. In the Bayesian world, our answer is very different. Because we defined our prior beliefs to say that the most likely value of theta is 0.5, we are only slightly swayed by that first flip. Think about this intuitively, if you really believed that a coin was fair, and you flipped it once and it came up heads, would that be enough evidence to convince you that the coin isn't fair? Probably not! \n",
    "\n",
    "The Bayesian approach performs much better than the Frequentist approach when there is relatively little data to work with. The viability of the Frequentist answer relies on the law of large numbers, and thus in the absence of large amounts of data, the results aren't always reliable.\n",
    "However, as we begin to observe more flips of the coin, we start to see our Bayesian answer become quite clear, and eventually we're placing all of our eggs in the p = 0.6 basket. After just 100 flips, we are assigning a very small probability to values which don't equal 0.6, and eventually the probability we assign to 0.6 converges to 1, or ~ 100%. This means that we are close to 100% sure that 60% of the time, our coin will be heads. \n",
    "\n",
    "In the background, the likelihood (or the observed data), is beginning to dominate the prior beliefs we established at the beginning. This is because the evidence is just overwhelming, and so we want to rely more and more on that. Again, imagine that you are flipping a coin and originally thought that the coin was fair (theta = 0.5). What if you flipped that coin 100 times and observed 100 heads, would you still think that the coin is fair? No! You would most certainly start to believe that the coin is very biased, and that the true probability of heads is closer to 100%. \n",
    "\n",
    "## Conclusion\n",
    "In this first blog post, we've looked at two different ways to estimate parameters. Under the Frequentist approach, let the data do all the talking, and we estimate the relationship between and X and Y by building a model that fits the data as closely as possible. Our model gives us a point estimate, the Maximum Likelihood Estimate, and uncertainty is captured by the model's standard error which is inversely proportional to the sample size. As such, a typical Frequentist endeavor is to collect as much data as possible about the world in order to estimate the relationship between variables.\n",
    "\n",
    "Under the Bayesian approach, we start off with an idea of what the relationship between our variables is: the prior. We then look at the data and update our beliefs about the parameter's distribution: this gives us the posterior. An important but subtle difference under the Bayesian framework is that we treat parameters as random variables in order to capture their uncertainty about their true values. This entails working with distributions at every stage of the modeling process.\n",
    "\n",
    "If we recall the plots we showed for the Frequentist approach, we realize that the Bayesian and Frequentist answers agree with each other as the sample size increases, and this is as it should be! As we gain fuller information about our parameter of interest (i.e observe more data), our answers should become more objective. We can imagine that in a world of full information - where every detail of what is occurring in the world is known to us - statistical inference becomes objective. We only have the need for these fancy estimation techniques because living in a world where we never have full information, there are always unknowns."
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