Bayesian Statistics The Fun Way - Python Solutions # CHAPTER 12.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "import math\n",
    "import numpy as np\n",
    "from scipy.stats import beta\n",
    "from scipy.stats import binom\n",
    "from scipy.stats import norm\n",
    "import matplotlib.pyplot as plt\n",
    "import seaborn as sns\n",
    "%matplotlib inline\n",
    "\n",
    "# this will make plots a little bit prettier\n",
    "sns.set(style='darkgrid')\n",
    "sns.set_context('talk')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# The Normal Distribution"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Solving the Fuse Problem"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "mean = 20.6\n",
    "std_dev = 1.62"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x241039c92b0>]"
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# plotting normal distribution with given parameters\n",
    "x = np.linspace(mean - 5*std_dev, mean + 5*std_dev, 1000)\n",
    "plt.plot(x, norm.pdf(x, mean, std_dev))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.054253694965280576"
      ]
     },
     "execution_count": 29,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# calculating PDF for values between 10 and 18 as in the book\n",
    "z = [10, 18]\n",
    "norm.cdf(z, loc=mean, scale=std_dev)[1] - norm.cdf(z, loc=mean, scale=std_dev)[0]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 1. What is the probability of observing a value five sigma greater than the mean or more?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "2.866515719235352e-07"
      ]
     },
     "execution_count": 30,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "mu = 0\n",
    "sigma = 1\n",
    "x = [5, 100]   # 5 or more standard deviations\n",
    "norm.cdf(x, loc=mu, scale=sigma)[1] - norm.cdf(x, loc=mu, scale=sigma)[0]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 2. A fever is any temperature greater than 100.4 degrees Fahrenheit. Given the following measurements, what is the probability that the patient has a fever?\n",
    "\n",
    "### 100.0, 99.8, 101.0, 100.5, 99.7"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {},
   "outputs": [],
   "source": [
    "obs = np.array([100.0, 99.8, 101.0, 100.5, 99.7])\n",
    "mu = obs.mean()\n",
    "sigma = obs.std()\n",
    "x = [100.4, 200]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.3402820504876537"
      ]
     },
     "execution_count": 38,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "norm.cdf(x, loc=mu, scale=sigma)[1] - norm.cdf(x, loc=mu, scale=sigma)[0]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 3. Suppose in Chapter 11 we tried to measure the depth of a well by timing coin drops and got the following values: 2.5, 3, 3.5, 4, 2\n",
    "### The distance an object falls can be calculated (in meters) with the following formula: distance = 1/2 × G × 𝐭𝐢𝐦𝐞𝟐 where G is 9.8 m/s/s. What is the probability that the well is over 500 meters deep?\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "metadata": {},
   "outputs": [],
   "source": [
    "# setting up function that will calculate distance based on time\n",
    "def calc_distance(time, G=9.8):\n",
    "    distance = 0.5 * G * time**2\n",
    "    return distance"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 71,
   "metadata": {},
   "outputs": [],
   "source": [
    "values = np.array([2.5, 3, 3.5, 4, 2])\n",
    "distances = []\n",
    "for val in values:\n",
    "    d = calc_distance(val)\n",
    "    distances.append(d)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 73,
   "metadata": {},
   "outputs": [],
   "source": [
    "distances = np.array([distances])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 76,
   "metadata": {},
   "outputs": [],
   "source": [
    "# manually checking what time do we need for 500 meters deep well using previous function\n",
    "x = calc_distance(10.10161)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 83,
   "metadata": {},
   "outputs": [],
   "source": [
    "x = [10.10161, 200]\n",
    "mu = values.mean()\n",
    "sigma = values.std()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 84,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.0"
      ]
     },
     "execution_count": 84,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "norm.cdf(x, loc=mu, scale=sigma)[1] - norm.cdf(x, loc=mu, scale=sigma)[0]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 4. What is the probability there is no well (i.e., the well is really 0 meters deep)? You’ll notice that probability is higher than you might expect, given your observation that there is a well. There are two good explanations for this probability being higher than it should be. The first is that the normal distribution is a poor model for our measurements; the second is that, when making up numbers for an example, I chose values that you likely wouldn’t see in real life. Which is more likely to you?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 90,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1.1037539870342583e-05"
      ]
     },
     "execution_count": 90,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x =[-1, 0]\n",
    "norm.cdf(x, loc=mu, scale=sigma)[1] - norm.cdf(x, loc=mu, scale=sigma)[0]"
   ]
  }
 ],
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