cc7768/foo.json

## foo.json
{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We begin by importing some packages called by the code that we will be using in this notebook."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "import scipy.interpolate as interp\n",
    "import scipy.stats as st\n",
    "import seaborn as sb\n",
    "import quantecon as qe\n",
    "\n",
    "from ipywidgets import interact, widgets\n",
    "from Wald_Friedman_utils import *\n",
    "\n",
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Sequential analysis\n",
    "\n",
    "Key ideas in  play are:\n",
    "\n",
    " * type I and type II statistical errors\n",
    "    \n",
    "    * a type I error occurs when you reject a  null hypothesis that is true\n",
    "    \n",
    "    * a type II error is when you accept a null hypothesis that is false \n",
    " \n",
    " * Dynamic programming\n",
    " \n",
    " * Bayes' Law\n",
    " \n",
    " * $\\ldots$ \n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "On pages 137-139 of his book **Two Lucky People** with Rose Friedman, Milton Friedman described a problem presented to him and Allen Wallis during World War II when they worked at the U.S. government's Statistical Research Group at Columbia University.  \n",
    "\n",
    "Let's listen to Milton Friedman tell what happened.\n",
    "\n",
    "   \"In order to understand the story, it is necessary to have an idea of a simple statistical problem, and of the\n",
    "   standard procedure for dealing with it.  The actual problem out of which sequential analysis grew will serve.\n",
    "   The Navy has two alternative designs (say A and B) for a projectile.  It wants to determine which is superior. \n",
    "   To do so it undertakes a series of paired firings. On each round it assigns the value 1 or 0 to A accordingly as\n",
    "   its performance is superior or inferio to that of B and conversely 0 or 1 to B.  The Navy asks the statistician \n",
    "   how to conduct the test and how to analyze the results. \n",
    "   \n",
    "   \"The standard statistical answer was to specify a number of firings (say 1,000) and a pair of percentages\n",
    "   (e.g., 53% and 47%) and tell the client that if A receives a 1 more than 53% of the firings, it can be regarded\n",
    "   as superior; if it receives a 1 in fewer than 47%, B can be regarded as superior; if the percentage is between\n",
    "   47% and 53%, neither can be so regarded.\n",
    "   \n",
    "   \"When Allen Wallis was discussing such a problem with (Navy) Captain Garret L. Schyler, the captain objected that     such a test, to quote from Allen's account, may prove wasteful.  If a wise and seasoned ordnance officer like   Schyler were on the premises, he would see after the first few thousand or even few hundred [rounds] that the   experiment need not be completed either because he new method is obviously inferior or because it is obviously   superior beyond what was hoped for $\\ldots$ \"\n",
    "  \n",
    "  Friedman and Wallis struggled with the problem but after realizing that they were not able to solve it themselves told Abraham Wald it.  That started  Wald on the path that led  *Sequential Analysis*. We'll formulate the problem using dynamic programming.\n",
    "  "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Dynamic programming formulation\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The following presentation of the problem closely follows Dmitri Berskekas's treatment in **Dynamic Programming and Stochastic Control**.  \n",
    "\n",
    "An i.i.d.  random variable $z$ can take on values \n",
    "\n",
    "  * $z \\in [ v_1,  v_2, \\ldots,  v_n]$ when $z$ is a discrete-valued random variable\n",
    "  \n",
    "  * $ z \\in V$ when $z$ is a continuous random variable.  \n",
    "\n",
    "A decision maker wants to  know which of two probability distributions governs  $z$. To formalize this idea,\n",
    "let $x \\in [x_0, x_1]$ be a hidden state that indexes the two distributions:\n",
    "\n",
    "$$ P(v_k | x) = \\begin{cases} f_0(v_k) & \\mbox{if } x = x_0, \\\\\n",
    "                              f_1(v_k) & \\mbox{if } x = x_1. \\end{cases} $$\n",
    "                              \n",
    "when $z$ is a discrete random variable and a density\n",
    "\n",
    "\n",
    "$$ P(v | x) = \\begin{cases} f_0(v) & \\mbox{if } x = x_0, \\\\\n",
    "                              f_1(v) & \\mbox{if } x = x_1. \\end{cases} $$\n",
    "                              \n",
    "when $v$ is continuously distributed.                              \n",
    "\n",
    "                              \n",
    "\n",
    "Before observing any outcomes, a decision maker believes that the probability that $x = x_0$ is $p_{-1}\\in (0,1)$: \n",
    "\n",
    "$$ p_{-1} = \\textrm{Prob}(x=x_0 | \\textrm{ no observations}) $$\n",
    "\n",
    "After observing $k+1$ observations $z_k, z_{k-1}, \\ldots, z_0$ he believes that the probability that the distribution is $f_0$ is\n",
    "\n",
    "$$ p_k = {\\rm Prob} ( x = x_0 | z_k, z_{k-1}, \\ldots, z_0) $$\n",
    "\n",
    "We can compute this $p_k$ recursively by applying Bayes' law:\n",
    "\n",
    "$$ p_0 = \\frac{ p_{-1} f_0(z_0)}{ p_{-1} f_0(z_0) + (1-p_{-1}) f_1(z_0) } $$\n",
    "\n",
    "and then\n",
    "\n",
    "$$ p_{k+1} = \\frac{ p_k f_0(z_{k+1})}{ p_k f_0(z_{k+1}) + (1-p_k) f_1 (z_{k+1}) }. $$\n",
    "\n",
    "\n",
    "After observing $z_k, z_{k-1}, \\ldots, z_0$, the decision maker believes that $z_{k+1}$ \n",
    "has probability distribution\n",
    "\n",
    "$$ p(z_{k+1}) = p_k f_0(z_{k+1}) + (1-p_k) f_1 (z_{k+1}). $$\n",
    "\n",
    "This is evidently a mixture of distributions $f_0$ and $f_1$, with the weight on $f_0$ being the posterior probability $f_0$ that the distribution is $f_0$. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's look at some examples of two distributions. Here we'll display the two beta distributions\n",
    "that we'll use later in this notebook.  First, we'll show the two distributions, then we'll show mixtures of these same two distributions with various mixing probabilities $p_k$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "# Create two distributions over 50 values for k\n",
    "# We are using a discretized beta distribution\n",
    "p_m1 = np.linspace(0, 1, 50)\n",
    "f0 = st.beta.pdf(p_m1, a=1, b=1)\n",
    "f0 = f0 / np.sum(f0)\n",
    "f1 = st.beta.pdf(p_m1, a=9, b=9)\n",
    "f1 = f1 / np.sum(f1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
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lY8zE2gettZ6GjyUiTZG2fJNgm9FjKnvO7Wdx9kr6temjXVNE5GvVZ7rFYaAU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7qu03jwAJWrV+C8cMHoTDprDrFL7u3xBDYljWX8/OCr1DhrWTz6du7OWISiKPxj6xnWbj/H3OwR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\n3TxZJQAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f1aec8b3908>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig = make_distribution_plots(f0, f1)\n",
    "\n",
    "fig.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Losses and costs\n",
    "\n",
    "\n",
    "After observing $z_k, z_{k-1}, \\ldots, z_0$, the decision maker chooses among three distinct actions:\n",
    "\n",
    "* He decides that $x = x_1$ and draws no more $z$'s\n",
    "\n",
    "* He decides that $x = x_0$ and draws no more $z$'s\n",
    "\n",
    "* He postpones deciding now and instead chooses to draw a $z_{k+1}$\n",
    "\n",
    "Associated with these three actions, the decision maker suffers three kinds of losses:\n",
    "\n",
    " \n",
    "* A loss $L_0$ if he decides $x = x_1$ when actually $x=x_0$\n",
    "\n",
    "* A loss $L_1$ if he decides $x = x_0$ when actually $x=x_1$\n",
    "\n",
    "* A cost $c$ if he postpones deciding and chooses instead to draw another  $z$ \n",
    "\n",
    "For example, suppose that we regard $x=x_0$ as a null hypothesis. Then  \n",
    "\n",
    "* We can think of $L_0$ as the loss associated with a type I error\n",
    "\n",
    "* We can think of $L_1$ as the loss associated with a type II error"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### A Bellman equation\n",
    "\n",
    "Let $J_k(p_k)$ be the  total loss for a decision maker who with posterior probability $p_k$ who chooses optimally.\n",
    "\n",
    "The loss functions $\\{J_k(p_k)\\}_k$ satisfy the Bellman equations\n",
    "\n",
    "$$ J_k(p_k) = \\min \\left[ (1-p_k) L_0, p_k L_1, c + E_{z_{k+1}} \\left\\{ J_{k+1} (p_{k+1} \\right\\} \\right] $$\n",
    "\n",
    "where $E_{z_{k+1}}$ denotes a mathematical expectation over the distribution of $z_{k+1}$ and  the minimization is over the three actions, accept $x_1$, accept $x_0$, and postpone deciding and draw \n",
    "a $z_{k+1}$.  \n",
    "\n",
    "Let \n",
    "\n",
    "$$ A_k(p_k) = E_{z_{k+1}} \\left\\{ J_{k+1} \\left[\\frac{ p_k f_0(z_{k+1})}{ p_k f_0(z_{k+1}) + (1-p_k) f_1 (z_{k+1})  } \\right] \\right\\} $$\n",
    "\n",
    "Then we can write out Bellman equation as\n",
    "\n",
    "$$ J_k(p_k) = \\min \\left[ (1-p_k) L_0, p_k L_1, c + A_k(p_k) \\right] $$\n",
    "\n",
    "where $p_k \\in [0,1]$.  \n",
    "\n",
    "Evidently,the optimal decision rule is characterized by two numbers $\\alpha_k, \\beta_k \\in (0,1) \\times (0,1)$\n",
    "that satisfy\n",
    "\n",
    "$$ (1- p_k) L_0 < \\min p_k L_1, c + A_k(p_k)  \\textrm { if } p_k \\geq \\alpha_k  $$\n",
    "\n",
    "and \n",
    "\n",
    "$$ p_k L_1 < \\min (1-p_k) L_0,  c + A_k(p_k) \\textrm { if } p_k \\leq \\beta_k $$\n",
    "\n",
    "The optimal decision rule is then\n",
    "\n",
    "$$ \\textrm { accept } x=x_0 \\textrm{ if } p_k \\geq \\alpha_k \\\\\n",
    "   \\textrm { accept } x=x_1 \\textrm{ if } p_k \\leq \\beta_k \\\\\n",
    "   \\textrm { draw another }  z \\textrm{ if }  \\beta_k \\leq p_k \\leq \\alpha_k $$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Infinite horizon version\n",
    "\n",
    "An infinite horizon version of this problem is associated with the limiting Bellman equation \n",
    "\n",
    "$$ J(p_k) = \\min \\left[ (1-p_k) L_0, p_k L_1, c + A(p_k) \\right] \\quad (*) $$\n",
    "\n",
    "where\n",
    "\n",
    "$$ A(p_k) = E_{z_{k+1}} \\left\\{ J \\left[\\frac{ p_k f_0(z_{k+1})}{ p_k f_0(z_{k+1}) + (1-p_k) f_1 (z_{k+1})  } \\right] \\right\\} $$\n",
    "\n",
    "and again the minimization is over the three actions, accept $x_1$, accept $x_0$, and postpone deciding and draw \n",
    "a $z_{k+1}$.\n",
    "\n",
    "Here\n",
    "\n",
    "  * $ (1-p_k) L_0$ is the expected loss associated with accepting $x_1$ (i.e., the cost of making a type I error)\n",
    "  \n",
    "  *  $p_k L_1$ is the expected loss associated with accepting $x_0$ (i.e., the cost of making a type II error)\n",
    "  \n",
    "  * $ c + A(p_k)$ is the expected cost associated with drawing one more  $z$\n",
    "\n",
    "\n",
    "Now the optimal decision rule is characterized by two probabilities $0 < \\beta < \\alpha < 1$ and \n",
    "\n",
    "\n",
    "$$ \\textrm { accept } x=x_0 \\textrm{ if } p_k \\geq \\alpha \\\\\n",
    "   \\textrm { accept } x=x_1 \\textrm{ if } p_k \\leq \\beta \\\\\n",
    "   \\textrm { draw another }  z \\textrm{ if } \\beta \\leq p_k \\leq \\alpha $$\n",
    "\n",
    "\n",
    "  "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "One sensible approach is to write the three components of the value function that appears on the rights side of the Bellman equation as separate functions.  Later, doing this will help us obey the don't repeat yourself (DRY) rule of coding.  Here goes:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def expect_loss_choose_0(p, L0):\n",
    "    \"For a given probability return expected loss of choosing model 0\"\n",
    "    return (1-p)*L0\n",
    "\n",
    "def expect_loss_choose_1(p, L1):\n",
    "    \"For a given probability return expected loss of choosing model 1\"\n",
    "    return p*L1\n",
    "\n",
    "def EJ(p, f0, f1, J):\n",
    "    \"\"\"\n",
    "    We will need to be able to evaluate the expectation of our Bellman\n",
    "    equation J. In order to do this, we need the current probability\n",
    "    that model 0 is correct (p), the distributions (f0, f1), and a\n",
    "    function that can evaluate the Bellman equation\n",
    "    \"\"\"\n",
    "    # Get the current distribution we believe (p*f0 + (1-p)*f1)\n",
    "    curr_dist = p*f0 + (1-p)*f1\n",
    "    \n",
    "    # Get tomorrow's expected distribution through Bayes law\n",
    "    tp1_dist = (p*f0) / (p*f0 + (1-p)*f1)\n",
    "    \n",
    "    # Evaluate the expectation\n",
    "    EJ = curr_dist @ J(tp1_dist)\n",
    "    \n",
    "    return EJ\n",
    "\n",
    "def expect_loss_cont(p, c, f0, f1, J):\n",
    "    return c + EJ(p, f0, f1, J)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "To approximate the solution of the Bellman equation (\\*) above, we can deploy a method known as value function iteration (iterating on the Bellman equation) on a grid of points. Because we are iterating on a grid, the current probability, $p_k$, is restricted to a set number of points. However, in order to evaluate the expectation of the Bellman equation for tomorrow, $A(p_{k})$, we must be able to evaluate at various $p_{k+1}$ which may or may not correspond with points on our grid. The way that we resolve this issue is by using *linear interpolation*. This means to evaluate $J(p)$ where $p$ is not a grid point, we must use two points: first, we use the largest of all the grid points smaller than $p$, and call it $p_i$, and, second, we use the grid point immediately after $p$, named $p_{i+1}$, to approximate the function value in the following manner:\n",
    "\n",
    "$$ J(p) = J(p_i) + (p - p_i) \\frac{J(p_{i+1}) - J(p_i)}{p_{i+1} - p_{i}}$$\n",
    "\n",
    "In one dimension, you can think of this as simply drawing a line between each pair of points on the grid.\n",
    "\n",
    "For more information on both linear interpolation and value function iteration methods, see the Quant-Econ [lecture](http://quant-econ.net/py/ifp.html) on the income fluctuation problem."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Iteration    Distance       Elapsed (seconds)\n",
      "---------------------------------------------\n",
      "5            8.545e-02      2.871e-02         \n",
      "10           3.743e-04      5.681e-02         \n",
      "15           1.468e-06      8.650e-02         \n"
     ]
    }
   ],
   "source": [
    "def bellman_operator(pgrid, c, f0, f1, L0, L1, J):\n",
    "    \"\"\"\n",
    "    Evaluates the value function for a given continuation value\n",
    "    function; that is, evaluates\n",
    "\n",
    "        J(p) = min(pL0, (1-p)L1, c + E[J(p')])\n",
    "\n",
    "    Uses linear interpolation between points\n",
    "    \"\"\"\n",
    "    n = np.size(pgrid)\n",
    "    assert n == np.size(J)\n",
    "    \n",
    "    J_out = np.empty(n)\n",
    "    J_interp = interp.interp1d(pgrid, J)\n",
    "\n",
    "    for (p_ind, p) in enumerate(pgrid):\n",
    "        # Payoff of choosing model 0\n",
    "        p_c_0 = expect_loss_choose_0(p, L0)\n",
    "        p_c_1 = expect_loss_choose_1(p, L1)\n",
    "        p_con = expect_loss_cont(p, c, f0, f1, J_interp)\n",
    "        \n",
    "        J_out[p_ind] = min(p_c_0, p_c_1, p_con)\n",
    "\n",
    "    return J_out\n",
    "\n",
    "# To solve\n",
    "pg = np.linspace(0, 1, 150)\n",
    "bell_op = lambda vf: bellman_operator(pg, 0.5, f0, f1, 5.0, 5.0, vf)\n",
    "J = qe.compute_fixed_point(bell_op, np.zeros(pg.size), error_tol=1e-6,\n",
    "                           verbose=True, print_skip=5)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now for some gentle criticisms of the preceding code. Although it works fine, by writing the code in terms of  functions, we have to  pass around many things that are constant throughout the problem,  i.e., $c$, $f_0$, $f_1$, $L_0$, and $L_1$. This is wasteful.  We can avoid that by taking advantage of the object oriented features of Python. \n",
    "\n",
    "So to illustrate a good alternative approach, we write a class that stores all of our parameters for us internally and incorporates  many of the same functions that we used above.  "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# %load -r 22-134 Wald_Friedman_utils.py\n",
    "\n",
    "class WaldFriedman(object):\n",
    "    \"\"\"\n",
    "    Insert relevant docstrings here\n",
    "    \"\"\"\n",
    "    def __init__(self, c, L0, L1, f0, f1, n=25):\n",
    "        self.c = c\n",
    "        self.L0, self.L1, self.f0, self.f1 = L0, L1, f0, f1\n",
    "        self.n = n\n",
    "        self.pgrid = np.linspace(0.0, 1.0, n)\n",
    "\n",
    "    def payoff_choose_f0(self, p):\n",
    "        \"For a given probability specify the cost of accepting model 0\"\n",
    "        return (1-p)*self.L0\n",
    "\n",
    "    def payoff_choose_f1(self, p):\n",
    "        \"For a given probability specify the cost of accepting model 1\"\n",
    "        return p*self.L1\n",
    "\n",
    "    def EJ(self, p, J):\n",
    "        \"\"\"\n",
    "        This function evaluates the expectation of the value function\n",
    "        at period t+1. It does so by taking the current probability\n",
    "        distribution over outcomes:\n",
    "\n",
    "            p(z_{k+1}) = p_k f_0(z_{k+1}) + (1-p_k) f_1(z_{k+1})\n",
    "\n",
    "        and evaluating the value function at the possible states\n",
    "        tomorrow J(p_{t+1}) where\n",
    "\n",
    "            p_{t+1} = p f0 / ( p f0 + (1-p) f1)\n",
    "\n",
    "        Parameters\n",
    "        ----------\n",
    "        p : Scalar(Float64)\n",
    "            The current believed probability that model 0 is the true\n",
    "            model.\n",
    "        J : Function\n",
    "            The current value function for a decision to continue\n",
    "\n",
    "        Returns\n",
    "        -------\n",
    "        EJ : Scalar(Float64)\n",
    "            The expected value of the value function tomorrow\n",
    "        \"\"\"\n",
    "        # Pull out information\n",
    "        f0, f1 = self.f0, self.f1\n",
    "\n",
    "        # Get the current believed distribution and tomorrows possible dists\n",
    "        # Need to clip to make sure things don't blow up (go to infinity)\n",
    "        curr_dist = np.clip(p*f0 + (1-p)*f1, 1e-8, 1-1e-8)\n",
    "        tp1_dist = np.clip((p*f0) / curr_dist, 0, 1)\n",
    "\n",
    "        # Evaluate the expectation\n",
    "        EJ = curr_dist @ J(tp1_dist)\n",
    "\n",
    "        return EJ\n",
    "\n",
    "    def payoff_continue(self, p, J):\n",
    "        \"\"\"\n",
    "        For a given probability distribution and value function give\n",
    "        cost of continuing the search for correct model\n",
    "        \"\"\"\n",
    "        return self.c + self.EJ(p, J)\n",
    "\n",
    "    def bellman_operator(self, J):\n",
    "        \"\"\"\n",
    "        Evaluates the value function for a given continuation value\n",
    "        function; that is, evaluates\n",
    "\n",
    "            J(p) = min(pL0, (1-p)L1, c + E[J(p')])\n",
    "\n",
    "        Uses linear interpolation between points\n",
    "        \"\"\"\n",
    "        payoff_choose_f0 = self.payoff_choose_f0\n",
    "        payoff_choose_f1 = self.payoff_choose_f1\n",
    "        payoff_continue = self.payoff_continue\n",
    "        c, L0, L1, f0, f1 = self.c, self.L0, self.L1, self.f0, self.f1\n",
    "        n, pgrid = self.n, self.pgrid\n",
    "\n",
    "        J_out = np.empty(n)\n",
    "        J_interp = interp.UnivariateSpline(pgrid, J, k=1, ext=0)\n",
    "\n",
    "        for (p_ind, p) in enumerate(pgrid):\n",
    "            # Payoff of choosing model 0\n",
    "            p_c_0 = payoff_choose_f0(p)\n",
    "            p_c_1 = payoff_choose_f1(p)\n",
    "            p_con = payoff_continue(p, J_interp)\n",
    "\n",
    "            J_out[p_ind] = min(p_c_0, p_c_1, p_con)\n",
    "\n",
    "        return J_out\n",
    "\n",
    "    def find_alpha_beta(self, J):\n",
    "        \"\"\"\n",
    "        This function takes a value function and returns the corresponding\n",
    "        cutoffs of where you transition between continue and choosing a\n",
    "        specific model\n",
    "        \"\"\"\n",
    "        payoff_choose_f0 = self.payoff_choose_f0\n",
    "        payoff_choose_f1 = self.payoff_choose_f1\n",
    "        n, pgrid = self.n, self.pgrid\n",
    "\n",
    "        # Evaluate cost at all points on grid for choosing a model\n",
    "        p_c_0 = payoff_choose_f0(pgrid)\n",
    "        p_c_1 = payoff_choose_f1(pgrid)\n",
    "\n",
    "        # The cutoff points can be found by differencing these costs with\n",
    "        # the Bellman equation (J is always less than or equal to p_c_i)\n",
    "        alpha = pgrid[np.searchsorted(p_c_1 - J, 1e-10) - 1]\n",
    "        beta = pgrid[np.searchsorted(J - p_c_0, -1e-10)]\n",
    "\n",
    "        return (alpha, beta)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now let's use our class  solve the Bellman equation (*) and check whether it gives same answer attained above."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Iteration    Distance       Elapsed (seconds)\n",
      "---------------------------------------------\n",
      "5            7.994e-02      1.295e-02         \n",
      "10           6.492e-04      2.481e-02         \n",
      "15           4.708e-06      3.659e-02         \n",
      "\n",
      "If this is true then both approaches gave same answer\n",
      "False\n"
     ]
    }
   ],
   "source": [
    "wf = WaldFriedman(0.5, 5.0, 5.0, f0, f1, n=150)\n",
    "wfJ = qe.compute_fixed_point(wf.bellman_operator, np.zeros(150),\n",
    "                             error_tol=1e-6, verbose=True, print_skip=5)\n",
    "\n",
    "print(\"\\nIf this is true then both approaches gave same answer\")\n",
    "print(np.allclose(J, wfJ))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Numerical Example\n",
    "\n",
    "Now let's specify the two probability distibutions (the ones that we plotted earlier)\n",
    "\n",
    "* for $f_0$ we'll assume a beta distribution with parameters $a=1, b=1$\n",
    "\n",
    "* for $f_1$ we'll assume a beta distribution with parameters $a=9, b=9$\n",
    "\n",
    "The density of a  beta probability distribution with parameters $a$ and $b$ is\n",
    "\n",
    "$$ f(z; a, b) = \\frac{\\Gamma(a+b) z^{a-1} (1-z)^{b-1}}{\\Gamma(a) \\Gamma(b)}$$\n",
    "\n",
    "where $\\Gamma$ is the gamma function \n",
    "\n",
    "$$\\Gamma(t) = \\int_{0}^{\\infty} x^{t-1} e^{-x} dx$$\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "# Choose parameters\n",
    "c = 0.5\n",
    "L0 = 5.0\n",
    "L1 = 5.0\n",
    "\n",
    "# Choose n points and distributions\n",
    "n = 1001\n",
    "# f0 = np.ones(n)/n\n",
    "f0 = st.beta.pdf(np.linspace(0, 1, n), a=1, b=1)\n",
    "f0 = f0 / np.sum(f0)\n",
    "f1 = st.beta.pdf(np.linspace(0, 1, n), a=9, b=9)\n",
    "f1 = f1 / np.sum(f1)  # Make sure sums to 1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# Create an instance of our WaldFriedman class\n",
    "wf = WaldFriedman(c, L0, L1, f0, f1, n=n)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Iteration    Distance       Elapsed (seconds)\n",
      "---------------------------------------------\n",
      "5            8.096e-02      1.578e-01         \n",
      "10           6.384e-04      3.174e-01         \n",
      "15           4.345e-06      4.770e-01         \n"
     ]
    }
   ],
   "source": [
    "# Solve using qe's `compute_fixed_point` function\n",
    "J = qe.compute_fixed_point(wf.bellman_operator, np.zeros(n),\n",
    "                           error_tol=1e-6, verbose=True, print_skip=5)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The value function equals $ p L_1$ for $p \\leq \\beta$, and $(1-p )L_0$ for $ p \\geq \\alpha$.\n",
    "Thus, the slopes of the two linear pieces of the value function are determined by $L_1$ and \n",
    "$- L_0$.  \n",
    "\n",
    "The value function is smooth in the interior region in which the probability assigned to distribution  $f_0$ is in the indecisive region $p \\in (\\beta, \\alpha)$.\n",
    "\n",
    "The decision maker continues to sample until the probability of making a  type II error falls below $\\beta$ or the probability of a making a type I error falles below  $1-\\alpha$.\n",
    "\n",
    "#### **Tom**:\n",
    "*Is there a reason for cutoff points to be labeled in the order $\\beta$ and then $\\alpha$? If not, I have weak preference for keeping them in order and I think it is easier to follow that way. Below is an equivalent paragraph with them switched*\n",
    "\n",
    "The value function equals $ p L_1$ for $p \\leq \\alpha$, and $(1-p)L_0$ for $ p \\geq \\beta$.\n",
    "Thus, the slopes of the two linear pieces of the value function are determined by $L_1$ and \n",
    "$- L_0$.  \n",
    "\n",
    "The value function is smooth in the interior region in which the probability assigned to distribution  $f_0$ is in the indecisive region $p \\in (\\alpha, \\beta)$.\n",
    "\n",
    "The decision maker continues to sample until the probability of making a  type II error falls below $\\alpha$ or the probability of a making a type I error falles below  $1-\\beta$."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now to have some fun, you can use the slider and watch the effects on the smoothness of the\n",
    "of the value function in the  middle range as you increase the numbers of functions in the \n",
    "piecewise linear approximation."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<function Wald_Friedman_utils.all_param_interact>"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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EpAeUVImIiIiIiPSAkioREREREZEeUFIlIiIiIiLSA0qqREREREREekBJlYiIiIiISA8o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\nREREREQW4P8HlleEV318ExUAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f1ae88c3da0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "col_slide = list(map(convert_rgb_hex, sb.color_palette(\"dark\", 7)))\n",
    "col_num = list(map(convert_rgb_hex, sb.color_palette(\"hls\", 7)))\n",
    "sliders = map(lambda a,b,c,d,e,f: widgets.FloatSlider(min=a, max=b, step=c, value=d,\n",
    "                                                      slider_color=e, color=f),\n",
    "             [0.5, 5.0, 5.0, 1.0, 1.0, 1.0, 1.0],\n",
    "             [2.5, 50.0, 50.0, 9.0, 9.0, 9.0, 9.0],\n",
    "             [0.25, 2.5, 2.5, 0.5, 0.5, 0.5, 0.5],\n",
    "             [1.25, 27.5, 27.5, 2.0, 2.5, 2.5, 2.0],\n",
    "             col_num, col_num)\n",
    "cslide, L0slide, L1slide, a0slide, b0slide, a1slide, b1slide = list(sliders)\n",
    "\n",
    "interact(all_param_interact, c=cslide, L0=L0slide, L1=L1slide,\n",
    "         a0=a0slide, b0=b0slide, a1=a1slide, b1=b1slide, n=(15, 251, 2))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
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