{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Problem 1\n",
    "## a)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The two net-gain equations are just\n",
    "\\begin{align*}\n",
    "G_A &= Y_A - b_A Y_A - b_B Y_B \\\\\n",
    "G_B &= Y_B - b_A Y_A - b_B Y_B\n",
    "\\end{align*}\n",
    "\n",
    "From these, we would like to prove that if Jill chooses $\\left\\{b_A, b_B\\right\\}$ such that either $G_A\\ge0$ or $G_B\\ge0$ (ie. the bet is not a sure loss), then $b_A \\in [0,1]$.\n",
    "\n",
    "Stated logically, this is:\n",
    "\\begin{equation*}\n",
    "(G_A\\ge0 \\vee G_B\\ge0) \\rightarrow b_A \\in [0,1] \\quad \\quad (1)\n",
    "\\end{equation*}\n",
    "\n",
    "Clearly, only the signs of $G_A$, and $G_B$ are important so let's scale them by dividing through by $Y_A$. The new $G$s are \n",
    "\\begin{align*}\n",
    "G_A &= 1 - b_A - b_B \\gamma \\\\\n",
    "G_B &= \\gamma - b_A - b_B \\gamma\n",
    "\\end{align*}\n",
    "\n",
    "where, \n",
    "\\begin{equation*}\n",
    "\\gamma \\equiv \\frac{Y_B}{Y_A}\n",
    "\\end{equation*}\n",
    "\n",
    "At this point, it is necessary to note the ranges of the involved variables. We assume that all $Y$ and $b$ are non-negative, which implies that $\\gamma$ is also non-negative.\n",
    "\n",
    "According to (1), it is sufficient to show individually that $G_A\\ge0 \\rightarrow b_A \\in [0,1])$, and $G_B\\ge0 \\rightarrow b_A \\in [0,1])$. Since if both of those conditions hold, then (1) holds. Let's do the $G_A$ case first.\n",
    "\n",
    "If $G_A\\ge 0$, then\n",
    "\\begin{equation*}\n",
    "1 - b_A - b_B\\gamma \\ge 0\n",
    "\\end{equation*}\n",
    "\n",
    "Or, written slightly differently,\n",
    "\\begin{equation*}\n",
    "1 - b_A \\ge b_B\\gamma\n",
    "\\end{equation*}\n",
    "\n",
    "The right hand side is strictly non-negative, which implies that $(1-b_A) \\ge 0$. This coupled with the assumption that $b_A$ itself must be non-negative implies that $b_A \\in [0,1]$. \n",
    "\n",
    "For the case of $G_B\\ge0$, simply redefine $\\gamma$ as $\\frac{Y_A}{Y_B}$ and the steps are identical. Together with the $G_A$ case, this proves (1). Note that because $b_A$, and $b_B$ enter the problem symetrically, a nearly identical proof can be made to show that $b \\in [0,1]$ also."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## b)\n",
    "\n",
    "The net-gain equations are\n",
    "\n",
    "\\begin{align*}\n",
    "G_1 &= (1-b_a)Y_A - b_B Y_B + (1-b_C)Y_C\\\\\n",
    "G_2 &= -b_A Y_A + (1-b_B) Y_B + (1-b_C)Y_C\\\\\n",
    "G_3 &=  -b_A Y_A - b_B Y_B - b_B Y_C\n",
    "\\end{align*}\n",
    "\n",
    "Let's first rewrite the above equations with the assumption that $b_C=b_A+b_B$ and gathering common terms in the $b$'s.\n",
    "\n",
    "\\begin{align*}\n",
    "G_1 &= (Y_A + Y_C) - (Y_A + Y_C)b_A - (Y_B + Y_C)b_B \\\\\n",
    "G_2 &= (Y_B + Y_C) - (Y_A + Y_C)b_A - (Y_B + Y_C)b_B \\\\\n",
    "G_3 &= - (Y_A + Y_C)b_A - (Y_B + Y_C)b_B\n",
    "\\end{align*}\n",
    "\n",
    "Noticing that $(Y_A + Y_C)$ and $(Y_B + Y_C)$ are common in the above equations, lets replace them with new variables, $\\alpha$ and $\\beta$, respectively.\n",
    "\n",
    "\\begin{align*}\n",
    "G_1 &= \\alpha - \\alpha b_A - \\beta b_B \\\\\n",
    "G_2 &= \\beta - \\alpha b_A - \\beta b_B \\\\\n",
    "G_3 &= -\\alpha b_A - \\beta b_B\n",
    "\\end{align*}\n",
    "\n",
    "For one last simplification, we note that we only care about the sign of the G's, so we are free to multiply/divide by any positive factor. So divide $G_1$ and $G_3$ by $\\alpha$ and $G_2$ by $\\beta$.\n",
    "\n",
    "\\begin{align*}\n",
    "G_1 &= 1 - b_A - \\gamma^{-1} b_B \\\\\n",
    "G_2 &= 1 - \\gamma b_A - b_B \\\\\n",
    "G_3 &= -b_A - \\gamma^{-1} b_B\n",
    "\\end{align*}\n",
    "\n",
    "Where $\\gamma \\equiv \\frac{\\alpha}{\\beta}$. What remains is to show that no value of $\\gamma$ can make all three $G$'s simultaneously negative. $G_3$ is always negative so at least one of $G_1$ and $G_2$ must be non-negative. Let's first consider what values of $\\gamma$ make $G_1$ negative.\n",
    "\n",
    "\\begin{align*}\n",
    "1 - b_A - \\gamma^{-1} b_B &< 0\\\\\n",
    "(1 - b_A)\\gamma - b_B &< 0 \\\\\n",
    "\\gamma &< \\frac{b_B}{1 - b_A} \\quad\\quad (2) \\\\\n",
    "\\end{align*}\n",
    "\n",
    "Now, we do the same thing for $G_2$,\n",
    "\\begin{align*}\n",
    "1 - \\gamma b_A - b_B &< 0 \\\\\n",
    "1 - b_B &< \\gamma b_A \\\\\n",
    "\\gamma &> \\frac{1-b_B}{b_A} \\quad\\quad (3) \\\\\n",
    "\\end{align*}\n",
    "\n",
    "So, if (2) and (3) describe disjoint regions in $\\gamma$, then $G_1$ and $G_2$ cannot be simultaneously negative. Notice that (2) forms an upper bound on $\\gamma$ and (3) a lower bound. If the upper bound is smaller than the lower bound, then clearly no value can satisfy both. So let's see if this is the case.\n",
    "\n",
    "\\begin{align*}\n",
    "&\\frac{b_B}{1 - b_A} - \\frac{1-b_B}{b_A} \\\\\n",
    "&= \\frac{b_B b_A}{b_A(1 - b_A)} - \\frac{(1-b_A)(1-b_B)}{b_A(1-b_A)} \\\\\n",
    "&= \\frac{(b_A + b_B) - 1}{b_A(1 - b_A)} < 0, \\quad \\mathrm{if }\\quad b_A + b_B < 1\\\\\n",
    "\\end{align*}\n",
    "\n",
    "So, finally, if we assume that $b_A + b_B < 1$, which seems reasonable, the set of $\\gamma$ that make $G_1$ and $G_2$ simultaneously negative is empty. Therefore, it is impossible for Jack to choose the Y's such that Jill has a sure loss."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Problem 2\n",
    "    "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "from scipy.stats import gamma, poisson\n",
    "import matplotlib.pyplot as plt\n",
    "%matplotlib inline\n",
    "plt.rcParams['figure.dpi']=150"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "N = 25\n",
    "B, dB = 9.4,  0.5\n",
    "S, dS = 17.3, 1.3\n",
    "\n",
    "def to_M_kappa(J, dJ):\n",
    "    return J**2/dJ**2, J/dJ**2\n",
    "\n",
    "MB, kappaB = to_M_kappa(B, dB)\n",
    "MS, kappaS = to_M_kappa(S, dS)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
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VEXGakicRESkV6ZlZ/OPbDZ5y5+Z1uLl3KwcjKh/Cw8N57rnnmP3Ff/lyxjQC3TNOmw+c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\nAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f91e48949b0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "def mlikelihood(N, MS, MB, mu, kappaS, kappaB, K=50000):\n",
    "    betaS = kappaS**-1\n",
    "    betaB = kappaB**-1\n",
    "    s = gamma.rvs(MS+1, scale=betaS, size=K)\n",
    "    b = gamma.rvs(MB+1, scale=betaB, size=K)\n",
    "    return np.sum(poisson.pmf(N, mu*s + b)) / K\n",
    "\n",
    "lhood = lambda mu: mlikelihood(N, MS, MB, mu, kappaS, kappaB)\n",
    "\n",
    "pH0 = lhood(0)\n",
    "mus = np.linspace(0,2,100)\n",
    "\n",
    "ratios = [lhood(mu)/pH0 for mu in mus]\n",
    "\n",
    "ratio_1_0 = lhood(1)/pH0\n",
    "\n",
    "plt.plot(mus, ratios)\n",
    "plt.plot([1], ratio_1_0, 'k.')\n",
    "plt.annotate(f'$\\\\frac{{p(H_1|D)}}{{p(H_0|D)}} = {ratio_1_0:4.2f}$',\n",
    "            xy=(1, ratio_1_0), xytext=(1.25, 3500),\n",
    "            arrowprops={'arrowstyle': '->'});\n",
    "plt.xlabel(r'$\\mu$')\n",
    "plt.ylabel(r'$\\frac{p(H_\\mu|D)}{p(H_0|D)}$')"
   ]
  }
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