{
 "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": 13,
   "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": 1,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "N = 25\n",
    "B = 9.4\n",
    "dB = 0.5\n",
    "S = 17.3\n",
    "dS = 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": 21,
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "data": {
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UkT5GyZOISB/11Nv72HnE2wMoNcW4+cIJAUck3S0jLYUvXTqJq2eP4PWtRzhQ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\nhFe/3sbG/Tne7Weu7o8jNNiPEYmI1J9fX9wbY9w/bzuUywdpmTV3EJE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Wv513+4+fbyS3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\nJKkCJ0+SJEmSVMF/AYvL6+7ev8r7AAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f11a49baef0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "def mlikelihood(N, MS, MB, mu, kappaS, kappaB, K=10):\n",
    "    \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(0,2,50)\n",
    "\n",
    "ratios = [lhood(mu)/pH0 for mu in mus]\n",
    "\n",
    "plt.plot(mus, ratios)\n",
    "plt.xlabel(r'$\\mu$')\n",
    "plt.ylabel(r'$\\frac{p(H_\\mu|D)}{p(H_0|D)}$')\n",
    "plt.text(0.75, 1000, r'$\\frac{{p(H_1|D)}}{{p(H_0|D)}} = {:4.2f}$'.format(lhood(1)/lhood(0)));"
   ]
  }
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