reproduceFigure29.12.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "import numpy as np\n",
    "import scipy.stats as st\n",
    "\n",
    "%matplotlib inline\n",
    "plt.style.use('ggplot')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x10d454d50>]"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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6XzNqMY5mEFF3UxI49BYAyEF1xhwFfh0y07PAmVMQy6utPTQSSWDrrH3fYGag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\nBGJVN9eNBqgAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10a9bfb10>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "niters= 400\n",
    "x0=10\n",
    "List = [x0]\n",
    "for i in range(niters):\n",
    "    if x0==20:\n",
    "        next = x0-1\n",
    "        List = List+[next]\n",
    "        x0=next\n",
    "    elif x0==0:\n",
    "        next = x0+1\n",
    "        List = List+[next]\n",
    "        x0=next\n",
    "    else:\n",
    "        next = x0+1 if np.random.random()>=0.5 else x0-1\n",
    "        List = List+[next]\n",
    "        x0=next\n",
    "\n",
    "plt.plot(List,linewidth=0.3)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x10d3a1610>]"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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+s5qjEIlEJEkLFy6UJAUCAZ07d07V1dWxbbxerwoLCzUwMDCbXQEAgCSYcVCwLEudnZ1a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\nCAoAAMCIoAAAAIwICgAAwOj/AfxtDxONyr/dAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10d48b6d0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "hist0, bin_edges0 = np.histogram(List, bins=20, normed=False)\n",
    "factor = 1.0\n",
    "bin_centers0 = (bin_edges0[:-1] + bin_edges0[1:]) / 2.\n",
    "\n",
    "bin_width0= bin_edges0[1]-bin_edges0[0]\n",
    "\n",
    "\n",
    "\n",
    "plt.step(bin_centers0, factor*hist0, linewidth=1)\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x10d3a1e10>]"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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Mao5COByWJC1YsECSNDg4qHPnzqmqqir6HK/Xq4KCAvX398/mUAAAIAFmHBQsy1JHR4dW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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10d3a1a50>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(bin_centers0, hist0, drawstyle='steps-mid', linestyle='-', alpha=1,)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[0, 20, 0, 40]"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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MmKMAJDi7Lt/r7T4ppWdZ3i+A+EJQABKYnZfvHReX7wGXAoICkMi4fA/AEBEUgEsAl+8B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\ngg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10d6c5910>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "List2=[np.random.randint(0,20) for i in range(niters)]\n",
    "hist2, bin_edges2 = np.histogram(List2, bins=20, normed=False)\n",
    "factor = 1.0\n",
    "bin_centers2 = (bin_edges2[:-1] + bin_edges2[1:]) / 2.\n",
    "\n",
    "bin_width2= bin_edges2[1]-bin_edges2[0]\n",
    "\n",
    "plt.step(bin_centers2, factor*hist2, linewidth=1)\n",
    "plt.axis([0,20,0,40])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def MHhistogram(ninters, initial):\n",
    "    x0=initial\n",
    "    List = [x0]\n",
    "    for i in range(niters):\n",
    "        if x0==20:\n",
    "            next = x0-1\n",
    "            List = List+[next]\n",
    "            x0=next\n",
    "        elif x0==0:\n",
    "            next = x0+1\n",
    "            List = List+[next]\n",
    "            x0=next\n",
    "        else:\n",
    "            next = x0+1 if np.random.random()>=0.5 else x0-1\n",
    "            List = List+[next]\n",
    "            x0=next\n",
    "\n",
    "    hist0, bin_edges0 = np.histogram(List, bins=20, normed=False)\n",
    "    bin_centers0 = (bin_edges0[:-1] + bin_edges0[1:]) / 2.\n",
    "\n",
    "    bin_width0= bin_edges0[1]-bin_edges0[0]\n",
    "\n",
    "\n",
    "\n",
    "    return bin_centers0, hist0\n",
    "\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 120,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(array([  0.5,   1.5,   2.5,   3.5,   4.5,   5.5,   6.5,   7.5,   8.5,\n",
       "          9.5,  10.5,  11.5,  12.5,  13.5,  14.5,  15.5,  16.5,  17.5,\n",
       "         18.5,  19.5]),\n",
       " array([ 2,  4,  7,  9, 10, 10, 13, 24, 27, 24, 27, 25, 23, 22, 24, 24, 19,\n",
       "        20, 25, 62]))"
      ]
     },
     "execution_count": 120,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "MHhistogram(400, 10)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x10d5c2210>]"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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IWQW/36/09PSr1mxtbVVbW1vIspycHFVXVystLY2wcVnA95l8ktLcaXJmZES7nbA5nU5l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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10d3e3b50>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(MHhistogram(1400, 10)[0],MHhistogram(1400, 10)[1],drawstyle='steps-mid', linestyle='-', alpha=1,)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x110b01e50>]"
      ]
     },
     "execution_count": 31,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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xY8fQ1NQEAIiNjcX8+fNhMBgAAOvXr++zuvKBBx5AXl6eSN0VyXczCarcX0M1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\n/wFJnJE+9C25qwAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x110841890>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "f, (ax1, ax2, ax3) = plt.subplots(3, sharex=True)\n",
    "ax1.plot(MHhistogram(100, 10)[0],MHhistogram(100, 10)[1], drawstyle='steps-mid', linestyle='-', alpha=1)\n",
    "ax1.set_title('Metropolis')\n",
    "plt.axis([0,20,0,60])\n",
    "ax2.plot(MHhistogram(400, 10)[0],MHhistogram(400, 10)[1], drawstyle='steps-mid', linestyle='-', alpha=1)\n",
    "ax3.plot(MHhistogram(1200, 10)[0],MHhistogram(1200, 10)[1], drawstyle='steps-mid', linestyle='-', alpha=1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [],
   "source": [
    "def randomhistogram(niters):\n",
    "    List2=[np.random.randint(0,20) for i in range(niters)]\n",
    "    hist2, bin_edges2 = np.histogram(List2, bins=20, normed=False)\n",
    "    bin_centers2 = (bin_edges2[:-1] + bin_edges2[1:]) / 2.\n",
    "    return bin_centers2, hist2\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x110df8e90>]"
      ]
     },
     "execution_count": 32,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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sLNx2221YvHgxoqOjsXDhwlYfy/F0LlKOp+QTMJOSkiwWJfo1Ly8vzJ8/36Lt0UcfxQsv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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x110b61e90>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "f, (ax1, ax2, ax3) = plt.subplots(3, sharex=True)\n",
    "ax1.plot(randomhistogram(100)[0],randomhistogram(100)[1], drawstyle='steps-mid', linestyle='-', alpha=1)\n",
    "ax1.set_title('independent sampling')\n",
    "plt.axis([0,20,0,100])\n",
    "ax2.plot(randomhistogram(400)[0],randomhistogram(400)[1], drawstyle='steps-mid', linestyle='-', alpha=1)\n",
    "ax3.plot(randomhistogram(1200)[0],randomhistogram(1200)[1], drawstyle='steps-mid', linestyle='-', alpha=1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
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   },
   "outputs": [],
   "source": []
  }
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