{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "71655f70",
   "metadata": {},
   "source": [
    "# Overview of Probability and Random Variables"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "a1b8b4c8",
   "metadata": {},
   "source": [
    "This function adjusts `matplotlib` settings for a uniform feel in the textbook. Note that with `usetex=True,` fonts are rendered with LaTeX. This may result in an error if LaTeX is not installed on your system. In that case, you can set `usetex` to `False.`"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "4c48b283",
   "metadata": {},
   "outputs": [],
   "source": [
    "if \"setup_text_plots\" not in globals():\n",
    "    from astroML.plotting import setup_text_plots\n",
    "setup_text_plots(fontsize=8, usetex=False)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "2823b358",
   "metadata": {},
   "source": [
    "## Probability axioms"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "f224fef1",
   "metadata": {},
   "source": [
    "Given an event $A$, such as the outcome of a coin toss, we assign it a real number $p(A)$, called the probability of $A$. Note that $p(A)$ could also correspond to a probability that a value of $x$ falls in a $dx$ wide interval around $x$. To qualify as a probability, $p(A)$ must satisfy three Kolmogorov axioms:"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "9179164d",
   "metadata": {},
   "source": [
    "1. $p(A) \\geq 0$ for each $A$.\n",
    "2. $p(\\Omega) = 1$, where $\\Omega$ is the set of all possible outcomes.\n",
    "3. If $A_1$, $A_2$, . . . are disjoint events, then $p (\\bigcup^{\\infty}_{i=1}A_i) = \\sum_{i=1}^{\\infty}p(A_i)$ where $\\bigcup$ stands for “union.”\n",
    "\n",
    "Several useful rules can be derived as a consequence of these axioms."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "3c067a63",
   "metadata": {},
   "source": [
    "**Sum rule**:  The probability that the union of two events, $A$ and $B$, will happen is given by,\n",
    "\n",
    "$$\\qquad\\qquad p(A \\cup B) = p(A) + p(B) - p(A \\cap B)\\qquad\\qquad\\qquad(1)$$\n",
    "\n",
    "\n",
    "which is the sum of $A$ and $B$'s respective probabilities minus the probability that both $A$ and $B$ will happen. The union of two events is the probability that *either* event occurs. The $\\cap$ in the equation stands for \"intersection\", and subtracting the last term, $p(A \\cap B)$, avoids double counting the places that $A$ and $B$ overlap. In the figure below, we show this in a diagram."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "dc8028a2",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 720x540 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "from matplotlib import pyplot as plt\n",
    "\n",
    "# create plot\n",
    "fig = plt.figure(figsize=(10, 7.5), facecolor='w')\n",
    "ax = plt.axes([0, 0, 1, 1], xticks=[], yticks=[], frameon=False)\n",
    "\n",
    "# draw intersecting circles\n",
    "ax.add_patch(plt.Circle((1.5, 0.2), 2.2, fc='gray', ec='black', alpha=0.5))\n",
    "ax.add_patch(plt.Circle((-1.5, 0.2), 2.2, fc='gray', ec='black', alpha=0.5))\n",
    "\n",
    "# add text\n",
    "text_kwargs = dict(ha='center', va='center', fontsize=16)\n",
    "ax.text(-1.6, 0.2, \"$p(A)$\", **text_kwargs)\n",
    "ax.text(1.6, 0.2, \"$p(B)$\", **text_kwargs)\n",
    "ax.text(0.0, 0.2, \"$p(A \\cap B)$\", **text_kwargs)\n",
    "ax.text(0, -2.3, \"$p(A \\cup B) = p(A) + p(B) - p(A \\cap B)$\", **text_kwargs)\n",
    "\n",
    "ax.set_xlim(-4, 4)\n",
    "ax.set_ylim(-3, 3)\n",
    "\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "4e63faf9",
   "metadata": {},
   "source": [
    "**Rule of complementary events**: The probability of an event happening plus the probability of it not happening is equal to 1.\n",
    "$$ p(A) + p(\\overline{A}) = 1 $$\n",
    "\n",
    "**Rule of multiplication**: The probability that both events $A$ and $B$ occur is equal to the probability that event $B$ occurs times the probability that event $A$ occurs given that $B$ has occurred. Switching $A$ and $B$ yields an equivalent statement.\n",
    "\n",
    "$$ p(A \\cap B) = p(A|B)p(B) = p(B|A)p(A)$$\n",
    "\n",
    "In the equation above, \"|\" is pronounced \"given,\" and $p(A|B)$ is the probability of event $A$ occurring given that B has occurred.\n",
    "\n",
    "**Example**: Find the probability of rolling an odd number greater than 2.\n",
    "\n",
    "> Event A: Rolling an odd number\n",
    ">\n",
    "> Event B: Rolling a number greater than 2\n",
    ">\n",
    ">$P(\\text{odd and greater than 2}) = P(\\text{odd|if} >2) \\times P(> 2)$\n",
    ">    \n",
    ">- All outcomes: 1 2 3 4 5 6\n",
    ">- $P(\\text{is}$ > 2) = count(3 4 5 6) / count (1 2 3 4 5 6) = 4/6\n",
    ">- the probability that a number is odd if it's greater than two:  3,5\n",
    ">- $P(\\text{is odd| if} > 2)$ = count(3 5) / count (3 4 5 6) = 1/2\n",
    ">   \n",
    "> $P(\\text{odd and greater than 2})$ = 4/6 $\\times$ 1/2 = $\\fbox{1/3}$\n",
    ">   \n",
    ">We can get the same answer by determining the odd numbers greater than two on a die (2) and dividing by the total possibilities (6) to get 1/3.\n",
    "    \n",
    "    \n",
    "\n",
    "**The law of total probability**: if events $B_i, i=1,..., N$ are disjoint and their union is the set of all possible outcomes, then\n",
    "\n",
    "$$p(A) = \\sum_i p(A \\cap B_i) = \\sum_i p(A|B_i)p(B_i).$$\n",
    "\n",
    "Conditional probabilities also satisfy the law of total probability. Assuming that an event $C$ is not mutually exclusive with $A$ or any of $B_i$,\n",
    "\n",
    "$$    p(A|C) = \\sum\\limits_{i}p(A|C \\cap B_i)p(B_i|C)  $$\n",
    "\n",
    "**Example**: Assume we have a box with three bags of marbles: one bag has 3 green and 7 blue marbles, another bag has 6 green and 4 blue marbles, and the last bag has 2 green and 8 blue marbles. We want to find the total probability of grabbing a green marble from any of the three bags.\n",
    "\n",
    "> $P(G)$ = probability of choosing a green marble:\n",
    ">\n",
    "> $P(G|B_i)$ = probability of choosing a green marble from bag B$_i$:\n",
    ">\n",
    "> - Bag 1: $P(G|B_1)$ = 3/10\n",
    "> - Bag 2: $P(G|B_2)$ = 6/10\n",
    "> - Bag 3: $P(G|B_3)$ = 2/10\n",
    ">\n",
    "> Using $P(G) = \\sum_i P(G|B_i)*P(B_i)$ where $B_1 = B_2 = B_3 = \\frac{1}{3}$\n",
    "> \n",
    "> $P(G) = \\big(\\frac{3}{10} \\times \\frac{1}{3}\\big) + \\big(\\frac{6}{10} \\times \\frac{1}{3}\\big) + \\big(\\frac{2}{10} \\times \\frac{1}{3}\\big) = \\frac{11}{30} = 0.37$\n",
    ">\n",
    "> Thus, if we randomly select one of the bags and then randomly select one marble from that bag, the probability we choose a green marble is 0.37.\n",
    "\n",
    "\n",
    "\n",
    "### Classical inference vs. Bayesian inference\n",
    "\n",
    "Classical inference and Bayesian inference differ fundamentally in the interpretation of the resulting probabilities, which will be discussed in detail in chapters 4 and 5. Briefly, classical statistical inference is concerned with $p(A)$, interpreted as the long-term outcome or frequency with which $A$ occurs (or would occur) in identical repeats of an experiment; events are restricted to propositions about random variables (see below). Bayesian inference is concerned with $p(A|B)$, interpreted as the plausibility of a proposition $A$, conditional on the truth of $B$, and $A$ and $B$ can be any logical proposition (i.e., they are not restricted to propositions about random variables).\n",
    "\n",
    "\n",
    "## Random variables\n",
    "\n",
    "A random, or stochastic, variable is, roughly speaking, a variable whose value results from the measurement of a quantity subject to random variations. Unlike normal mathematical variables, a random variable can take on a set of possible different values, each with an associated probability.\n",
    "\n",
    "There are two main types of random variables: discrete and continuous.\n",
    "* The outcomes of **discrete** random variables form a **countable set.** \n",
    "* The outcomes of **continuous** random variables **usually map onto the real number set** (though one can define mapping to the complex plane or use matrices instead of real numbers, etc.). \n",
    "\n",
    "The function which ascribes a probability value to each outcome of the random variable is the **probability density function (pdf).** *Note that other sources may use **\"probability mass function\"** for discrete variables.*\n",
    "\n",
    "**Independent identically distributed (iid)** random variables are drawn from the same distribution and are independent. Two random variables, $x$ and $y$ are independent if and only if\n",
    "\n",
    "$$p(x,y) = p(x)p(y)$$\n",
    "\n",
    "for all values of $x$ and $y$. Recall that $p(x,y) = p(x)p(y|x)$ is true of any variables, but for independent variables, $p(y|x) = p(y)$ since the knowledge of the value of $x$ tells us **nothing** about the value of $y$.\n",
    "\n",
    "\n",
    " \n",
    "\n",
    "\n",
    "**Example**: Find the probability of rolling a 1 and then rolling a 3.\n",
    "    \n",
    "> p(second is 3, first is 1) = p(second is 3 | first is 1) $\\times$ p(first is 1)\n",
    ">\n",
    ">= p(second is 3) $\\times$  p(first is 1)\n",
    ">\n",
    ">= 1/6 $\\times$  1/6 = 1/36\n",
    ">\n",
    "> Because the two events are independent since the first roll tells us nothing about the second roll, the term $\\text{p(second is 3}| \\text{first is 1})$ simplified to $\\text{p(second is 3})$.\n",
    "\n",
    "\n",
    "**Example:** Suppose we have a deck of cards (52 cards) with 13 of each suit (spades, clubs, diamonds, and hearts). What's the probability of drawing two diamonds in a row?\n",
    "\n",
    "> These are dependent events, so we will use $p(x,y) = p(x|y)p(y)$\n",
    ">\n",
    "> $p(y)$: Drawing a diamond on the first draw = 13/52 \n",
    "> - there is an equally likely chance of drawing any of the 4 suits in a full deck of cards\n",
    ">\n",
    "> $p(x|y)$: Drawing a diamond on the second draw = 12/51\n",
    "> - given that we don't replace the card we just drew, we now have a deck of 51 cards.\n",
    "> - since we are assuming we've drawn a diamond on the first draw (x \"given\" y), we now have 12 diamonds in the deck.\n",
    ">\n",
    "> $p(x,y) = \\frac{13}{52} \\times \\frac{12}{51} = \\frac{1}{17}$\n",
    ">\n",
    "> **However, assume we put the card we drew back**\n",
    ">\n",
    "> $p(y)$ stays the same, but $p(x|y)$ becomes $p(x)$ since the first draw now tells us nothing about the second draw; these have become independent events. Drawing a diamond on the second draw now has the same probability as our first draw.\n",
    ">\n",
    "> $p(x,y) = \\frac{13}{52} \\times \\frac{13}{52} = \\frac{1}{16}$\n",
    "\n",
    " \n",
    "\n",
    "\n",
    "## Conditional probability and Bayes’ rule\n",
    "\n",
    "When two continuous random variables are not independent, it follows from eq. 1\n",
    "\n",
    "$$\\qquad\\qquad p(x,y) = p(x|y)p(y) = p(y|x)p(x).\\qquad\\qquad\\qquad\\quad\\,(2)$$\n",
    "    \n",
    "The *marginal probability function* is defined as\n",
    "\n",
    "$$\\qquad\\qquad\\qquad p(x) = \\int p(x,y)\\:dy \\qquad\\qquad\\qquad\\qquad\\qquad\\, (3) $$\n",
    "\n",
    "and analogously for $p(y)$. Note that complete knowledge of the conditional pdf $p(y|x)$, and the marginal probability $p(x)$, is sufficient to fully reconstruct $p(x,y)$ (the same is true with $x$ and $y$ reversed).\n",
    "\n",
    "Combining eq. 2 and 3, we get a continuous version of the law of total probability,\n",
    "\n",
    "$$\\qquad\\qquad\\qquad p(x) = \\int p(x|y)\\: p(y)\\: dy \\qquad\\qquad\\qquad\\qquad\\: (4)$$"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "7359ed25",
   "metadata": {},
   "source": [
    "In the figure below, we will show an example of a two-dimensional probability distribution together with corresponding marginal and conditional probability distributions. Note that $x$ and $y$ are **not** independent in this case. \n",
    "\n",
    "- The marginal probabilities will be the left and bottom panels of the graph on the left. From equation 3 above, we see that the marginal probabilities will be the integral along the $x$ direction for a given $y$ (left side panel) or the integral along the $y$ direction for a given $x$ (bottom panel).\n",
    "\n",
    "\n",
    "- The three panels on the right will show the conditional probability (of x) for three y values: $y = 0.5, 1,$ and $1.5$ Note that the conditional probability distributions $p(x|y = y_0)$ are simply one-dimensional “slices” through the two-dimensional image $p(x,y)$ at given values of $y_0$, and then divided (renormalized) by the value of the marginal distribution $p(y)$ at $y = y_0$. As a result of this renormalization, the integral of $p(x|y)$ (over $x$) is unity.\n",
    "\n",
    "First we will define a random 2D distribution, generate the data, and compute the normalized 2D histogram."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "1282ad32",
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "from matplotlib import pyplot as plt\n",
    "from matplotlib.ticker import NullFormatter\n",
    "\n",
    "def banana_distribution(N=10000):\n",
    "    \"\"\"This generates random points in a banana shape\"\"\"\n",
    "    # create a truncated normal distribution\n",
    "    theta = np.random.normal(0, np.pi / 8, 10000)\n",
    "    theta[theta >= np.pi / 4] /= 2\n",
    "    theta[theta <= -np.pi / 4] /= 2\n",
    "    # define the curve parametrically\n",
    "    r = np.sqrt(1. / abs(np.cos(theta) ** 2 - np.sin(theta) ** 2))\n",
    "    r += np.random.normal(0, 0.08, size=10000)\n",
    "    x = r * np.cos(theta + np.pi / 4)\n",
    "    y = r * np.sin(theta + np.pi / 4)\n",
    "    return (x, y)\n",
    "\n",
    "# Generate the data and compute the normalized 2D histogram\n",
    "np.random.seed(0)\n",
    "x, y = banana_distribution(10000)\n",
    "\n",
    "Ngrid = 41\n",
    "grid = np.linspace(0, 2, Ngrid + 1)\n",
    "\n",
    "H, xbins, ybins = np.histogram2d(x, y, grid)\n",
    "H /= np.sum(H)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "010b540a",
   "metadata": {},
   "source": [
    "Next, we'll plot the results."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "6dbcc91f",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1008x432 with 7 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# plot the result\n",
    "fig = plt.figure(figsize=(14, 6))\n",
    "\n",
    "# define axes\n",
    "ax_Pxy = plt.axes((0.2, 0.34, 0.27, 0.52))\n",
    "ax_Px = plt.axes((0.2, 0.14, 0.27, 0.2))\n",
    "ax_Py = plt.axes((0.1, 0.34, 0.1, 0.52))\n",
    "ax_cb = plt.axes((0.48, 0.34, 0.01, 0.52))\n",
    "ax_Px_y = [plt.axes((0.65, 0.62, 0.32, 0.23)),\n",
    "           plt.axes((0.65, 0.38, 0.32, 0.23)),\n",
    "           plt.axes((0.65, 0.14, 0.32, 0.23))]\n",
    "\n",
    "# set axis label formatters\n",
    "ax_Px_y[0].xaxis.set_major_formatter(NullFormatter())\n",
    "ax_Px_y[1].xaxis.set_major_formatter(NullFormatter())\n",
    "\n",
    "ax_Pxy.xaxis.set_major_formatter(NullFormatter())\n",
    "ax_Pxy.yaxis.set_major_formatter(NullFormatter())\n",
    "\n",
    "ax_Px.yaxis.set_major_formatter(NullFormatter())\n",
    "ax_Py.xaxis.set_major_formatter(NullFormatter())\n",
    "\n",
    "# draw the joint probability\n",
    "plt.axes(ax_Pxy)\n",
    "H *= 1000\n",
    "plt.imshow(H, interpolation='nearest', origin='lower', aspect='auto',\n",
    "           extent=[0, 2, 0, 2], cmap=plt.cm.binary)\n",
    "\n",
    "cb = plt.colorbar(cax=ax_cb)\n",
    "cb.set_label('$p(x, y)$', fontsize = 14)\n",
    "plt.text(0, 1.02, r'$\\times 10^{-3}$',\n",
    "         transform=ax_cb.transAxes)\n",
    "\n",
    "# draw p(x) distribution\n",
    "ax_Px.plot(xbins[1:], H.sum(0), '-k', drawstyle='steps')\n",
    "\n",
    "# draw p(y) distribution\n",
    "ax_Py.plot(H.sum(1), ybins[1:], '-k', drawstyle='steps')\n",
    "\n",
    "# define axis limits\n",
    "ax_Pxy.set_xlim(0, 2)\n",
    "ax_Pxy.set_ylim(0, 2)\n",
    "ax_Px.set_xlim(0, 2)\n",
    "ax_Py.set_ylim(0, 2)\n",
    "\n",
    "# label axes\n",
    "ax_Pxy.set_xlabel('$x$', fontsize = 14)\n",
    "ax_Pxy.set_ylabel('$y$', fontsize = 14)\n",
    "ax_Px.set_xlabel('$x$', fontsize = 14)\n",
    "ax_Px.set_ylabel('$p(x)$', fontsize = 14)\n",
    "ax_Px.yaxis.set_label_position('right')\n",
    "ax_Py.set_ylabel('$y$', fontsize = 14)\n",
    "ax_Py.set_xlabel('$p(y)$', fontsize = 14)\n",
    "ax_Py.xaxis.set_label_position('top')\n",
    "\n",
    "ax_Px.tick_params(axis='both', which='major', labelsize=10)\n",
    "ax_Py.tick_params(axis='both', which='major', labelsize=10)\n",
    "\n",
    "# draw marginal probabilities\n",
    "iy = [3 * Ngrid // 4, Ngrid // 2, Ngrid // 4]\n",
    "colors = 'rgc'\n",
    "axis = ax_Pxy.axis()\n",
    "for i in range(3):\n",
    "    # overplot range on joint probability\n",
    "    ax_Pxy.plot([0, 2, 2, 0],\n",
    "                [ybins[iy[i] + 1], ybins[iy[i] + 1],\n",
    "                 ybins[iy[i]], ybins[iy[i]]], c=colors[i], lw=1)\n",
    "    Px_y = H[iy[i]] / H[iy[i]].sum()\n",
    "    ax_Px_y[i].plot(xbins[1:], Px_y, drawstyle='steps', c=colors[i])\n",
    "    ax_Px_y[i].yaxis.set_major_formatter(NullFormatter())\n",
    "    ax_Px_y[i].set_ylabel('$p(x | y = %.1f)$' % ybins[iy[i]], fontsize = 14)\n",
    "    ax_Px_y[i].tick_params(axis='both', which='major', labelsize=10)\n",
    "ax_Pxy.axis(axis)\n",
    "\n",
    "ax_Px_y[2].set_xlabel('$x$', fontsize = 14)\n",
    "\n",
    "ax_Pxy.set_title('Joint Probability', fontsize = 18)\n",
    "ax_Px_y[0].set_title('Conditional Probability', fontsize = 18)\n",
    "\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "27381112",
   "metadata": {},
   "source": [
    "Eq's. 2 and 4 can be combined to yield *Bayes' rule*:\n",
    "\n",
    "\n",
    "$$ \\qquad\\qquad p(y|x) = \\frac{p(x|y)p(y)}{p(x)} = \\frac{p(x|y)p(y)}{\\int p(x|y)p(y)dy} \\qquad\\qquad\\qquad(5) $$\n",
    "\n",
    "Bayes’ rule relates conditional and marginal probabilities to each other. In the case of a discrete random variable, $y_j$, with $M$ possible values, the integral in eq. 5 becomes a sum:\n",
    "\n",
    "$$p(y_j|x) = \\frac{p(x|y_j)p(y_j)}{p(x)} = \\frac{p(x|y_j)p(y_j)}{\\sum_{j=1}^M p(x|y_j)p(y_j)} $$"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "401e5875",
   "metadata": {},
   "source": [
    "## Example: Monty Hall problem\n",
    "\n",
    "The following problem illustrates how different probabilistic inferences can be derived about the same physical system depending on the available prior information.\n",
    "\n",
    "There are $N=1000$ boxes, of which 999 are empty, and one contains some “prize.” You choose a box at random; the probability that it contains the prize is 1/1000. This box remains closed while another person who knows which box contains the prize opens 998 **empty boxes** chosen from the 999 remaining boxes. \n",
    "\n",
    "At this point, two boxes remain: the one you chose at random and the last unopened box. This remaining box is almost certain to contain the prize; the probability is 999/1000 because there is a chance of only 1 in 1000 that the prize is in the box you chose initially, and the probabilities for the two unopened boxes must add up to 1. If you were offered to switch the box you initially chose with another unopened box, you would increase the chances of getting the prize by a factor of 999 (from 1/1000 to 999/1000). \n",
    "\n",
    "On the other hand, if a third person walked in and had to choose one of the two remaining unopened boxes, but without knowing that initially there were 1000 boxes, nor which one you initially chose, **they would pick the box with the prize with a probability of 1/2**. The difference in expected outcomes is due to different prior information, and it nicely illustrates that the probabilities we assign to events reflect the state of our knowledge."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "1a2b666e",
   "metadata": {},
   "source": [
    "#### Formal derivation of the solution using Bayes’ rule\n",
    "\n",
    "\n",
    "* $H_i$ is the hypothesis that the prize is in the $i$th box\n",
    "* $p(H_i|I) = 1/N$ is its prior probability given background information $I$. \n",
    "* The \"data\" that $N − 2$ boxes, all but the first box and the $k$th box $(k > 1)$, are empty is $d_k$\n",
    "\n",
    "Without a loss of generality, the box chosen initially can be enumerated as the first box. The probability that the prize is in the first box, given $I$ and $k$, can be evaluated using Bayes’ rule (see eq. 3.11)\n",
    "\n",
    "$$p(H_1|d_k,I) = \\frac{p(d_k|H_1,I)p(H_1|I)}{p(d_k|I)} $$\n",
    "\n",
    "The probability that the $k$th box remains unopened given that $H_1$ is true, $p(d_k|H_1,I)$ is $1/(N−1)$ because this box is randomly chosen from $N − 1$ boxes. The denominator can be expanded using\n",
    "the law of total probability,\n",
    "\n",
    "$$ p(d_k|I) = \\sum\\limits_{i=1}^N p(d_k|H_i, I)p(H_i|I) $$\n",
    "\n",
    "The probability that the $k$th box stays unopened, given that $H_i$ is true, is\n",
    "\n",
    "$$ p(d_k| H_i, I) =  \\begin{cases} 1 \\text{ for } k = i\\\\0 \\text{ otherwise} \\end{cases} $$\n",
    "\n",
    "except when $i = 1$. This reduces the sum to only two terms:\n",
    "\n",
    "$$ p(d_k|I) = p(d_k|H_1,I)p(H_1|I)+ p(d_k|H_k,I)p(H_k|I) = \\frac{1}{(N-1)N}+\\frac{1}{N}=\\frac{1}{N-1} $$\n",
    "\n",
    "This result might appear to agree with our intuition because there are $N − 1$ ways to choose one box out of $N − 1$ boxes, but this interpretation is not correct: the $k$th box is not chosen randomly in the case when the prize is not in the first box, but instead, it must be chosen (the second term in the sum above). Hence, from eq. 3.12, the probability that the prize is in the first (initially chosen) box is\n",
    "\n",
    "$$p(H_1|d_k,I) = \\frac{\\frac{1}{(N-1)}\\frac{1}{N}}{\\frac{1}{(N-1)}} = \\frac{1}{N}$$\n",
    "\n",
    "It is easy to show that $p(H_k|d_k,I) = (N −1)/N$. Note that $p(H_1|d_k,I)$ is equal to the prior probability $p(H_1|I)$; that is, the opening of $N − 2$ empty boxes (data $d_k$) did not improve our knowledge of the content of the first box (but it did improve our knowledge of the content of the $k$th box by a factor of $N −1$)."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "52829c78",
   "metadata": {},
   "source": [
    "## Example: 2×2 contingency table\n",
    "\n",
    "Assume we have a test for a disease. One variable is the result of the test T: the test can be negative (0) or positive (1); the second variable is the presence of disease D: the patient can have a disease (1) or not (0). \n",
    "\n",
    "There are four possible combinations in this sample space: \n",
    "$$T =0;D=0 \\quad\\text{True negative}$$\n",
    "$$T =0;D=1 \\quad\\text{False negative}$$\n",
    "$$T =1;D=0 \\quad\\text{False positive}$$\n",
    "$$T =1;D=1 \\quad\\text{True positive}$$\n",
    "\n",
    "We also know that the probabilities for false positive and false negative are \n",
    "$$p(T =1|D=0) = \\epsilon_{fP}$$\n",
    "$$p(T =0|D=1) = \\epsilon_{fN}$$\n",
    "\n",
    "where $\\epsilon_{fP}$ and $\\epsilon_{fN}$ are typically small. Then the probabilities for true positive and true negative are\n",
    "$$p(T =0|D=0) = 1-\\epsilon_{fP}$$\n",
    "$$p(T =1|D=1) = 1-\\epsilon_{fN}$$\n",
    "\n",
    "We'll visualize the information so far in a contingency table below."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "512337ee",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 288x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "from matplotlib import pyplot as plt\n",
    "\n",
    "fig = plt.figure(figsize=(4, 4), facecolor='w')\n",
    "ax = fig.add_axes((0, 0, 1, 1), xticks=[], yticks=[], frameon=False)\n",
    "\n",
    "for i in [-1, 0, 1]:\n",
    "    ax.plot([i, i], [-1, 1], '-k')\n",
    "    ax.plot([-1, 1], [i, i], '-k')\n",
    "\n",
    "kwds = dict(ha='center', va='center', size=18)\n",
    "\n",
    "ax.text(-0.5, 1.15, '0', **kwds)\n",
    "ax.text(0.5, 1.15, '1', **kwds)\n",
    "ax.text(0, 1.25, 'T', **kwds)\n",
    "\n",
    "ax.text(-1.15, 0.5, '0', **kwds)\n",
    "ax.text(-1.15, -0.5, '1', **kwds)\n",
    "ax.text(-1.25, 0, 'D', **kwds)\n",
    "\n",
    "kwds['size'] = 18\n",
    "\n",
    "ax.text(0.5, 0.5, '$\\epsilon_{fP}$', **kwds)\n",
    "ax.text(-0.5, 0.5, '$1 - \\epsilon_{fP}$', **kwds)\n",
    "ax.text(-0.5, -0.5, '$\\epsilon_{fN}$', **kwds)\n",
    "ax.text(0.5, -0.5, '$1 - \\epsilon_{fN}$', **kwds)\n",
    "\n",
    "ax.set_xlim(-1.5, 1.2)\n",
    "ax.set_ylim(-1.2, 1.5)\n",
    "\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "dc64c2ca",
   "metadata": {},
   "source": [
    "Let us assume that we also know that the prior probability (in the absence of any testing based on some large population studies unrelated to our test) for the disease in question is $p(D = 1) = \\epsilon_D$, where $\\epsilon_D$ is a small number. This makes $p(D = 0) = 1-\\epsilon_D$."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "0f889a64",
   "metadata": {},
   "source": [
    "Our patient takes a test and it comes out positive $(T=1)$ What is the probability that our patient has contracted the disease, $p(D = 1|T = 1)$? Using Bayes’ rule (eq. 5), we have\n",
    "\n",
    "$$p(D=1|T=1) = \\frac{p(T=1|D=1)p(D=1)}{p(T=1|D=0)p(D=0) + p(T=1|D=1)p(D=1)}. $$\n",
    "\n",
    "Given our assumptions,\n",
    "\n",
    "$$ p(D=1|T=1) = \\frac{(1-\\epsilon_{fN})\\epsilon_{D}}{\\epsilon_{fP}(1-\\epsilon_D)+(1-\\epsilon_{fN})\\epsilon_{D}}, $$\n",
    "\n",
    "which simplifies to\n",
    "\n",
    "$$ p(D =1|T=1) = \\frac{\\epsilon_D-\\epsilon_{fN}\\epsilon_D}{\\epsilon_D+\\epsilon_{fP}- [\\epsilon_D(\\epsilon_{fP}+\\epsilon_{fN})]} \\approx \\frac{\\epsilon_D}{\\epsilon_D + \\epsilon_{fP}}.$$\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "5a9e27cd",
   "metadata": {},
   "source": [
    "This is an interesting result: we can only reliably diagnose a disease (i.e., p(D = 1|T = 1) $\\sim$ 1) if $\\epsilon_{fP} \\ll \\epsilon_D$. For rare diseases, the test must have an exceedingly low false-positive rate! On the other hand, if $\\epsilon_{fP} \\gg \\epsilon_D$, then $p(D = 1|T = 1) \\sim \\epsilon_D/\\epsilon_{fP} \\ll 1$ and the testing does not produce conclusive evidence. The false-negative rate is not quantitatively important as long as it is not much larger than the other two parameters.\n",
    "\n",
    "Consider a sample of 1000 tested people. Assume we have a disease rate of 1% ($\\epsilon_D = 0.01$) and a false positive rate of 2% ($\\epsilon_{fp} = 0.02$).\n",
    "\n",
    "$$ p(D=1|T=1) = \\frac{0.01}{0.02+0.01} = 0.33 $$\n",
    " \n",
    "\n",
    "Then in a sample of, e.g., 1000 people, 10 people test positive and actually have the disease (1000 $\\times$  0.01), but another 20 will test positive while healthy (1000 $\\times$  0.02). Therefore, in that sample of 30 people who tested positive, only 1/3 has the disease (not 98%)."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "4ba6e452",
   "metadata": {},
   "source": [
    "## Transformations of random variables\n",
    "\n",
    "Any function of a random variable is itself a random variable. It is a common case in practice that we measure the value of some variable $x$, but the interesting final result is a function $y(x)$. If we know the probability density distribution $p(x)$, where $x$ is a random variable, what is the distribution $p(y)$, where $y = \\Phi(x)$ (with $x = \\Phi−1(y)$)? It is easy to show that\n",
    "\n",
    "$$ p(y) = p\\big[\\Phi ^ {-1} (y)\\big] \\bigg|\\frac{d\\Phi^{-1}(y)}{dy}\\bigg|.$$\n",
    "\n",
    "For example, if $y=\\Phi(x)= \\text{exp}(x)$, then $x=\\Phi^{−1}(y)=\\text{ln}(y)$. If $p(x)=1 $ for $0\\leq x \\leq 1 $ and 0 otherwise (a uniform distribution), the equation above leads to $p(y) = 1/y$, with $1 \\leq y \\leq e$. That is, a uniform distribution of $x$ is transformed into a nonuniform distribution of $y$.\n",
    "\n",
    "Below is an example of transforming a uniform distribution. In the left panel, $x$ is sampled from a uniform distribution of unit width centered on $x = 0.5$ ($\\mu = 0$ and $W = 1$; see §3.3.1). In the right panel, the distribution is transformed via $y$ = exp($x$). The form of the resulting pdf is computed from the equation above."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "id": "d1cf2105",
   "metadata": {},
   "outputs": [
    {
     "data": {
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\n",
      "text/plain": [
       "<Figure size 1008x432 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "import numpy as np\n",
    "from scipy import stats\n",
    "from matplotlib import pyplot as plt\n",
    "\n",
    "# Set up the data\n",
    "np.random.seed(0)\n",
    "\n",
    "# create a uniform distribution\n",
    "uniform_dist = stats.uniform(0, 1)\n",
    "x_sample = uniform_dist.rvs(1000)\n",
    "x = np.linspace(-0.5, 1.5, 1000)\n",
    "Px = uniform_dist.pdf(x)\n",
    "\n",
    "# transform the data\n",
    "y_sample = np.exp(x_sample)\n",
    "y = np.exp(x)\n",
    "Py = Px / y\n",
    "\n",
    "#------------------------------------------------------------\n",
    "# Plot the results\n",
    "fig = plt.figure(figsize=(14, 6))\n",
    "fig.subplots_adjust(left=0.11, right=0.95, wspace=0.3, bottom=0.17, top=0.9)\n",
    "\n",
    "ax = fig.add_subplot(121)\n",
    "ax.hist(x_sample, 20, histtype='stepfilled', fc='#CCCCCC', density=True)\n",
    "ax.plot(x, Px, '-k')\n",
    "ax.set_xlim(-0.2, 1.2)\n",
    "ax.set_ylim(0, 1.4001)\n",
    "ax.xaxis.set_major_locator(plt.MaxNLocator(6))\n",
    "ax.text(0.95, 0.95, r'$p_x(x) = {\\rm Uniform}(x)$',\n",
    "        va='top', ha='right',\n",
    "        transform=ax.transAxes, fontsize = 12)\n",
    "ax.set_xlabel('$x$', fontsize = 14)\n",
    "ax.set_ylabel('$p_x(x)$', fontsize = 14)\n",
    "\n",
    "\n",
    "ax = fig.add_subplot(122)\n",
    "ax.hist(y_sample, 20, histtype='stepfilled', fc='#CCCCCC', density=True)\n",
    "ax.plot(y, Py, '-k')\n",
    "ax.set_xlim(0.85, 2.9)\n",
    "ax.xaxis.set_major_locator(plt.MaxNLocator(6))\n",
    "ax.text(0.95, 0.95, '$y=\\exp(x)$\\n$p_y(y)=p_x(\\ln y) / y$',\n",
    "        va='top', ha='right',\n",
    "        transform=ax.transAxes, fontsize = 12)\n",
    "ax.set_xlabel('$y$',fontsize = 14)\n",
    "ax.set_ylabel('$p_y(y)$', fontsize = 14)\n",
    "\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "2bc006ed",
   "metadata": {},
   "source": [
    "If some value of $x$, say $x_0$, is determined with an uncertainty $\\sigma_x$, then we can use a Taylor series expansion to estimate the uncertainty in $y$, say $\\sigma_y$, at $y_0 = \\Phi(x_0)$ as\n",
    "\n",
    "$$\\sigma_y = \\bigg|\\frac{d\\Phi(x)}{dx}\\bigg|_0 \\sigma_x $$.\n",
    "\n",
    "\n",
    "where the derivative is evaluated at $x_0$. While often used, this approach can produce misleading results when it is insufficient to keep only the first term in the Taylor series. For example, if the flux measurements follow a Gaussian distribution with a relative accuracy of a few percent, then the corresponding distribution of astronomical magnitudes (the logarithm of flux; see appendix C) is close to a Gaussian distribution. However, if the relative flux accuracy is 20% (corresponding to the so-called “$5 − \\sigma$” detection limit), then the distribution of magnitudes is skewed and non-Gaussian. Furthermore, the mean magnitude is not equal to the logarithm of the mean flux (but the medians still correspond to each other!).\n",
    "\n",
    "Below is an example of relatively high Gaussian flux errors becoming non-Gaussian magnitude errors; additionally, we'll show relatively low Gaussian flux errors becoming mostly Gaussian magnitude errors. The dotted line shows the location of the mean flux $-$ note that this is not coincident with the peak of the magnitude distribution for high Gaussian flux errors. However, for low Gaussian flux errors, the dotted line roughly passes through the peak of the magnitude distribution."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "id": "a8084c1b",
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "from matplotlib import pyplot as plt\n",
    "from scipy.stats import norm\n",
    "np.random.seed(1)\n",
    "\n",
    "# create distribution with 1% flux errors\n",
    "dist = norm(1, 0.01)\n",
    "flux = dist.rvs(10000)\n",
    "flux_fit = np.linspace(0.001, 2, 1000)\n",
    "pdf_flux_fit = dist.pdf(flux_fit)\n",
    "\n",
    "# transform this distribution into magnitude space\n",
    "mag = -2.5 * np.log10(flux)\n",
    "mag_fit = -2.5 * np.log10(flux_fit)\n",
    "pdf_mag_fit = pdf_flux_fit.copy()\n",
    "pdf_mag_fit[1:] /= abs(mag_fit[1:] - mag_fit[:-1])\n",
    "pdf_mag_fit /= np.dot(pdf_mag_fit[1:], abs(mag_fit[1:] - mag_fit[:-1]))\n",
    "\n",
    "# create distribution with 25% flux errors\n",
    "dist25 = norm(1, 0.20)\n",
    "flux25 = dist25.rvs(10000)\n",
    "flux_fit25 = np.linspace(0.001, 2, 1000)\n",
    "pdf_flux_fit25 = dist25.pdf(flux_fit25)\n",
    "\n",
    "# transform this distribution into magnitude space\n",
    "mag25 = -2.5 * np.log10(flux25)\n",
    "mag_fit25 = -2.5 * np.log10(flux_fit25)\n",
    "pdf_mag_fit25 = pdf_flux_fit25.copy()\n",
    "pdf_mag_fit25[1:] /= abs(mag_fit25[1:] - mag_fit25[:-1])\n",
    "pdf_mag_fit25 /= np.dot(pdf_mag_fit25[1:], abs(mag_fit25[1:] - mag_fit25[:-1]))"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "2f1db32c",
   "metadata": {},
   "source": [
    "Next, we'll plot the distributions."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "id": "75582414",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 936x792 with 4 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = plt.subplots(2,2)                \n",
    "fig.set_size_inches(13,11)   \n",
    "fig.tight_layout(w_pad=4, h_pad=7)\n",
    "\n",
    "#------------------------------------------------------------ 1% flux error\n",
    "ax[0,0].hist(flux, bins=np.linspace(0.75, 1.25, 50),\n",
    "        histtype='stepfilled', fc='gray', alpha=0.5, density=True)\n",
    "ax[0,0].plot(flux_fit, pdf_flux_fit, '-k')\n",
    "ax[0,0].plot([1, 1], [0, 42], ':k', lw=1)\n",
    "ax[0,0].set_xlim(0.75, 1.25)\n",
    "ax[0,0].set_xlabel(r'${\\rm flux}$', fontsize = 12)\n",
    "ax[0,0].set_ylabel(r'$p({\\rm flux})$', fontsize = 12)\n",
    "ax[0,0].text(0.04, 0.95, r'${\\rm 1\\%\\ flux\\ error}$',\n",
    "        ha='left', va='top', transform=ax[0,0].transAxes)\n",
    "\n",
    "#------------------------------------------------------------ 1% magnitude error\n",
    "ax[0,1].hist(mag, bins=np.linspace(-0.25, 0.25, 50),\n",
    "        histtype='stepfilled', fc='gray', alpha=0.5, density=True)\n",
    "ax[0,1].plot(mag_fit, pdf_mag_fit, '-k')\n",
    "ax[0,1].plot([0, 0], [0, 42], ':k', lw=1)\n",
    "ax[0,1].set_xlim(-0.25, 0.25)\n",
    "ax[0,1].set_xlabel(r'${\\rm mag}$', fontsize = 12)\n",
    "ax[0,1].set_ylabel(r'$p({\\rm mag})$', fontsize = 12)\n",
    "ax[0,1].text(0.04, 0.95, r'${\\rm mag} = -2.5\\log_{10}({\\rm flux})$',\n",
    "        ha='left', va='top', transform=ax[0,1].transAxes)\n",
    "\n",
    "#------------------------------------------------------------ 20% flux error\n",
    "ax[1,0].hist(flux25, bins=np.linspace(0, 2, 50),\n",
    "        histtype='stepfilled', fc='gray', alpha=0.5, density=True)\n",
    "ax[1,0].plot(flux_fit25, pdf_flux_fit25, '-k')\n",
    "ax[1,0].plot([1, 1], [0, 2.1], ':k', lw=1)\n",
    "ax[1,0].set_xlim(0, 2)\n",
    "ax[1,0].set_ylim(0, 2.1)\n",
    "ax[1,0].set_xlabel(r'${\\rm flux}$', fontsize = 12)\n",
    "ax[1,0].set_ylabel(r'$p({\\rm flux})$', fontsize = 12)\n",
    "ax[1,0].text(0.04, 0.95, r'${\\rm 20\\%\\ flux\\ error}$',\n",
    "        ha='left', va='top', transform=ax[1,0].transAxes)\n",
    "\n",
    "#------------------------------------------------------------ 20% magnitude error\n",
    "ax[1,1].hist(mag25, bins=np.linspace(-1, 1, 50),\n",
    "        histtype='stepfilled', fc='gray', alpha=0.5, density=True)\n",
    "ax[1,1].plot(mag_fit25, pdf_mag_fit25, '-k')\n",
    "ax[1,1].plot([0, 0], [0, 2], ':k', lw=1)\n",
    "ax[1,1].set_xlim(-1, 1)\n",
    "ax[1,1].set_xlabel(r'${\\rm mag}$', fontsize = 12)\n",
    "ax[1,1].set_ylabel(r'$p({\\rm mag})$', fontsize = 12)\n",
    "ax[1,1].text(0.04, 0.95, r'${\\rm mag} = -2.5\\log_{10}({\\rm flux})$',\n",
    "        ha='left', va='top', transform=ax[1,1].transAxes);"
   ]
  }
 ],
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  "kernelspec": {
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