p-value.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# How to determine a `p-value` via Monte Carlo simulation "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "By Joseph Catanzarite 02 April 2020\n",
    "\n",
    "Maintained at at https://github.com/jcatanza/fastai_notebooks"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Abstract\n",
    "This notebook was inspired by Jeremy's Lesson 2 discussion of Figure 1(a) in the paper \"High Temperature and High Humidity Reduce the Transmission of COVID-19\" at https://papers.ssrn.com/sol3/papers.cfm?abstract_id=3551767. \n",
    "\n",
    "We show how to empirically determine the **`p-value`** via Monte Carlo simulation, and apply this method to the data from Figure 1(a).\n",
    "\n",
    "The notebook is organized as follows:\n",
    "\n",
    "In **Section 1** we  work out how to generate random synthetic data sets that are consistent with the null hypothesis, and look qualitatively similar to the actual data in Figure 1(a). Because we don't have the actual datapoints, we rely on our eyeballs to tell us when our synthetic data looks close to the actual data.\n",
    "\n",
    "In **Section 2**, we examine one of our synthetic data sets. \n",
    "\n",
    "Next, in **Section 3** we perform a Monte Carlo simulation, generating an ensemble of 10,000 randomly drawn synthetic data sets. For each data set, we measure and record the slope of the fitted linear R-value vs. Temperature model. \n",
    "\n",
    "Then, in **Section 4**, we determine the `p-value for rejection of the null hypothesis`, which is the fraction of the 10,000 synthetic data sets for which the slope was **steeper than -0.023**, the slope in the actual data set. \n",
    "\n",
    "Finally, in **Section 5**, we discuss the significance of the `p-value` obtained."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Here is the actual R-value vs. Temperature data Fig 1 (a) from the paper"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<IPython.core.display.Image object>"
      ]
     },
     "execution_count": 1,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from IPython.display import Image\n",
    "Image(\"R_vs_T_actual.png\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "%matplotlib inline\n",
    "import matplotlib.pyplot as plt"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 1. Select parameters to generate null-hypothesis data sets that are qualitatively similar to the actual data set. \n",
    "This requires a bit of eyeballing and trial-and-error. We found a reasonable visual fit (see the plots below) to the data for temperatures with mean around 7 degrees and standard deviation of  7.5 degrees, and R values with mean 1.75 and standard deviation of 0.35"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Simulation control parameters\n",
    "n_data_sets = 10000\n",
    "n_cities = 100\n",
    "# my parameters\n",
    "mu_R = 1.75\n",
    "sigma_R = 0.35\n",
    "mu_T = 7.0\n",
    "sigma_T = 7.5\n",
    "# Jeremy's parameters\n",
    "# mu_R = 1.9\n",
    "# sigma_R = 0.5\n",
    "# mu_T = 5.\n",
    "# sigma_T = 5.\n",
    "\n",
    "R0 = 1.99\n",
    "M0 = -0.023"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Building the linear model\n",
    "The linear model for the dependence of **`R-value`** on temperature **`T`** is\n",
    "\n",
    "**`R(T) = intercept + slope*T`** *equ. (1)*\n",
    "\n",
    "where **`T`** is a column vector of temperatures for all the cities, and **`R`** is a column vector of corresponding **`R`** values in these cities\n",
    "\n",
    "\n",
    "If we now define a **design matrix** **`A`**as a matrix whose first column is a vector of **`n_cities`** **ones**, and whose second column is the vector **`T`**,\n",
    "\n",
    "then the linear model in *equ. (1)* can be written in matrix form as follows:\n",
    "\n",
    "**`R = A@P`** *equ. (2)*\n",
    "\n",
    "Where **`P = [intercept, slope]`** -- a column vector -- is the fitted parameters vector. \n",
    "\n",
    "\n",
    "With the above definitions, we see that equations (1) and (2) are equivalent."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Fitting the linear model\n",
    "Equation (2) can be solved by multiplying both sides by the **Moore-Penrose pseudo-inverse** of the design matrix **`A`**, which we call **`pinv(A)`**. The pseudo-inverse has the same shape as A transpose, and has the property that **`pinv(A)@A = I`**, where **`I`** is the identity matrix with dimension **`A.shape[1]`**, andn **`@`** is matrix multiplication. Since **`A`** has **`2`** columns, **`I`** is the **`2x2`** identity matrix. \n",
    "\n",
    "the solution to equation (2) for the linear model parameters is\n",
    "\n",
    "**`P = pinv(A)@R`**\n",
    "\n",
    "From the definition of **`P`**, we have: \n",
    "\n",
    "intercept = **`P[0]`** and \n",
    "\n",
    "slope = **`P[1]`**\n",
    "\n",
    "The **Moore-Penrose pseudo-inverse** is implemented in **`numpy`** as the function **`numpy.linalg.pinv()`**"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Let's create a function that combines the above two steps.\n",
    "We will generate a synthetic data set, then fit the linear model and return the fitted slope."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "def fit_slope(n_cities,mu_R, sigma_R, mu_T, sigma_T):\n",
    "\n",
    "    # Generate the data vector, and the R vector for n_cities cities\n",
    "    R = np.random.normal(mu_R, sigma_R, n_cities)[:,None]\n",
    "    T = np.random.normal(mu_T, sigma_T, n_cities)[:,None]\n",
    "\n",
    "    # Build the design matrix A\n",
    "    ONES = np.ones(n_cities)[:,None]\n",
    "    A = np.hstack((ONES,T))\n",
    "\n",
    "    # Fit the linear parameters and return the slope\n",
    "    P = np.linalg.pinv(A)@R\n",
    "    intercept = P[0]\n",
    "    slope = P[1]\n",
    "    return slope, intercept, R, T, A"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 2. Generate and examine a random synthetic data set\n",
    "Using the function we created above, we'll generate a random data set, then we'll do some Exploratory Data Analysis (EDA)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "slope, intercept, R, T, A = fit_slope(n_cities,mu_R, sigma_R, mu_T, sigma_T)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Temperature Distribution"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
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9DVnu6sBnEGZmluUEYWZmWU4QZmaW5QRhZmZZThBmZpblBGFmZln1fKPcRZKWSJpTKjtN0gJJs9LnoAGmPUDSw5IelXRKvWI0M7OB1fMM4mLggEz52RGxS/pcVz1Q0prAfwMHAjsCR0rasY5xmplZRt0SRETcDjwzgkn3AB6NiMci4k9AD3DIKg3OzMyGpIio38ylycA1EbFz6j8NOAZ4HpgBnBQRz1ZNcyhwQEQcl/o/AuwZEZ8cYBlTgakAnZ2du/X09NDX10dHR0c9qtRQ7VIPaJ26zF6wdFTTd46HxctWUTANMGXShGx5I7bHaNd1raq3yUB1bnXN+o50d3fPjIiu3LBGP2rj28CXgUh/zwSOrRpHmekGzGIRMQ2YBtDV1RWVSoXe3l4qlcoqCbiZ2qUe0Dp1OWaUj384acpyzpw9dp5QM++oSra8EdtjtOu6VtXbZKA6t7pW+Y6UNfQupohYHBGvRMSrwHcompOqzQe2LvVvBSxsRHxmZrZCQxOEpC1KvR8A5mRGuw/YTtIbJK0NHAFc3Yj4zMxshbqdK0u6FKgAm0iaD5wKVCTtQtFkNA/4eBp3S+CCiDgoIpZL+iRwI7AmcFFEzK1XnGZmlle3BBERR2aKLxxg3IXAQaX+64DX3AJrZmaN419Sm5lZlhOEmZllOUGYmVmWE4SZmWWNnV/8WNto1LuKzWx0fAZhZmZZThBmZpblBGFmZllOEGZmluUEYWZmWU4QZmaW5QRhZmZZThBmZpblBGFmZllOEGZmllW3BCHpIklLJM0plf2npIckPSDpSkkbDTDtPEmzJc2SNKNeMZqZ2cDqeQZxMXBAVdl0YOeIeDPwG+DfB5m+OyJ2iYiuOsVnZmaDqFuCiIjbgWeqym6KiOWp925gq3ot38zMRmfYCULSRElvXgXLPha4foBhAdwkaaakqatgWWZmNkyKiKFHknqB91E8HnwW8CRwW0T86xDTTQauiYidq8o/B3QBH4xMAJK2jIiFkjajaJb6VDojyS1jKjAVoLOzc7eenh76+vro6OgYsl6trl3qASvXZfaCpU2OZuQ6x8PiZc2OonZTJk3Iljfif6tR27l6mwxU51bXrO97d3f3zIGa8mt9H8SEiHhe0nHAdyPiVEkPjCQYSUcDBwP75pIDQEQsTH+XSLoS2APIJoiImAZMA+jq6opKpUJvby+VSmUk4bWUdqkHrFyXY8bw+yBOmrKcM2ePndeozDuqki1vxP9Wo7Zz9TYZqM6trhW/77U2MY2TtAVwGHDNSBcm6QDgM8D7IuKlAcZZX9IG/d3A/sCc3LhmZlY/tSaILwI3Ao9GxH2S3gg8MtgEki4F7gK2lzRf0seAc4ENgOnpFtbz0rhbSrouTdoJ3CnpV8C9wLURccOwa2ZmZqNS67nyonRrKgAR8ZikswabICKOzBRfOMC4C4GD+ucNvKXGuMzMrE5qPYP4Zo1lZmbWJgY9g5D0N8DbgE0lle9Y2hBYs56BmZlZcw3VxLQ20JHG26BU/jxwaL2CMjOz5hs0QUTEbcBtki6OiMcbFJOZmbWAWi9SryNpGjC5PE1EvKseQZmZWfPVmiB+DJwHXAC8Ur9wzMysVdSaIJZHxLfrGomZmbWUWm9z/amkT0jaQtLG/Z+6RmZmZk1V6xnE0envyaWyAN64asMxM7NWUVOCiIg31DsQMzNrLTUlCEl/nyuPiO+t2nDMzKxV1NrEtHupe11gX+B+wAnCzKxN1drE9Klyv6QJwPfrEpGZmbWEkb6T+iVgu1UZiJmZtZZar0H8lOKuJSge0rcD8KN6BWVmZs1X6zWI/yp1Lwcej4j5dYjHzMxaRE1NTOmhfQ9RPNF1IvCnWqaTdJGkJZLmlMo2ljRd0iPp78QBpj06jfNIeo+1mZk1UE0JQtJhFK///DDFe6nvkVTL474vBg6oKjsFuCUitgNuSf3Vy9sYOBXYE9gDOHWgRGJmZvVRaxPT54DdI2IJgKRNgZuB/x1sooi4XdLkquJDgErqvgToBT5TNc57gOkR8Uxa3nSKRHNpjfGamdkoKSKGHkmaHRFTSv1rAL8qlw0y7WTgmojYOfU/FxEblYY/GxETq6b5NLBuRJye+j8PLIuI8rWQ/nGnAlMBOjs7d+vp6aGvr4+Ojo4h69Xq2qUesHJdZi9Y2uRoRq5zPCxe1uwoRq9d6gGvrcuUSROaF8woNOv73t3dPTMiunLDaj2DuEHSjaw4gj8cuG5VBDcAZcqymSwipgHTALq6uqJSqdDb20ulUqljeI3RLvWAletyzCnXNjeYUThpynLOnF3r16Z1tUs94LV1mXdUpXnBjEIrft8HvQYhaVtJe0fEycD5wJuBtwB3kXbKI7BY0hZp/lsASzLjzAe2LvVvBSwc4fLMzGwEhrpIfQ7wAkBEXBER/xoR/0Jx9nDOCJd5NSueDns08JPMODcC+0uamC5O75/KzMysQYZKEJMj4oHqwoiYQfH60UFJupTibGN7SfMlfQw4A9hP0iPAfqkfSV2SLkjzfwb4MnBf+nyp/4K1mZk1xlCNkOsOMmz8UDOPiCMHGLRvZtwZwHGl/ouAi4ZahpmZ1cdQZxD3SfqH6sJ0JjCzPiGZmVkrGOoM4kTgSklHsSIhdAFrAx+oZ2BmZtZcgyaIiFgMvE1SN7BzKr42In5W98jMzKypan0fxK3ArXWOxczMWkh7/FLGRmRyA3+wdtKU5WP6B3Jmq6ORvjDIzMzanBOEmZllOUGYmVmWE4SZmWU5QZiZWZYThJmZZTlBmJlZlhOEmZllOUGYmVmWE4SZmWU5QZiZWVbDE4Sk7SXNKn2el3Ri1TgVSUtL43yh0XGama3uGv6wvoh4GNgFQNKawALgysyod0TEwY2MzczMVmh2E9O+wG8j4vEmx2FmZlUUEc1buHQRcH9EnFtVXgEuB+YDC4FPR8TcAeYxFZgK0NnZuVtPTw99fX10dHTUNfZGqHc9Zi9YWrd5V+scD4uXNWxxdeN6tJ7qukyZNKF5wYxCs/Zb3d3dMyOiKzesaQlC0toUO/+d0pvrysM2BF6NiD5JBwFfj4jthppnV1dXzJgxg97eXiqVSl3ibqR616PR74M4c/bYf/2I69F6qusy74z3NjGakWvWfkvSgAmimU1MB1KcPSyuHhARz0dEX+q+DlhL0iaNDtDMbHXWzARxJHBpboCkzSUpde9BEefTDYzNzGy115RzTEnrAfsBHy+VHQ8QEecBhwL/KGk5sAw4Ipp5scTMbDXUlAQRES8Br6sqO6/UfS5wbvV0ZmbWOM2+zdXMzFqUE4SZmWU5QZiZWZYThJmZZTlBmJlZlhOEmZllOUGYmVmWE4SZmWU5QZiZWVZ7PM7RzCxp5FOKq43VJ8kOxGcQZmaW5QRhZmZZThBmZpblBGFmZllOEGZmltW0BCFpnqTZkmZJmpEZLknfkPSopAckvbUZcZqZra6afZtrd0Q8NcCwA4Ht0mdP4Nvpr5mZNUArNzEdAnwvCncDG0naotlBmZmtLtSsVz1L+h3wLBDA+RExrWr4NcAZEXFn6r8F+ExEzKgabyowFaCzs3O3np4e+vr66OjoaEQ16qre9Zi9YGnd5l2tczwsXtawxdWN69F6WqkuUyZNGPG0zdpvdXd3z4yIrtywZjYx7R0RCyVtBkyX9FBE3F4arsw0r8lmKbFMA+jq6opKpUJvby+VSqUuQTdSvetxTAN/cXrSlOWcObvZLZqj53q0nlaqy7yjKiOethX3W01rYoqIhenvEuBKYI+qUeYDW5f6twIWNiY6MzNrSoKQtL6kDfq7gf2BOVWjXQ38fbqbaS9gaUQsanCoZmarrWadl3UCV0rqj+GHEXGDpOMBIuI84DrgIOBR4CXgo02K1cxstdSUBBERjwFvyZSfV+oO4IRGxmVmZiu08m2uZmbWRE4QZmaW5QRhZmZZThBmZpblBGFmZllOEGZmluUEYWZmWU4QZmaW5QRhZmZZThBmZpblBGFmZllOEGZmluUEYWZmWU4QZmaW1Rrv6WsBkxv4+s1anTRleUNfC2pmozOa/chovu/zznjviJc7GJ9BmJlZVsMThKStJd0q6UFJcyX9c2aciqSlkmalzxcaHaeZ2equGU1My4GTIuL+9F7qmZKmR8Svq8a7IyIObkJ8ZmZGE84gImJRRNyful8AHgQmNToOMzMbnIpXPzdp4dJk4HZg54h4vlReAS4H5gMLgU9HxNwB5jEVmArQ2dm5W09PD319fXR0dAwrltkLlo6gBvXVOR4WL2t2FKtGu9TF9Wg97VKX0dRjyqQJI15ud3f3zIjoyg1rWoKQ1AHcBnwlIq6oGrYh8GpE9Ek6CPh6RGw31Dy7urpixowZ9Pb2UqlUhhVPq97FdObs9rjRrF3q4nq0nnapy2jqMZq7mCQNmCCacheTpLUozhB+UJ0cACLi+YjoS93XAWtJ2qTBYZqZrdaacReTgAuBByPirAHG2TyNh6Q9KOJ8unFRmplZM87L9gY+AsyWNCuVfRbYBiAizgMOBf5R0nJgGXBENPNiiZnZaqjhCSIi7gQ0xDjnAuc2JiIzM8vxL6nNzCzLCcLMzLKcIMzMLMsJwszMspwgzMwsywnCzMyynCDMzCzLCcLMzLKcIMzMLMsJwszMspwgzMwsywnCzMyynCDMzCzLCcLMzLKcIMzMLMsJwszMspr1TuoDJD0s6VFJp2SGryPpsjT8HkmTGx+lmdnqrRnvpF4T+G/gQGBH4EhJO1aN9jHg2YjYFjgb+GpjozQzs2acQewBPBoRj0XEn4Ae4JCqcQ4BLknd/wvsK2nQ15SamdmqpYho7AKlQ4EDIuK41P8RYM+I+GRpnDlpnPmp/7dpnKcy85sKTE292wMPA5sArxl3DGqXekD71MX1aD3tUpdm1eP1EbFpbsC4RkcC5M4EqrNULeMUhRHTgGkrTSzNiIiukYXXOtqlHtA+dXE9Wk+71KUV69GMJqb5wNal/q2AhQONI2kcMAF4piHRmZkZ0JwEcR+wnaQ3SFobOAK4umqcq4GjU/ehwM+i0W1hZmaruYY3MUXEckmfBG4E1gQuioi5kr4EzIiIq4ELge9LepTizOGIYS5m2tCjjAntUg9on7q4Hq2nXerScvVo+EVqMzMbG/xLajMzy3KCMDOzrLZKEJI+LGmupFcldVUN+/f06I6HJb2nWTEOl6TTJC2QNCt9Dmp2TMMx1GNVxhJJ8yTNTtthRrPjqZWkiyQtSb8v6i/bWNJ0SY+kvxObGWOtBqjLmPuOSNpa0q2SHkz7rH9O5S21XdoqQQBzgA8Ct5cL06M8jgB2Ag4AvpUe+TFWnB0Ru6TPdc0OplY1PlZlrOlO26Gl7lcfwsUU//dlpwC3RMR2wC2pfyy4mNfWBcbed2Q5cFJE7ADsBZyQvhsttV3aKkFExIMR8XBm0CFAT0S8HBG/Ax6leOSH1Vctj1WxOouI23nt74jKj7O5BHh/Q4MaoQHqMuZExKKIuD91vwA8CEyixbZLWyWIQUwCnij1z09lY8UnJT2QTq/HRFNAMtbXe7UAbpI0Mz3iZSzrjIhFUOysgM2aHM9ojdXvCOlp1bsC99Bi22XMJQhJN0uak/kMdmRa86M7mmGIOn0b+CtgF2ARcGZTgx2ell7vI7B3RLyVosnsBEnvaHZABozh74ikDuBy4MSIeL7Z8VRrxrOYRiUi3j2CyWp5vEfT1FonSd8BrqlzOKtSS6/34YqIhenvEklXUjSh3T74VC1rsaQtImKRpC2AJc0OaKQiYnF/91j6jkhaiyI5/CAirkjFLbVdxtwZxAhdDRyRXkT0BmA74N4mx1ST9E/S7wMUF+LHiloeqzImSFpf0gb93cD+jK1tUa38OJujgZ80MZZRGYvfkfT6gguBByPirNKgltoubfVLakkfAL4JbAo8B8yKiPekYZ8DjqW4e+DEiLi+aYEOg6TvU5w6BzAP+Hh/G+VYkG45PIcVj1X5SpNDGhFJbwSuTL3jgB+OlbpIuhSoUDxOejFwKnAV8CNgG+D3wIcjouUv/g5Qlwpj7DsiaR/gDmA28Goq/izFdYiW2S5tlSDMzGzVWV2amMzMbJicIMzMLMsJwszMspwgzMwsywnCzMyynJrsIvwAAAYNSURBVCBsxCS9rvQEzT9UPVFz7WbHlyPpWEmbN2G5x0k6p9HLHQ5Je0m6Mz199yFJ0ySNH2T8d0u6apDhW0u6rD7RWiOMuV9SW+uIiKcp7j9H0mlAX0T8V1ODKmJZMyJeGWDwscD9wB+GMb9xEbF8lQQ3SukHVoqIV4cceXjz3QK4jOK++3slrQF8GOgAlo1knhHxBHD4qovSGs1nEFYXko6WdG86m/iWpDUkjZP0nKT/lHS/pBsl7SnpNkmP9T/HPx1tX5mGPyzpP2qc7+mS7gX2kPRFSfelZ1qdp8LhFAntsv6zHEnzJW2U5r2XpJtT9+mSzpc0HfhuWsZZadkPSDquhnVwnKTfSOqleKRzf3mnpCskzUjz2yuVbybplrRuvpXOyDaStG1/PSiS2xaSDpR0Vxr3svTrbiTtntbnTEnXS+pM5f8i6deSfiXpfzLhfgq4MCLuBYiIVyPisoh4UlKHpItTrL+U9P8ydX1XmvesFNP6Ke5ZpXVxTmn8GyTtk9br91W8Z2OOpH8aar1aA0WEP/6M+gOcBnw6de9M8Uvdcal/GvC3FGesAeyXyn8KXJ/KdwNmpPLjgAXARGB94NcUO/ah5vvBUjwbp78CLgUOTP13AruUxpsPbJS69wJuTt2nUzyOZd3U/wnglNS9DvBLYJtB1sdWwOPA64C1gbuBc9Kwy4C9UvdkYE7qPg84OXUfnOq0EbAtxa9td0/DNgNuA9ZL/Z+j+BXuOsAvgE1S+VHAtNS9CFg7dW+Uifdq4L0D1OVrwBGpeyLwG2Bd4N3AVan8emDP1N1B8cv5bSmeZtC/Tc8pzfMGYB9gT+D6UvlrYvOneR83MVk9vBvYHZhRtIgwnhWP/V4WEdNT92xgaUQslzSbYmfZ78aIeBYgtXPvQ5EIBprvn1jxKAyAfSWdTLEj2wSYSbETG46fRMQfU/f+wA6Sjkj9Eyie6fX7Aabdi+LFL0+nOvQ/PgGK9bN9qgPAxNTWvw/wFYCIuEbSC6X5/TYi7kvdb6N4AdMv0jzWpkh8O1C8FOvmVL4mRQIEmAv8j6SfUCTZ4dgfOFAr3gi4bqku/X4OnCPph8DlEdFXqt9gHqVYF18HrgNuGmZsVkdOEFYPonju0udXKpTGUezI+70KvFzqLv8/Vj8DJoaY77JIh6CS1gPOBd4aEQsknU6xU8tZzoqm1upxXqyq0yci4pYB5pMz0HNsBOwRxUuUVhQOvketjuWGiPhI1fS7Ag9ExNsz078HeCfFC2n+Q9LOsfJ1mrkUZ3HXDhDv+yPit1XL+0uSiIjTJV0NvBe4T1KFletfXs+Q1nVEPC3pzRSPUP8n4EPAWH/XRtvwNQirh5uBwyRtAn+526n6iHMo+6f29/Uodmo/H8Z8x1MknKdUPIH1Q6VhLwAblPrnUewYqRqv2o3AJ1IyQtL2ksZLWlOl9yOX3E1xFrOxiju6Di0Nuxk4ob9H0i6p807gsFR2UFWcZb8A3qniAYL9T5rdjqIpbpKkPVL52pJ2UvHq160i4mfAyRQPs1yvap7fBD6m9C73dM3maEmbprr/5dpASkQrkfRXEfFARPx/iua37atGmQfsmuY7mbTO0/wVET+mePDeWweoszWBzyBslYuI2ZK+SNHUsQbwZ+B4hvcuiDuBH1K8COb7EdF/sXPI+aaj0ksoHvv8OMUTMvt9F7hA0jKK9zmcBnxH0h8Y/BHw51M0q8xKB/pLKBLXBDIvRoqI+enM5e4U34zS4BOAb0v6KMV38NZUdirwQ0lHAT+jeFrpixRNZOV5L5b0MYqL7f23E382Ih6RdCjwjZQYx1G8POfRNN8NKA4KvxrFay7L81wo6W+Br0t6HcXRfy/Fk0W/SNF8NDtN/yivfXXspyW9nSIxP0DRVFRO3rdRXFeaTbFdZqXyrYEL09lTAJ+pXpfWPH6aq7UcFXcI7RwRJzY7lqFIej+wZUR8axXMa11gebomsw/FRd2uUQdpNkI+gzAbhYgY7gXfwUwGLk1NQi8DH1+F8zYbNp9BmJlZli9Sm5lZlhOEmZllOUGYmVmWE4SZmWU5QZiZWdb/ASNUAjr+mdVuAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.hist(T)\n",
    "plt.grid()\n",
    "plt.xlabel('Temperature, degrees Celsius')\n",
    "plt.ylabel('Counts')\n",
    "plt.title('Simulated Temperatures for '+str(n_cities)+' cities')\n",
    "png_name = 'temperature.png'\n",
    "plt.savefig(png_name)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### R-value Distribution"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "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": [
    "plt.hist(R)\n",
    "plt.xlabel('R value: # of secondary infections per case')\n",
    "plt.ylabel('Counts')\n",
    "plt.title('Simulated R values for '+str(n_cities)+' cities')\n",
    "plt.grid()\n",
    "png_name = 'R-value.png'\n",
    "plt.savefig(png_name)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Scatter plot of R-value vs. Temperature\n",
    "The red line is the fitted linear model for the data set in Figure 1(a) of the paper)\n",
    "Does the synthetic data look similar to the original data in Figure 1(a)?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "scrolled": true
   },
   "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": [
    "plt.scatter(T,R)\n",
    "plt.grid()\n",
    "plt.plot()\n",
    "plt.xlabel('Temperature, degrees Celsius')\n",
    "plt.ylabel('R value: # of secondary infections per case')\n",
    "plt.title('Synthetic data set: R values vs. Temperature, for '+str(n_cities)+' cities')\n",
    "axes = plt.gca()\n",
    "x_vals = np.array(axes.get_xlim())\n",
    "y_vals = R0 + M0 * x_vals\n",
    "plt.plot(x_vals, y_vals, '--', color = 'red')\n",
    "plt.legend(['intercept = '+str(R0)+', slope = '+str(M0)])\n",
    "png_name = 'R_vs_T.png'\n",
    "plt.savefig(png_name)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 3. Generate synthetic data sets and measure slopes\n",
    "Now we are ready to generate the synthetic data that will allow us to determine the p-value.\n",
    "We'll run a **Monte Carlo simulation** to generate an ensemble of 100,000 synthetic data sets and measures the slope of the linear model for each data set. The function below returns a column vector of the 100,000 fitted slopes."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [],
   "source": [
    "def get_slopes(n_data_sets = n_data_sets):\n",
    "    slopes = np.array([fit_slope(n_cities,mu_R, sigma_R, mu_T, sigma_T)[0] for n in range(n_data_sets)])\n",
    "    return slopes"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Run the simulation and get the slopes:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [],
   "source": [
    "slopes = get_slopes(n_data_sets)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 4. Determine the the `p-value` for rejection of the null hypothesis\n",
    "The `p-value` is the fraction of the synthetic data sets for which the fitted slope was `steeper than -0.023`"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Let's see what the distribution of fitted slopes looks like:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "scrolled": true
   },
   "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": [
    "plt.hist(slopes,100)\n",
    "plt.grid()\n",
    "plt.xlabel('Slope of linear Temperature model')\n",
    "plt.ylabel('Counts')\n",
    "plt.title('Distribution of slopes over '+str(n_data_sets)+' simulated data sets')\n",
    "plt.axvline(x=-0.023,color = 'red')\n",
    "plt.legend(['slope = -0.023'])\n",
    "png_name = 'slopes.png'\n",
    "plt.savefig(png_name)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Let's determine the p-value:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0 out of 10000 slopes were steeper than -0.023\n",
      "The p-value for rejection of the null hypothesis is therefore [0.]\n"
     ]
    }
   ],
   "source": [
    "n_steep = sum(slopes<-0.023)\n",
    "p_value = n_steep/n_data_sets\n",
    "print(str(n_steep.item()) + ' out of ' + str(n_data_sets) + ' slopes were steeper than -0.023')\n",
    "print('The p-value for rejection of the null hypothesis is therefore ' + str(p_value))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 5. Discussion"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We find that none of our 100,000 synthetic data sets had slopes steeper than -0.023, the slope from the actual data set! The `p-value` is `0`, `much` smaller than the broadly accepted threshold of `0.01`, therefore we have sufficient grounds to reject the `null hypothesis` (i.e. that `R` is constant and therefore the `slope` is 0). We conclude that the slope of **`-0.023`** measured from the actual data set is **quite inconsistent** with data generated from random noise, and is therefore probably **significant**."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
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