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  "name": "",
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  {
   "cells": [
    {
     "cell_type": "heading",
     "level": 1,
     "metadata": {},
     "source": [
      "Simulation of KMR"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "First, we compute a transition matrix for each revison protocol, simultenious revisions and sequential revisions."
     ]
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "(1)Simultenious revisions"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "from __future__ import division\n",
      "import numpy as np\n",
      "from scipy.stats import binom\n",
      "import matplotlib.pyplot as plt\n",
      "from mc_tools import mc_compute_stationary, mc_sample_path\n",
      "from quantecon.mc_tools import MarkovChain\n",
      "import quantecon as qe\n",
      "\n",
      "%matplotlib inline"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 1
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "def KMR_2x2_P_simultaneous(N, p, epsilon):\n",
      "          P = np.empty((N+1, N+1), dtype=float)\n",
      "          for x in range(N+1):\n",
      "                                                           \n",
      "            if x/N < p: \n",
      "                P[x,:]  = binom.pmf(range(N+1), N, epsilon/2)\n",
      "            elif x/N == p:\n",
      "                P[x,:]  = binom.pmf(range(N+1), N, 1/2)           \n",
      "            else:\n",
      "                P[x,:]  = binom.pmf(range(N+1), N, 1-epsilon/2) \n",
      "          return P\n",
      "      "
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 2
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "#Parameter\n",
      "p = 1/3\n",
      "N = 6\n",
      "epsilon = 0.1"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 3
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "kmr_simul=KMR_2x2_P_simultaneous(N, p, epsilon)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 7
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "print(kmr_simul)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "[[  7.35091891e-01   2.32134281e-01   3.05439844e-02   2.14343750e-03\n",
        "    8.46093750e-05   1.78125000e-06   1.56250000e-08]\n",
        " [  7.35091891e-01   2.32134281e-01   3.05439844e-02   2.14343750e-03\n",
        "    8.46093750e-05   1.78125000e-06   1.56250000e-08]\n",
        " [  1.56250000e-02   9.37500000e-02   2.34375000e-01   3.12500000e-01\n",
        "    2.34375000e-01   9.37500000e-02   1.56250000e-02]\n",
        " [  1.56250000e-08   1.78125000e-06   8.46093750e-05   2.14343750e-03\n",
        "    3.05439844e-02   2.32134281e-01   7.35091891e-01]\n",
        " [  1.56250000e-08   1.78125000e-06   8.46093750e-05   2.14343750e-03\n",
        "    3.05439844e-02   2.32134281e-01   7.35091891e-01]\n",
        " [  1.56250000e-08   1.78125000e-06   8.46093750e-05   2.14343750e-03\n",
        "    3.05439844e-02   2.32134281e-01   7.35091891e-01]\n",
        " [  1.56250000e-08   1.78125000e-06   8.46093750e-05   2.14343750e-03\n",
        "    3.05439844e-02   2.32134281e-01   7.35091891e-01]]\n"
       ]
      }
     ],
     "prompt_number": 8
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "(2)Sequential revisions"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "def KMR_2x2_P_sequential(N, p, epsilon):\n",
      "          P = np.zeros((N+1, N+1), dtype=float)\n",
      "          \n",
      "          P[0, 0], P[0, 1] = 1 - epsilon * (1/2), epsilon * (1/2)    \n",
      "          P[N, N-1], P[N, N] = epsilon * (1/2), 1 - epsilon * (1/2) \n",
      "     \n",
      "          \n",
      "          for x in range(1, N):\n",
      "             \n",
      "                if x/N >p:\n",
      "                    P[x, x-1] = (x/N)*epsilon * (1/2)\n",
      "                    P[x, x+1] = (1-(x/N))*(1 - epsilon*(1/2))\n",
      "                    P[x, x] = 1 - P[x, x-1] - P[x, x+1] \n",
      "                elif x/N<p:\n",
      "                    P[x, x-1] =(x/N)*(1 - epsilon*(1/2))\n",
      "                    P[x, x+1] =(1-(x/N))*epsilon * (1/2)\n",
      "                    P[x, x] = 1 - P[x, x-1] - P[x, x+1]     \n",
      "                else:\n",
      "                    P[x, x-1] = (x/N)*(1/2)\n",
      "                    P[x, x+1] = (1-(x/N))*(1/2)\n",
      "                    P[x, x] = 1 - P[x, x-1] - P[x, x+1]           \n",
      "          return P\n",
      "               \n",
      "               "
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 49
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "kmr_seq=KMR_2x2_P_sequential(N, p, epsilon)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 50
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "print(kmr_seq)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "[[ 0.95        0.05        0.          0.          0.          0.          0.        ]\n",
        " [ 0.15833333  0.8         0.04166667  0.          0.          0.          0.        ]\n",
        " [ 0.          0.16666667  0.5         0.33333333  0.          0.          0.        ]\n",
        " [ 0.          0.          0.025       0.5         0.475       0.          0.        ]\n",
        " [ 0.          0.          0.          0.03333333  0.65        0.31666667\n",
        "   0.        ]\n",
        " [ 0.          0.          0.          0.          0.04166667  0.8\n",
        "   0.15833333]\n",
        " [ 0.          0.          0.          0.          0.          0.05        0.95      ]]\n"
       ]
      }
     ],
     "prompt_number": 51
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Simulation"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "mc_kmr_simul = MarkovChain(kmr_simul)\n",
      "path_kmr_simul = mc_kmr_simul.simulate(init=0, sample_size=10000)\n",
      "\n",
      "mc_kmr_seq = MarkovChain(kmr_seq)\n",
      "path_kmr_seq = mc_kmr_seq.simulate(init=0, sample_size=10000)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 52
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "fig, ax = plt.subplots(figsize=(9, 6))\n",
      "ax.grid()\n",
      "ax.plot(path_kmr_simul, label=r'Transition of state $x$')\n",
      "ax.legend(loc='lower right')"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 53,
       "text": [
        "<matplotlib.legend.Legend at 0xa0df690>"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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gL7jDkUG0h7qFfESn28oXOXEL+cgHKhyIRekuWF7vhjXabn68DUC1ynM8S+c7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\nAACR+/+LuPaB0MDUfAAAAABJRU5ErkJggg==\n",
       "text": [
        "<matplotlib.figure.Figure at 0x860c9b0>"
       ]
      }
     ],
     "prompt_number": 53
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "fig, ax = plt.subplots(figsize=(9, 6))\n",
      "ax.grid()\n",
      "ax.plot(path_kmr_seq, label=r'Transition of state $x$')\n",
      "ax.legend(loc='lower right')"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 54,
       "text": [
        "<matplotlib.legend.Legend at 0xb65cb30>"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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J/fznrenGSQvwlqubNcs/jaR5OvHE4GUOOSQ8vQsvbJ3+uc+Fz1/PX09PsjzG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\ndf8ftsZdeJuQ/0YAAAAASUVORK5CYII=\n",
       "text": [
        "<matplotlib.figure.Figure at 0xb39c330>"
       ]
      }
     ],
     "prompt_number": 54
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Stationary distribution"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "kmr_simul_m=qe.MarkovChain(kmr_simul)\n",
      "kmr_simul_s=kmr_simul_m.stationary_distributions\n",
      "print(kmr_simul_s)\n",
      "\n",
      "\n",
      "kmr_seq_m=qe.MarkovChain(kmr_seq)\n",
      "kmr_seq_s=kmr_seq_m.stationary_distributions\n",
      "print(kmr_seq_s)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "[[  3.61056918e-04   1.27332652e-04   1.29925777e-04   2.18376082e-03\n",
        "    3.05555912e-02   2.32002930e-01   7.34639402e-01]]\n",
        "[[  2.03067386e-03   6.41265430e-04   1.60316358e-04   2.13755143e-03\n",
        "    3.04601079e-02   2.31496820e-01   7.33073265e-01]]\n"
       ]
      }
     ],
     "prompt_number": 55
    },
    {
     "cell_type": "heading",
     "level": 1,
     "metadata": {},
     "source": [
      "Fraction with respsct to $\\varepsilon$"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "\"\"\"\n",
      "Average dist of the states.\n",
      "\n",
      "\"\"\"\n",
      "\n",
      "def kmr_simulate_dist(matrix, init, T, num_reps):\n",
      "    \n",
      "    mc = MarkovChain(matrix)\n",
      "    x = []\n",
      "    for i in range(num_reps):\n",
      "        x.append(mc.simulate(init=init, sample_size=T+1))\n",
      "    x_array = np.array(x)\n",
      "    y = np.empty(matrix.shape[0])\n",
      "    for i in range(matrix.shape[0]):\n",
      "        y[i] = (x_array == i).sum() / ((T + 1) * num_reps) \n",
      "    return y"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 56
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "\"\"\"\n",
      "Compute a fraction of states.\n",
      "\n",
      "\"\"\"\n",
      "\n",
      "\n",
      "def kmr_simul_simulate_state(N, p, init, T, eps_min, eps_max, eps_length, num_reps, state):\n",
      "   \n",
      "     epsilons = np.linspace(eps_min, eps_max, eps_length)\n",
      "   \n",
      "     fraction_sim_simul = np.zeros(eps_length)\n",
      "     for i, epsilon in enumerate(epsilons):\n",
      "         fraction_sim_simul[i] = kmr_simulate_dist(KMR_2x2_P_simultaneous(N, p, epsilon), init, T, num_reps)[state]\n",
      "     return fraction_sim_simul\n",
      "\n",
      "def kmr_seq_simulate_state(N, p, init, T, eps_min, eps_max, eps_length, num_reps, state):\n",
      "   \n",
      "     epsilons = np.linspace(eps_min, eps_max, eps_length)\n",
      "\n",
      "     fraction_sim_seq = np.zeros(eps_length)\n",
      "     for i, epsilon in enumerate(epsilons):\n",
      "         fraction_sim_seq[i] = kmr_simulate_dist(KMR_2x2_P_sequential(N, p, epsilon), init, T, num_reps)[state]\n",
      "     return fraction_sim_seq"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 68
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "frac_simul_6=kmr_simul_simulate_state(N, p, init=0, T=1000, eps_min=0.00001, eps_max=0.1, eps_length=100, num_reps=100,state=6)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 69
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "fig, ax = plt.subplots(figsize=(9, 6))\n",
      "ax.grid()\n",
      "ax.set_xlabel(r'Value of $\\varepsilon$')\n",
      "ax.set_ylabel('Fraction of state 6')\n",
      "ax.set_xlim(eps_min, eps_max)\n",
      "ax.plot(epsilons, frac_simul_6)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 70,
       "text": [
        "[<matplotlib.lines.Line2D at 0xba17070>]"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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7G2EU5kvuvrrG52PM7G4z29HdVyafbOjQofTo0QOADh060KdPny8r6qq5TW3n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\nRAqOChgREREpOP8f5iBoWcCr2A8AAAAASUVORK5CYII=\n",
       "text": [
        "<matplotlib.figure.Figure at 0xba17210>"
       ]
      }
     ],
     "prompt_number": 70
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "frac_seq_6=kmr_seq_simulate_state(N, p, init=0, T=1000, eps_min=0.00001, eps_max=0.1, eps_length=100, num_reps=100,state=6)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 71
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "fig, ax = plt.subplots(figsize=(9, 6))\n",
      "ax.grid()\n",
      "ax.set_xlabel(r'Value of $\\varepsilon$')\n",
      "ax.set_ylabel('Fraction of state 6')\n",
      "ax.set_xlim(eps_min, eps_max)\n",
      "ax.plot(epsilons, frac_seq_6)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 72,
       "text": [
        "[<matplotlib.lines.Line2D at 0x88bed50>]"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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KSelRAiMikUoOH9UtzD3wwDAz6OOPs5s6napNm1CkO3curFgRFqzba6/09x5x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\n4kljyblrrP6luRSTeFE84kc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       "text": [
        "<matplotlib.figure.Figure at 0x88befd0>"
       ]
      }
     ],
     "prompt_number": 72
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [],
     "language": "python",
     "metadata": {},
     "outputs": []
    }
   ],
   "metadata": {}
  }
 ]
}