AiLearning-Theory-Applying/notebook_必备数学基础/贝叶斯分析/贝叶斯建模.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 估计模型参数"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "from IPython.display import Image\n",
    "import matplotlib.pyplot as plt\n",
    "import numpy as np\n",
    "import pandas as pd\n",
    "import pymc3 as pm  # 贝叶斯相关包，需要安装\n",
    "import scipy\n",
    "import scipy.stats as stats\n",
    "import scipy.optimize as opt\n",
    "import statsmodels.api as sm\n",
    "%matplotlib inline\n",
    "\n",
    "plt.style.use('bmh')\n",
    "colors = ['#348ABD','#A60628','#7A68A6','#467821','#D55E00',\n",
    "          '#CC79A7','#56B4E9','#009E73','#F0F442','#0072B2']\n",
    "\n",
    "messages = pd.read_csv('hangout_chat_data.csv')  # 某人的聊天数据，如回复信息的速度等"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**贝叶斯看待数据的思维**\n",
    "\n",
    "假设蹲在山上数羊 12，33，20，29，20，30，18（每天数看到几只羊，得到一周的数据）\n",
    "\n",
    "按照贝叶斯的思想，数据已经定下来了，减下来就是找到参数的概率分布\n",
    "\n",
    "我们的数据是非负的整数，在这里我们用泊松分布来建模，泊松分布只需要μ，它描述数据的均值和方差\n",
    "<img src=\"assets/20201128183746.png\" width=\"30%\">"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 864x360 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# 画出泊松分布的图\n",
    "fig = plt.figure(figsize=(12,5))\n",
    "ax = fig.add_subplot(111)\n",
    "x_lim = 60\n",
    "mu = [5,20,40]\n",
    "for i in np.arange(x_lim):\n",
    "    plt.bar(i,stats.poisson.pmf(mu[0],i),color=colors[3])\n",
    "    plt.bar(i,stats.poisson.pmf(mu[1],i),color=colors[4])\n",
    "    plt.bar(i,stats.poisson.pmf(mu[2],i),color=colors[5])\n",
    "    \n",
    "_ = ax.set_xlim(0,x_lim)\n",
    "_ = ax.set_ylim(0,0.2)\n",
    "_ = ax.set_ylabel('Probability mass')\n",
    "_ = ax.set_title('Poisson distribution')\n",
    "_ = plt.legend(['$\\mu$ = %s' % mu[0], '$\\mu$ = %s' % mu[1], '$\\mu$ = %s' % mu[2]])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "不同的mu值下的泊松分布长相\n",
    "\n",
    "回消息的反应时间的分布情况"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 864x360 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig = plt.figure(figsize=(12,5))\n",
    "_ = plt.title('Frequency of messages by response time')\n",
    "_ = plt.xlabel('Response time (seconds)')\n",
    "_ = plt.ylabel('Number of messages')\n",
    "_ = plt.hist(messages['time_delay_seconds'].values,\n",
    "             range=[0, 60], bins=60, histtype='stepfilled')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "y轴是回复的样本个数，x轴是消息发来的回复时间。\n",
    "\n",
    "10秒的时候回复最多"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**极大似然估计求μ**\n",
    "\n",
    "在用贝叶斯方法之前，先用最大似然估计来求解。\n",
    "<ul>\n",
    "    <li>poisson_logprob()根据泊松模型和参数值返回观测数据的总似然值。\n",
    "    <li>opt.minimize_scalar找到最合适的取值。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The estimated value of mu is: 18.2307692323807\n",
      "Wall time: 996 µs\n"
     ]
    }
   ],
   "source": [
    "y_obs = messages['time_delay_seconds'].values\n",
    "\n",
    "def poisson_logprob(mu, sign=-1):\n",
    "    return np.sum(sign*stats.poisson.logpmf(y_obs, mu=mu))\n",
    "\n",
    "freq_results = opt.minimize_scalar(poisson_logprob)\n",
    "%time print(\"The estimated value of mu is: %s\" % freq_results['x'])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "得到结果μ = 18.2307692323807，但这仅仅是一个值。\n",
    "\n",
    "下面展示这个过程，不断爬坡的过程。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "x = np.linspace(1, 60)\n",
    "y_min = np.min([poisson_logprob(i, sign=1) for i in x])\n",
    "y_max = np.max([poisson_logprob(i, sign=1) for i in x])\n",
    "\n",
    "fig = plt.figure(figsize=(6,4))\n",
    "_ = plt.plot(x, [poisson_logprob(i, sign=1) for i in x])\n",
    "_ = plt.fill_between(x, [poisson_logprob(i, sign=1) for i in x], \n",
    "                     y_min, color=colors[0], alpha=0.3)\n",
    "\n",
    "_ = plt.title('Optimization of $mu$')\n",
    "_ = plt.xlabel('$mu$')\n",
    "_ = plt.ylabel('Log probability of $mu$ given data')\n",
    "_ = plt.vlines(freq_results['x'], y_max, y_min, colors='red', linestyles='dashed')\n",
    "_ = plt.scatter(freq_results['x'], y_max, s=110, c='red', zorder=3)\n",
    "_ = plt.ylim(ymin=y_min, ymax=0)\n",
    "_ = plt.xlim(xmin=1, xmax=60)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "代入参数后分布的样子"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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x9RDtYfpBvPwg0QguNxGNrwzwJ3F9fUQ/yf6Q+CS0eH450cgYo9v6CHDNROsrmDbuSUpFy0z5Gk1nW+Jl/pJoFIRjo+tnnBMdx5se3/8CL4620BvfP6no9fhLoj2lR4gOl7iF40+abATuiF/PAFwbT9/H8aOUTJolL54Ed2FR3XuAm6d4bcfL5Hyi9/NAXPtXgeUF82+m6ITCSZ7/uG0pmH4xx49SUh5vYxcvjiByAwXtc7z1UnQiYzztaqK9qS8QHb/9a5x4cvSk2xgv85tEv2gNEI0+cdU46zrhfTTB69BCNPJIB9F78rGCvI97LQoeMzy6THz/Q/G6+uP3zdUzqWei90s8bzVRx3D0vdZKdNjI2hI/B7ZTWttI9FlBtPf6DqJzbkbr/B8cfyLspNsywWsz0Wf5hJ83E+UVTxsEriu4P+X/Cbpl+zb6H6qIiEimxHuDv0g0PNuRtOvJMouunLonhHBd2rWILEQ6aVJERDLBzP4r0SEhXUQn1X0U+Ad1tkUkbfN2DLeZbbPoClt74mMai+dfZGa7LLoi4NuK5r3LzH4R3941XzWLiIgr5wD/THTYxkeIDiMovqqjiMi8m5dDSiw6a/kJomHdngHuA64OITxSsMwaouMV/ytwewjh6/H0RqLjFs8jOnZqJ9HxeIfnvHARERERkYTmaw/3ZqJju54M0QUHbiU6M3lMCGFfCOEhohM+Cl0GfDdEwxEdJrqwxbb5KFpEREREJKn56nCvBJ4uuP9MPG2uHysiIiIikqr5OmmylKtNJXrsd77zndDW1oaZEUKgoaGB5uZmjh49SllZNJb9yMgI5eXlDA9HV4pevHjxjOYfPXoUM6OsrIzh4WHKysoIIXDs2LGx+YsWLWLRokUMDw+zePFijh07Nu35ZsbIyAiLFy9mZGSEEMLY/Cxt06JFizh27FimtimLOU20TUNDQyxatChT25TFnCaqeXh4mIqKikxtUxZzGm/+0NAQixcvztQ2ZTGnibZpdH6WtimLOY23TUePHu3YunVrM9MwXx3uZ4jGNB51CtGYyqU+9uKix24vXqiuro7zzy++qJh48MILL7BkyQnX/RAnlJ9vys8vZeeb8vNr165drdN9zHwdUnIfcHp8la0KoosI3F7iY+8iupJgg0VXErw0nnac0W+L4k9bW1vaJUgCys835eeXsvNN+eXLvHS4QwjDRFcOuwt4FPhaCGF3fAnetwCY2SvN7BngSuCvzWx3/Nguoqts3RffbomnHcdsvCNPxIPy8tm8gq7MN+Xnm/LzS9n5pvzyZd4ufBNCuIPocqyF0z5Y8Pd9RIeLjPfYLxBdInZCo8fdiD/19fVplyAJKD/flJ9fys435ZcvmbnS5OiB7+JPR0cH1dXVaZchM6T8fFN+fik730rNL4RAX18f83HdFDmemVFTUzMrR1FkpsOtPdx+6Vu+b8rPN+Xnl7LzrdT8+vr6WLJkCRUVFXNckRQbGhqir6+P2traxM81b5d2n2v65ufX0NBQ2iVIAsrPN+Xnl7LzrdT8QgjqbKekoqJi1vqXmelwHztWfIFK8WJgYCDtEiQB5eeb8vNL2fmm/PIlMx1une3rV0tLS9olSALKzzfl55ey80355UtmOtwah9svjUXqm/LzTfn5pex8U375kpkO96JFmdmU3NGxab4pP9+Un1/Kzjdv+X3gAx/gwx/+8Iwf//zzz/POd76Tr371qyfMe+yxx7jgggvm5EvIDTfcwPr169myZctx0z/zmc/w6le/mi1btnDdddcxODg46+sulJlRStTh9ms2zv6V9Cg/35SfX8rOt5nmd9XHNs1qHbfeuLOk5U4//XQaGhpmvJ6TTjqJtWvXcs4555ww74wzzmDVqlVzcpjNNddcw3vf+15+53d+Z2zas88+y9/8zd/w05/+lKqqKt797nfzzW9+k2uuuWbW1z8qM71UjcPtV2dnZ9olSALKzzfl55ey881bfvfffz+vfOUrEz3HI488wplnnnnC9P7+fmpqahI990S2bNky7heF4eFhBgcHGR4eZmBgYM6Pqc/MHu7FizOzKbmT5BuzpE/5+ab8/FJ2vnnL77nnnuPkk0/mG9/4BkNDQzz77LM0NTVx7bXX8tOf/pR//Md/5MILL6SiooLvf//7XHLJJRw+fBiAq6++muHhYfbv3893v/tddu7cyU033cS3v/1tjh49yuOPP84rXvEKgHGfv9Ab3/hG+vr6Tqjvlltu4eKLLy5pW17ykpdwww03cM4551BZWckll1zC6173ukSvz1Qys4dbwwL6paGRfFN+vik/v5Sdb57y6+7upr6+nl/84hd8//vf5+qrr6asrIw1a9YAjF2JsaWlhUsvvZTdu3ezefNmLrvsMh566CEAHn74Yd7whjewbds2BgcHeeCBB7j77ru56qqrqK6u5rzzzpvw+Qvdcccd3HPPPSfcSu1sAxw5coTvfOc7PPDAAzzyyCM8//zzfO1rX0v6Mk1KHW5J3VyfqCBzS/n5pvz8Una+ecrvvvvuY9OmTXzta1/jsssuA+DBBx9k06boePLzzz+fp556ivPOO4+BgQEaGxtpbGxk586dY3uu//3f/50LLrgAgMcff5wvfvGLvP71rweizvjGjRsnfP5Cb3zjG7noootOuG3fvr3k7dm+fTunnnoqy5Yto7y8nDe96U3s2LFjxq9PKTJzHIbG4fZLY5HOvlJOqin1RJmpKD/flJ9fys43T/nt3LmT1772tXzkIx/hrW99K0NDQ/T29vLzn/+cLVu28Pzzz1NVVQXAAw88MNbJ/td//Vfe//7389BDD9HT08MFF1zAkSNHKCsro7q6mtNPP52hoSEGBgbYtWsX3d3dY9MKn7/QHXfckXh7TjnlFO6///6xuu+55x5e/vKXJ37eyWSmw61xuP1qa2tj9erVaZchM6T8fFN+fik73zzlt2bNGnbs2MEHP/hB7r77bh5//HHWrVvHwYMHgWhYv1e/+tVAdGLkhRdeCMCqVau4++67ueaaa6itreXOO++ku7ubj3/84xw4cGDsuV760pfS3t7O29/+9nGfP4nrrruOn/zkJ3R2drJhwwZuuukm3vGOd/CWt7yFSy65hLKyMs455xze9a53JV7XZGy2rhGftnvuuSe87GUvS7sMmYGDBw+yYsWKtMvIlPncw638fFN+fik730rNr6enh7q6unmoSMYz3uu/a9eunVu3bj1vOs+TmWO4NQ63X6M/Q4lPys835eeXsvNN+eVLZnqpGofbr9Fhg8Qn5eeb8vNL2fmm/PIlMx1ujcPtV1NTU9olSALKzzfl55ey80355UtmOtwaFtCv3t7etEuQBJSfb8rPL2Xnm/LLl8zsFlaH26+hoaG0S3Bhrk6ETPq8ys835eeXsvOt1PzMjKGhISoqKua4Iik2NDQ0dlGfpDLT4dY43H55GotUTqT8fFN+fik730rNr6amhr6+PlcXyskKM6OmpmZWniszHW6Nw+2Xp7FI5UTKzzfl55ey863U/MyM2traeahI5lJmjuHWsIB+aWgk35Sfb8rPL2Xnm/LLl8z0UmfrGBuZfzouzTfl55vy80vZ+ab88iUzHe6RkZG0S5AZ6u7uTrsESUD5+ab8/FJ2vim/fMlMh1vjcPu1bNmytEuQBJSfb8rPL2Xnm/LLl8x0uLWH2y99y/dN+fmm/PxSdr4pv3zJTIc7hJB2CTJDGmHGN+Xnm/LzS9n5pvzyJTMdbo3D7ZfGkvVN+fmm/PxSdr4pv3zJTIdb3xT9amtrS7sESUD5+ab8/FJ2vim/fMlMh7usrCztEmSGqqur0y5BElB+vik/v5Sdb8ovXzLT4Ra/9GXJN+Xnm/LzS9n5pvzyJTMdbo1S4ldPT0/aJUgCys835eeXsvNN+eVLZjrcOmnSr+bm5rRLkASUn2/Kzy9l55vyy5fMdLiHh4fTLkFmqKurK+0SJAHl55vy80vZ+ab88iUzHW7xS2Oo+6b8fFN+fik735RfvmSmw61Lu/uln9V8U36+KT+/lJ1vyi9fMtNL1Tjcfh08eJDVq1enXYaU6KqPbTru/uZV29jx9J1j92+9ced8lyQJqP35pex8U375kpk93Bpex6+ampq0S5AEDvU9nXYJkoDan1/Kzjflly+Z6XCLiIiIiCxEmelwaxxuv/r6+tIuQRJYXrMq7RIkAbU/v5Sdb8ovXzJzDLfG4fZrxYoVaZeQmuLjocez0I+JfvTQjrRLkATy3P68U3a+Kb98ycwebo3D7Vd7e3vaJUgC65dN/aVBFi61P7+UnW/KL18y0+EWv8ws7RIkgZGgL7ueqf35pex8U375kpkOt8bh9quxsTHtEiSBfV270y5BElD780vZ+ab88iUzHW6Nw+2XflbzbX3zuWmXIAmo/fml7HxTfvkybx1uM9tmZo+b2R4zu2mc+UvM7LZ4/s/MbE08vdzMvmxmPzezR83sj8Z7fo3D7VddXV3aJUgCbb370i5BElD780vZ+ab88mVeOtxmVgZ8GngDcBZwtZmdVbTYe4DDIYR1wCeAj8bTrwSWhBBeBmwCfmu0My7ZoCEdfStftCTtEiQBtT+/lJ1vyi9f5msP92ZgTwjhyRDCEHArcHnRMpcDX47//jqw1aIzCgJQbWaLgSpgCOgpXoHeuH719/enXYIk0FR9ctolSAJqf34pO9+UX77M15mGK4HC6z8/A7xqomVCCMNm1g00EXW+LweeA04Cfi+E0FW8gu7ubi644AIWL17MyMgIV1xxBddffz1tbW1UV1dTVlZGT08Pzc3NdHV1EUKgubmZgwcPjl1eta+vjxUrVtDe3o6Z0djYSHt7O3V1dYyMjNDf309LSwttbW2Ul5dTX19PR0cH9fX1DA0NMTAwMDa/oqKC2tpaOjs7aWhoYGBggMHBwbH5lZWVVFVVcfjwYZqamujt7WVoaGhsflVVFRUVFXR3d7Ns2TK6u7s5evTo2PwsbVNjYyOtra2Z2qZSc1rTsAGILh7z6KEdrF+2iZEwzL6u3axvPpe23n10dHTQ399PdXkdG1q2MHi0nwM9ezitaSMHuvdQXVHP0qpmdrfdS2trKxUVFTRXn8LaxrPZf+QxllYup66ykd1t97KhZQs9g10cGTxEa2srTU1NbFixheqKurH5Rwba6R/qZmX9OvZ2PsjKunW0traObdNpjRs5euwFWmrX8ET7LgiwaeXreaJjJ2cu30xnZ2fmcsrie290m0ZGRhgcHMzUNmUxp/G2aWRkhMOHD2dqm7KY00TbZGb09/dnapuymNN42zQTFkKY0QOntRKzK4HLQgjXxfffAWwOIbyvYJnd8TLPxPf3Eu0ZPwP4XeBaoAH4EfCGEMKThevYvn172Lhx45xvi8y+1tZWVq9enXYZqZjOhW8WwrLjLb951TZ2PH3nuMvKwpfn9uedsvNN+fm1a9eunVu3bj1vOo+Zr0NKngEKr/98CvDsRMvEh4/UA13ANcCdIYSjIYRDwE+AEzZS41n6pauE+jZ4VD+Leqb255ey80355ct8dbjvA043s7VmVgFcBdxetMztwLviv98G/CBEu9/3A6+zSDVwPvBY8Qo0Solf9fX1aZcgCRzo2ZN2CZKA2p9fys435Zcv89LhDiEMAzcAdwGPAl8LIew2s1vM7C3xYp8HmsxsD/D7wOjQgZ8GaoCHiTruXwwhPFS8Dl3a3a+Ojo60S5AETmvSoVyeqf35pex8U375Mm+XZwwh3AHcUTTtgwV/DxINAVj8uL7xphfTHm6/9C3ftwPd2sPtmdqfX8rON+WXL5m50uR8nPwpc2OmZ/zKwlBdof80PFP780vZ+ab88iUzHe5jx46lXYLM0MDAQNolSAJLq5rTLkESUPvzS9n5pvzyJTMdbp3t61dLS0vaJUgCu9vuTbsESUDtzy9l55vyy5fMdLiPHj2adgkyQ21tbWmXIAlsaNmSdgmSgNqfX8rON+WXL5npcC9alJlNyZ2Kioq0S5AE+od60i5BElD780vZ+ab88iUzvVR1uP2qra1NuwRJ4FDf/rRLkATU/vxSdr4pv3zJTC9V43D71dnZmXYJksDaxrPTLkESUPvzS9n5pvzyJTMd7sWL521IcZllDQ0NaZcgCew/cnaFaD0AACAASURBVMKFX8URtT+/lJ1vyi9fMtNL1bCAfg0MDFBXV5d2GTJDSyuX09a7b9x5V31s05SPv/XGnbNckUyH2p9fys435ZcvmdnDrQ63X4ODg2mXIAnUVTamXYIkoPbnl7LzTfnlS2Y63BqH2y+NReqbxuH2Te3PL2Xnm/LLl8x0uDUOt18ai9Q3jcPtm9qfX8rON+WXL5npcGtYQL8qKyvTLkES6BnsSrsESUDtzy9l55vyy5fM9FLV4farqqoq7RIkgSODh9IuQRJQ+/NL2fmm/PIlM71UjcPt1+HDh9MuQRI4dekZaZcgCaj9+aXsfFN++ZKZDrfG4farqakp7RIkgae6Hk67BElA7c8vZeeb8suXzHS4NSygX729vWmXIAksrzk17RIkAbU/v5Sdb8ovX9ThltQNDQ2lXYIkUF2hCzd4pvbnl7LzTfnlS2Y63BqH2y+NReqbxuH2Te3PL2Xnm/LLl8wc+KxxuP1qa2tj9erVaZcxa/J2OfMNLVvY8fSdaZchM5S19pcnys435ZcvmdnDrWEB/dLQSL4dGWhPuwRJQO3PL2Xnm/LLl8z0Us0s7RJkhioqKtIuQRLoH+pOuwRJQO3PL2Xnm/LLl8x0uEdGRtIuQWaou1sdNs9W1q9LuwRJQO3PL2Xnm/LLl8x0uDUOt1/Lli1LuwRJYG/ng2mXIAmo/fml7HxTfvmSmQ639nD7pW/5vq2s0x5uz9T+/FJ2vim/fMlMhzuEkHYJMkMaYca3yvLqtEuQBNT+/FJ2vim/fMlMh1vjcPulsUh90zjcvqn9+aXsfFN++TKjDreZXWJmF812MUnom6JfbW1taZcgCWxo2ZJ2CZKA2p9fys435ZcvJXW4zeyHZnZB/PcfArcC/8/M/ngui5uOsrKytEuQGaqu1iEJnnX2P5d2CZKA2p9fys435Zcvpe7hPhv4t/jv9wIXA+cDvz0HNUnO6MuSb0ePvZB2CZKA2p9fys435ZcvpXa4FwHBzE4DLITwaAjhaaBh7kqbHo1S4ldPT0/aJUgCLbVr0i5BElD780vZ+ab88qXUwat/DHwKOBn4FkDc+e6Yo7qmTSdN+tXc3Jx2CZLAE+270i5BElD780vZ+ab88qXUPdzXAkeAh4D/Hk87A/jkHNQ0I8PDw2mXIDPU1dWVdgmSwJrGDWmXIAmo/fml7HxTfvlS0h7uEEIn8MdF0/5lTiqS3NEY6r6Vma7y6pnan1/Kzjflly+ljlLy+2b28vjv881sv5k9aWavntvySqdLu/uln9V8e6JjZ9olSAJqf34pO9+UX76UekjJ7wFPxX//OfBx4M+Av5yLomZC43D7dfDgwbRLkATOXL457RIkAbU/v5Sdb8ovX0rdLVwfQug2s1pgI/DLIYQRM/tfc1jbtGh4Hb9qamrSLkESONT3dNolSAJqf34pO9+UX76U2uF+2sy2ABuAe+LOdh2gsfhERERERCZR6iElfwB8HfhvwIfiaW8CdsxFUTOhcbj96uvrS7sESWB5zaq0S5AE1P78Una+Kb98KXWUkjuAlxRN/of4tiBoHG6/VqxYkXYJksCjh2bne/dVH9s05TK33qgTNGeb2p9fys435Zcvpe7hBsDMas1srZm9FFgV3xYEjcPtV3t7e9olSALrl03dUZaFS+3PL2Xnm/LLl5L2cJvZWcDfE50wGQCL/wXQ2YqSiJmlXYIkMBL0ZdcztT+/lJ1vyi9fSt3D/RngbqAR6AEagL8G3jVHdU2bxuH2q7GxMe0SJIF9XbvTLkESUPvzS9n5pvzypdQO90bgD0MIRwALIXQTnUj5ockfNn80Drdf+lnNt/XN56ZdgiSg9ueXsvNN+eVLqR3uQWD0rMQOMzs1fmzTnFQ1AxqH26+6urq0S5AE2nr3pV2CJKD255ey80355UupHe4fAb8W//114DvAD4EflLoiM9tmZo+b2R4zu2mc+UvM7LZ4/s/MbE3BvHPM7KdmttvMfm5mlaWuVxY+DenoW/miJWmXIAmo/fml7HxTfvlSUoc7hPBrIYQvxXf/GPgL4LPAr5fyeDMrAz4NvAE4C7g6PhGz0HuAwyGEdcAngI/Gj10M/B3w2yGEDcDFwAnHj+iN61d/f3/aJUgCTdUnp12CJKD255ey80355cu0zzQMIRwDvjLNh20G9oQQngQws1uBy4FHCpa5HLg5/vvrwKcsOoX3UuChEMKD8fo7x1uBxuH2q6WlJe0SJIHdbfemXYIkoPbnl7LzTfnlS6nDAtYD/wl4BVBTOC+EcGkJT7ESeLrg/jPAqyZaJoQwbGbdRMeIrweCmd0FNAO3hhA+VryCQ4cO8d73vpfFixczMjLCFVdcwfXXX09bWxvV1dWUlZXR09NDc3MzXV1dhBBobm7m4MGD1NREm9TX18eKFStob2/HzGhsbKS9vZ26ujpGRkbo7++npaWFtrY2ysvLqa+vp6Ojg/r6eoaGhhgYGBibX1FRQW1tLZ2dnTQ0NDAwMMDg4ODY/MrKSqqqqjh8+DBNTU309vYyNDQ0Nr+qqoqKigq6u7tZtmwZ3d3dHD16dGx+lrZpZGSEsrKyzGzT5lXb2N12LxtattDZ/xxHj71AS+0anmjfxZrGDZTZYgYHBzl48CBrGjYA0dUaHz20g/XLNjEShtnXtZv1zefS1ruPjo4O+vv7qS6vY0PLFgaP9nOgZw+nNW3kQPceqivqWVrVzO62e2ltbaWiooLm6lNY23g2+488xtLK5dRVNo7V1DPYxZHBQ7S2ttLU1MSGFVuorqgbm39koJ3+oW5W1q9jb+eDrKxbR2tr69g2n9a48bhtuuilV3Cgey9PdOzkzOWb6ezsHMupdknjuNtUvmgJTdUnj9VcXl5O00knj7tNG1q20D/Uw6G+/bS2tqo9zfI2HThwgPXr12dqm7KY03jbtGfPHlatWpWpbcpiThNtU29vL2vXrs3UNmUxp/G2aSYshDD1Qmb/SjTe9reAgcJ5IYTPl/D4K4HLQgjXxfffAWwOIbyvYJnd8TLPxPf3Eu0ZfzdwPfBK4Hng+8AHQgjfL1zHD3/4w3DOOedMuS2y8Dz77LO85CXFFzL1azpXTPS27HjLn9PyGh5q+1FJy85mHTI7stb+8kTZ+ab8/Nq1a9fOrVu3njedx5R6SMn5QFMIYaZj7z3D8VelPAV4doJlnomP264HuuLpPwwhdACY2R3AuUQd7zEapcSv+vr6tEuQBA707Em7BElA7c8vZeeb8suXUkcp+TFwZoL13AecHl8WvgK4Cri9aJnbefFCOm8DfhCi3e93AeeY2UlxR/y1HH/sN6BLu3vW0dGRdgmSwGlNG9MuQRJQ+/NL2fmm/PKl1D3c1wJ3mNnPgIOFM0IIt0z14PiY7BuIOs9lwBdCCLvN7Bbg/hDC7cDnga+Y2R6iPdtXxY89bGYfJ+q0B+COEMK/FK9De7j90rd83w50aw+3Z2p/fik735RfvpTa4f4zosM99gGFI7VPfQD46IIh3AHcUTTtgwV/DwJXTvDYvyMaGnCy5y+1FFlgZnoCgiwM1RX6T8MztT+/lJ1vyi9fSu1wXwWsDyE8N5fFJHHs2LG0S5AZGhgYmHohWbCWVjWnXYIkoPbnl7LzTfnlS6nHcD/JOBebWUg0DrdfGovUN43D7Zvan1/Kzjflly+ldri/AtxuZleb2esKb3NZ3HQcPbqgvw/IJNra2tIuQRLY0LIl7RIkAbU/v5Sdb8ovX0o9pOT6+N+PFE0PwEtnr5yZW7So1O8OstBUVFSkXYIk0D/Uk3YJkoDan1/Kzjflly8ldbhDCGvnupCk1OH2q7a2Nu0SJIFDffvTLkESUPvzS9n5pvzyJTO9VI3D7dfopcDFp7WNZ6ddgiSg9ueXsvNN+eVLZjrcixeXenSMLDQNDQ1plyAJ7D/yWNolSAJqf34pO9+UX75kppeqYQH9GhgYoK6ubuoFU3TVxzZNucytN+6ch0oWnqWVy2nr3Zd2GTJDHtqfjE/Z+ab88iUze7jV4fZrcHAw7RIkgbrKxrRLkATU/vxSdr4pv3wpqcNtZh83s5fPdTFJaBxuvzQWqW8ah9s3tT+/lJ1vyi9fSt3DXQ7cZWYPm9kfmtkpc1nUTGgcbr80FqlvGofbN7U/v5Sdb8ovX0rqcIcQ3ge8BLgJeDnwqJl9z8zeaWY1c1lgqTQsoF+VlZVplyAJ9Ax2pV2CJKD255ey80355UvJvdQQwkgI4Z9DCFcD5wPNwJeANjP7nJmtnKMaS6IOt19VVVVplyAJHBk8lHYJkoDan1/Kzjflly8l91LNrM7M3mNmdwP3AD8DXgOcCfQB35mbEkujcbj9Onz4cNolSAKnLj0j7RIkAbU/v5Sdb8ovX0oaFtDMvg5cRtTR/ivg2yGEFwrm/z7QPScVlkjjcPvV1NSUdgmSwFNdD6ddgiSg9ueXsvNN+eVLqXu4/w04PYTwKyGE2wo72wAhhGPAilmvbho0LKBfvb29aZcgCSyvOTXtEiQBtT+/lJ1vyi9fSt0t/JoQwv8snmhm3wwhXAEQQnh+ViubJnW4/RoaGkq7BEmgumL+L9ygCxHNHrU/v5Sdb8ovX0rdw33JBNMvnqU6EtM43H5pLFLfNA63b2p/fik735Rfvky6h9vMbon/rCj4e9RLgdY5qWoGNA63X21tbaxevTrtMmSGNrRsYcfTd6ZdhsyQ2p9fys435ZcvUx1Ssir+d1HB3wABeBq4eQ5qmhENC+iXhkby7chAe9olSAJqf34pO9+UX75M2uEOIbwbwMzuDSF8dn5KmhkzS7sEmaGKioq0S5AE+odSHaBIElL780vZ+ab88mXC3cJmtqbg7vfN7KXj3ea8whKNjIykXYLMUHe3Omyeraxfl3YJkoDan1/Kzjflly+T7eH+OVAb/72H6DCS4t3IASibg7qmTeNw+7Vs2bK0S5AE9nY+mHYJkoDan1/Kzjflly8T7uEOIdQW/L0ohFAW/1t4WxCdbdAebs/0Ld+3lXXaw+2Z2p9fys435ZcvmTnTMISQdgkyQxphxrfK8uq0S5AE1P78Una+Kb98mfA4DDP7EdEhI5MKIVw0qxXNkMbh9ktjkfqmcbh9U/vzS9n5pvzyZbIDnz83b1XMAn1T9Etjkfqmcbh9U/vzS9n5pvzyZcIOdwjhy/NZSFJlZQvmcHKZpupqHZLgWWf/c2mXIAmo/fml7HxTfvky2SEl7wghfCX++zcnWi6E8IW5KEzyQ1+WfDt67IW0S5AE1P78Una+Kb98meyQkquBr8R/v2OCZQKwIDrcGqXEr56eHhoaGtIuQ2aopXYN+488lnYZMkNqf34pO9+UX75MdkjJGwv+vmR+ypk5nTTpV3Nzc9olSAJPtO9KuwRJQO3PL2Xnm/LLl5KHBTSzpWb262b2B/G/S+eysOkaHh5OuwSZoa6urrRLkATWNG5IuwRJQO3PL2Xnm/LLl5I63Gb2OmAf8J+AVwLvA/aZ2da5K03yQmOo+1ZmusqrZ2p/fik735RfvpT6P+WngP8YQvja6AQzuxL4NHDGXBQ2Xbq0u1/6Wc23Jzp2pl2CJKD255ey80355Uuph5S8BPhG0bRvAQtm1HaNw+3XwYMH0y5BEjhz+ea0S5AE1P78Una+Kb98KbXD/bfA9UXTfieeviBoeB2/ampq0i5BEjjU93TaJUgCan9+KTvflF++lHpp90XA75jZjcABYCWwAvi3Oa9QRERERMSx6Vza/bNzWUhSGofbr76+PpqamtIuQ2Zoec0q9h3enXYZMkNqf34pO9+UX75k5tLuGofbrxUrVqRdgiTw6KEdaZcgCaj9+aXsfFN++TKdcbhXmNmbzezdZvabo7e5LG46NA63X+3t7WmXIAmsX7Yp7RIkAbU/v5Sdb8ovX0oaS8/MfhX4O+AXwAZgN3A28GMWyKXdxS8zS7sESWAk6MuuZ2p/fik735RfvpS6h/vDwLtDCK8A+uN//yOwYAbg1TjcfjU2NqZdgiSwr0vHb3um9ueXsvNN+eVLqR3uU0MI/1A07cvAO2e5nhnTONx+6Wc139Y3n5t2CZKA2p9fys435ZcvpXa4D5nZ6NH9+8zs1cBpwIIZ/FrjcPtVV1eXdgmSQFvvvrRLkATU/vxSdr4pv3wptcP9WeDC+O9PAHcDDwKfmYuiJF80pKNv5YuWpF2CJKD255ey80355UtJBz6HED5a8Pffmtl2oDqE8GipKzKzbcAnifaKfy6E8BdF85cQXblyE9AJvD2EsK9g/qnAI8DNIYT/Wfz8euP61d/fz7Jly9IuQ2aoqfpk9nY9mHYZE7rqY1OPonLrjQvmdJR5p/bnl7LzTfnly3SGBSwzswvM7EpgFfDEdB4LfBp4A3AWcLWZnVW02HuAwyGEdUR70T9aNP8TwHcmWofG4farpaUl7RIkgd1t96ZdgiSg9ueXsvNN+eVLSR1uMzuHaEjAfwD+IP73F2a2scT1bAb2hBCeDCEMAbcClxctcznRiZgAXwe2WjxmTjws4ZNEwxGOSydN+tXW1pZ2CZLAhpYtaZcgCaj9+aXsfFN++VLqHu4vEO2hXhlC2AysBD5F6WNwrwSeLrj/TDxt3GVCCMNAN9BkZtXAHwJ/OtkKNJ6lX/p1wrfBo/1plyAJqP35pex8U375Uurg1euBvwwhBIAQQjCzTwI3l/j48XrDocRl/hT4RAihb7JO9eHDh7ngggtYvHgxIyMjXHHFFVx//fW0tbVRXV1NWVkZPT09NDc309XVRQiB5uZmDh48SE1NDQB9fX2sWLGC9vZ2zIzGxkba29upq6tjZGSE/v5+WlpaaGtro7y8nPr6ejo6Oqivr2doaIiBgYGx+RUVFdTW1tLZ2UlDQwMDAwMMDg6Oza+srKSqqorDhw/T1NREb28vQ0NDY/OrqqqoqKigu7ubZcuW0d3dzdGjR8fmZ2mb6uvraW1tnddtuuWb17KhZQv9Qz0c6tvP2saz2X/kMZZWLqeuspHdbffywSu+NLZNm1dt46muh1lecyrVFXXsbruXDS1bODLQTv9QNyvr19Hf3093dzebV20bm9/Z/xxHj71AS+0anmjfxZrGDZTZYgYHBzl48CBrGjYAsLxmFY8e2sH6ZZsYCcPs69rN+uZzaevdR0dHB/39/VSX17GhZQuDR/s50LOH05o2cqB7D9UV9SytamZ32720trZSUVFBc/Up427ThpYt9Ax2cWTwEK2trTQ1NbFhxZYJt2lv54OsrFtHa2vr2Gt6WuPG47apdkkjm1a+nic6dnLm8s10dnaO5VS7pHHcbSpftISm6pPHai4vL6fppJPH3abCnFpbW2loaOCM5s3jbtOpS88Yy2m05s2rto27TZXl1WOP7+joyEx7mu5nxPPPP8/g4GCmtimLOY23Tc8//zyHDx/O1DZlMaeJtimEQH9/f6a2KYs5jbdNM2FxH3ryhcxuBW4LIXyrYNqvEp3YeHUJj3810cmOl8X3/wgghPDnBcvcFS/zUzNbDLQBzcA9RMeMAywFjgEfDCF8qnAd27dvDxs3lnqEiywkra2trF69el7XOd0T6aazfJaXHW/5zau2sePpO0tadrbqmMvty5s02p/MDmXnm/Lza9euXTu3bt163nQeM+EebjP7Ci/uhS4DbjWznUSHfawiGk3kH0tcz33A6Wa2FjgAXAVcU7TM7cC7gJ8CbwN+EO9Rf01BTTcDfcWdbdA43J7V19enXYIkcKB7T9olSAJqf34pO9+UX75MdkhJ8f+iDxf8/QhwV6krCSEMm9kN8WPKgC+EEHab2S3A/SGE24HPA18xsz1AF1GnvGSl7KmXhWmmP8/IwlBdof80PFP780vZ+ab88mXCDncIYdKTFKcrhHAHcEfRtA8W/D0IXDnFc9w80bxjx44lrFDSMjAwkHYJksDSqua0S5AE1P78Una+Kb98KfWkSczsEuAdRKOJHAD+LoTwg7kqbLp0tq9fGovUN43D7Zvan1/Kzjflly+ljsN9HXAb0YmM3wSeA75qZu+dw9qmReNw+6WxSH3TONy+qf35pex8U375Uuoe7huB14cQxq7fbGa3Ad8APjsXhU3XokUlXzRTFpiKioq0S5AE+od60i5BElD780vZ+ab88qXUXmoT0YmShR4HGme3nJlTh9uv2tratEuQBA717U+7BElA7c8vZeeb8suXUnupPwY+bmYnAcRXf/wfwII5eHN4eDjtEmSGRi+UIj6tbTw77RIkAbU/v5Sdb8ovX0rtcP828DKg28wOAkeAjcBvzVVh07V4ccnnf8oC09DQkHYJksD+I4+lXYIkoPbnl7LzTfnly5Qdbouup14F/DKwFngzsDaE8NoQwrNzXF/JNCygXxoaybellcvTLkESUPvzS9n5pvzyZcrdwiGEYGY/B2pDCM8Az8x9WdOnDrdfg4ODaZcgCdRVLphTOWQG1P78Una+Kb98KfWQkgeA9XNZSFIah9svjUXqm8bh9k3tzy9l55vyy5dSO9zbgTvN7GYze4+Z/ebobQ5rmxaNw+2XxiL1TeNw+6b255ey80355UupZxpeADwFvLZoegC+MKsVzZCGBfSrsrIy7RIkgZ7BrrRLkATU/vxSdr4pv3wpqcMdQrhkrgtJSh1uv6qqqtIuQRI4Mngo7RIkAbU/v5Sdb8ovXybtpZrZSWb2ETO7PT6cZMl8FTZdGofbr8OHD6ddgiRw6tIz0i5BElD780vZ+ab88mWq3cKfIhoG8DHgbcD/nPOKZkjjcPvV1NSUdgmSwFNdD6ddgiSg9ueXsvNN+eXLVB3uNwCXhhBujP9+09yXNDMaFtCv3t7etEuQBJbXnJp2CZKA2p9fys435ZcvU3W4q0MIzwGEEJ4G6ue+pJlRh9uvoaGhtEuQBKor6tIuQRJQ+/NL2fmm/PJlquMwFpvZJYBNcJ8Qwg/mqrjp0DjcfmksUt80Drdvan9+KTvflF++TLWH+xDRsH+fj2+dRfc/N6fVTYPG4fZLY5H6pnG4fVP780vZ+ab88mXSPdwhhDXzVEdiGhbQLw2N5NuRgfa0S5g1V31s05TL3HrjznmoZP6o/fml7HxTfvmSmV6qmU29kCxIFRUVaZcgCfQPdaddgiSg9ueXsvNN+eVLZjrcIyMjaZcgM9TdrQ6bZyvr16VdgiSg9ueXsvNN+eVLZjrcGofbr2XLlqVdgiSwt/PBtEuQBNT+/FJ2vim/fMlMh1t7uP3St3zfVtZpD7dnan9+KTvflF++ZKbDHUJIuwSZIY0w41tleXXaJUgCan9+KTvflF++ZKbDrXG4/dJYpL5pHG7f1P78Una+Kb98yUyHW98U/dJYpL5pHG7f1P78Una+Kb98yUyHu6ysLO0SZIaqq3VIgmed/c+lXYIkoPbnl7LzTfnlS2Y63OKXviz5dvTYC2mXIAmo/fml7HxTfvmSmQ63Rinxq6enJ+0SJIGW2jVplyAJqP35pex8U375kpkOt06a9Ku5uTntEiSBJ9p3pV2CJKD255ey80355UtmOtzDw8NplyAz1NXVlXYJksCaxg1plyAJqP35pex8U375kpkOt/ilMdR9KzNd5dUztT+/lJ1vyi9fMtPh1qXd/dLPar490bEz7RIkAbU/v5Sdb8ovXzLT4dY43H4dPHgw7RIkgTOXb067BElA7c8vZeeb8suXzOwW1vA6ftXU1MzK81z1sU1TLnPrjdobO9sO9T2ddgmSwGy1P5l/ys435ZcvmdnDLSIiIiKyEGWmw61xuP3q6+tLuwRJYHnNqrRLkATU/vxSdr4pv3zJTIdb43D7tWLFirRLkAQePbQj7RIkAbU/v5Sdb8ovXzLT4dY43H61t7enXYIksH7Z1MfOy8Kl9ueXsvNN+eVLZk6aFL/MLO0SJIGRkN8vu1OdqOvhJF21P7+UnW/KL18ys4db43D71djYmHYJksC+rt1plyAJqP35pex8U375kpkOt8bh9ks/q/m2vvnctEuQBNT+/FJ2vim/fMlMh1vjcPtVV1eXdgmSQFvvvrRLkATU/vxSdr4pv3zJTIdb/NKQjr6VL1qSdgmSgNqfX8rON+WXL5npcOuN61d/f3/aJUgCTdUnp12CJKD255ey80355UtmOtwah9uvlpaWtEuQBHa33Zt2CZKA2p9fys435Zcv89bhNrNtZva4me0xs5vGmb/EzG6L5//MzNbE019vZjvN7Ofxv68b7/l10qRfbW1taZcgCWxo2ZJ2CZKA2p9fys435Zcv89LhNrMy4NPAG4CzgKvN7Kyixd4DHA4hrAM+AXw0nt4BvDmE8DLgXcBXJljHXJQu80C/Tvg2eFQ/i3qm9ueXsvNN+eXLfO3h3gzsCSE8GUIYAm4FLi9a5nLgy/HfXwe2mpmFEB4IITwbT98NVJrZCWdpaZQSv+rr69MuQRI40LMn7RIkAbU/v5Sdb8ovX+brajErgacL7j8DvGqiZUIIw2bWDTQR7eEe9R+AB0IILxSvoL29nQsuuIDFixczMjLCFVdcwfXXX09bWxvV1dWUlZXR09NDc3MzXV1dhBBobm7m4MGD1NTUANDX18eKFStob2/HzGhsbKS9vZ26ujpGRkbo7++npaWFtrY2ysvLqa+vp6Ojg/r6eoaGhhgYGBibX1FRQW1tLZ2dnTQ0NDAwMMDg4ODY/MrKSqqqqjh8+DBNTU309vYyNDQ0Nr+qqoqKigq6u7tZtmwZ3d3dHD16dGx+lrZpZGSEsrKyxNt06tIzKF+0hKbqk9nddi8bWrYweLSfAz17OK1pIwe693Do0CEGBgaoLq9jQ8sW+od6ONS3n7WNZ7P/yGMsrVxOXWUju9vupbW1dWybNq/axlNdD7O85lSqK+rGnv/IQDv9Q92srF9Hf38/3d3dbF61bWx+Z/9zHD32Ai21a3iifRdrGjdQZosZHBzk4MGDrGnYAMDymlU8emgH65dtYiQMs69rsOwGJAAAFPNJREFUN+ubz6Wtdx8dHR309/eP1Vy8TdUV9Sytah6ruaKigubqU8bdpg0tW+gZ7OLI4CFaW1tpampiw4otE27T3s4HWVm3jtbW1rEcT2vceNw2XbDmcg507+WJjp2cuXwznZ2dYznVLmkcd5sKc2ptbaW8vJymk04ed5sKc2ptbaWhoYEzmjePu02nLj1jLKfRmjev2jbuNlWWV489vqOjg7KyMjav2nZcTqPbdKjv6bGcBgcHx957SyuXj7tNozn19/cv+M+IAwcOsH79+gX9GZHFz73Z2Ka9e/eyatWqTG1TFnOaaJt6e3tZu3ZtprYpizmNt00zYSGEGT1wWisxuxK4LIRwXXz/HcDmEML7CpbZHS/zTHx/b7xMZ3x/A3A7cGkIYW/xOn70ox+Fs88+e863RWbfkSNHWLp0aeLnmeoy2/Dipbans+xcPre3ZcdbfmXduuP2cufldStleQ+Xdp+t9ifzT9n5pvz82rVr186tW7eeN53HzNchJc8AqwrunwI8O9EyZrYYqAe64vunAN8C3jleZxtgPr44yNyY6bdFWRiqK/SzqGdqf34pO9+UX77MV4f7PuB0M1trZhXAVUR7qwvdTnRSJMDbgB+EEIKZLQX+BfijEMJPJlrBsWPH5qBsmQ8DAwNplyAJLK1qTrsESUDtzy9l55vyy5d56XCHEIaBG4C7gEeBr4UQdpvZLWb2lnixzwNNZrYH+H1gdOjAG4B1wJ+Y2b/Ht+XF69DZvn5pLFLfNA63b2p/fik735RfvszbONwhhDtCCOtDCKeFEP4snvbBEMLt8d+DIYQrQwjrQgibQwhPxtM/HEKoDiG8vOB2qPj5NQ63XxqL1DeNw+2b2p9fys435ZcvmbnS5KJFmdmU3KmoqEi7BEmgf6gn7RIkAbU/v5Sdb8ovXzLTS1WH26/a2tq0S5AEDvXtT7sESUDtzy9l55vyy5f5God7zg0PD6ddgsxQZ2fn2NiY4s/axrNp738m7TIWvOkOOThf1P78Una+Kb98ycxu4cWLM/PdIXcaGhrSLkES2H/ksbRLkATU/vxSdr4pv3zJTIdbwwL6paGRfFtaecKgQeKI2p9fys435Zcv6nBL6gYHB9MuQRKoq2xMuwRJQO3PL2Xnm/LLl8x0uDUOt18ai9Q3jcPtm9qfX8rON+WXL5npcGscbr80FqlvGofbN7U/v5Sdb8ovXzLT4dawgH5VVlamXYIk0DPYlXYJkoDan1/Kzjflly+ZGdpDHW6/qqqqJpy3UIdSkxcdGTzhwq/iyGTtTxY2Zeeb8suXzPRSNQ63X4cPH067BEng1KVnpF2CJKD255ey80355UtmOtwah9uvpqamtEuQBJ7qejjtEiQBtT+/lJ1vyi9fMtPh1rCAfvX29qZdgiSwvObUtEuQBNT+/FJ2vim/fFGHW1I3NDSUdgmSQHVFXdolSAJqf34pO9+UX75kpsOtcbj90likvmkcbt/U/vxSdr4pv3zJzIHPGofbr7a2NlavXp12GTJDG1q2sOPpO9MuI1Pmc3QetT+/lJ1vyi9fMrOHW8MC+qWhkXw7MtCedgmSgNqfX8rON+WXL5nppZpZ2iXIDFVUVKRdgiTQP9SddgmSgNqfX8rON+WXL5npcI+MjKRdgsxQd7c6bJ6trF+XdgmSgNqfX8rON+WXL5npcGscbr+WLVuWdgmSwN7OB9MuQRJQ+/NL2fmm/PIlMx1u7eH2S9/yfVtZpz3cnqn9+aXsfFN++ZKZDncIIe0SZIY0woxvleXVaZcgCaj9+aXsfFN++ZKZDrfG4fZLY5H6pnG4fVP780vZ+ab88iUzHW59U/Srra0t7RIkgQ0tW9IuQRJQ+/NL2fmm/PIlMx3usrKytEuQGaqu1iEJnnX2P5d2CZKA2p9fys435Zcvmelwi1/6suTb0WMvpF2CJKD255ey80355UtmxtLTKCV+9fT00NDQkHYZMkMttWvYf+SxtMvIraSXgVf780vZ+ab88iUze7h10qRfzc3NaZcgCTzRvivtEiQBtT+/lJ1vyi9fMtPhHh4eTrsEmaGurq60S5AE1jRuSLsESUDtzy9l55vyy5fMHFIifhT/BL5p5evZeeC7x02b7CdwWVjKTB8jnukaBn4pO9+UX75kZg+3Lu3u1xMd6lx7pvx808/afik735RfvmSmw61xuP06c/nmtEuQBJSfbwcPHky7BJkhZeeb8suXzHS4NbyOX4f6nk67BElA+flWU1OTdgkyQ8rON+WXLzoOQ0QkJ8YbQnBNwwb2Hd49dl/nT4iIzL7M7OHWONx+La9ZlXYJkoDy8035+dXX15d2CZKA8suXzHS4NQ63X48e2pF2CZKA8vNN+fm1YsWKtEuQBJRfvmSmw61xuP1av2zqK+XJwqX8fFN+frW3t6ddgiSg/PIlMx1u8Wsk6MuSZ8rPN+Xnl5mlXYIkoPzyJTMnTWocbr/2de2eeiFZsJSfbxPlN94JlsV0gmW6Ghsb0y5BElB++ZKZPdwah9uv9c3npl2CJKD8fFN+fumQBN+UX75kZrewxuFOV5K9YW29+2a5GplPys835edXXV1d2iVIAsovXzKzh1v8Kl+0JO0SJAHl55vy80vD4fqm/PIlM3u49cb1q6n6ZPZ2PZh2GTJDys+32chPx3uno7+/n2XLlqVdhsyQ8suXzOzh1jjcfu1uuzftEiQB5eeb8vOrpaUl7RIkAeWXL5nZw62TJv3a0LKFHU/fmXYZMkPKz7c08tMe8dnR1tbG6tWr0y5DZkj55cu87eE2s21m9riZ7TGzm8aZv8TMbovn/8zM1hTM+6N4+uNmdtl4z3/kyJG5K17m1M9++EDaJUgCys835efXt7/97bRLkASUn19dXV3TPhZoXvZwm1kZ8Gng9cAzwH1mdnsI4ZGCxd4DHA4hrDOzq4CPAm83s7OAq4ANwEuA75nZ+hDCcQdtq8M9++ZrL9TOH/+c8166PPHzSDqUn28LPT/tDZ/YN7/5Td7//venXYbMkPLzq6enp3m6j5mvQ0o2A3tCCE8CmNmtwOVAYYf7cuDm+O+vA5+y6DJMlwO3hhBeAJ4ysz3x8/20cAUhhDndAJk7SxaflHYJkoDy8y1L+U2nc56FjvzwsK4S6pnyyxebj46qmb0N2BZCuC6+/w7gVSGEGwqWeThe5pn4/l7gVUSd8H8LIfxdPP3zwHdCCF8vXMc//dM/DR46dGhsr3ddXV17Y2Njx9xumcyGrq6uZcrKL+Xnm/LzS9n5pvz8euGFF37pjW98Y+10HjNfe7htnGnFPf2Jlinlsbz5zW+unEFdIiIiIiJzar5OmnwGWFVw/xTg2YmWMbPFQD3QVeJjRUREREQWpPnqcN8HnG5ma82sgugkyNuLlrkdeFf899uAH4ToeJfbgaviUUzWAqcDO+apbhERERGRROblkJIQwrCZ3QDcBZQBXwgh7DazW4D7Qwi3A58HvhKfFNlF1CknXu5rRCdYDgPXF49QIiIiIiKyUM3LSZNzycy2AZ8k6sh/LoTwFymXJJMwsy8AbwIOhRDOjqc1ArcBa4B9wK+FEA6nVaOMz8xWAX8LtADHgL8JIXxS+flgZpXAPcASop0tXw8h/Pf4l8NbgUZgF/COEMJQepXKROIhdu8HDoQQ3qTs/DCzfUAvMAIMhxDO02enH2a2FPgccDbReYS/CTzONPJzfWn3gvG93wCcBVwdj9stC9eXgG1F024Cvh9COB34fnxfFp5h4L+EEM4Ezgeuj9ub8vPhBeB1IYSNwMuBbWZ2PtE1Dz4R53eY6JoIsjC9H3i04L6y8+WSEMLLQwjnxff12enHJ4E7QwhnABuJ2uG08nPd4aZgfO/4W/3o+N6yQIUQ7iE6ZKjQ5cCX47+/DPzqvBYlJQkhPBdC2BX/3Uv0gbMS5edCiPTFd8vjWwBeR3TtA1B+C5aZnQL8CtFeNuLrVCg73/TZ6YCZ1QEXER36TAhhKIRwhGnm573DvRJ4uuD+M/E08WVFCOE5iDp1wMK97J0AYGZrgFcAP0P5uWFmZWb278Ah4LvAXuBICGH0Chz6DF24/hK4kehwLoD/396dx9pVlWEc/r0MYoFCkZahFEoAGSyRgimoKFYRCKQQooCaShgUQWkURcUWBMUWJCIULJUoWiRYhjCJODBD6lQioAwWA1KgtRNzabVYyusfax26e723vWBvb8/N+yQnd5+9z177O3sl535nnW/tvTnpu3Zi4DZJ90v6XF2Xz872sAPwLDBF0oOSLpO0EW+y/9o94e7WNbojYvWRtDFwPXCK7YW9HU90n+1ltodTLq+6N7BbZy9bs1HFqkhqzXtp3voy///ay76296KUwJ4sab/eDii6bT1gL+CHtvcEFvMWyn/aPeHONbr7hvmStgaofxf0cjzRBUnrU5Ltn9u+oa5O/7WZ+nPoPZRa/AH13geQz9C11b7AYXXi3dWUUpKJpO/ahu059e8C4EbKF958draH2cBs29Pr8+soCfib6r92T7i7c33vWPs1r8F+DPCLXowlulBrRn8CzLB9QWNT+q8NSBpUZ9ojqR/wUUod/t2Uex9A+m+tZHus7SG2t6f8n7vL9mjSd21B0kaS+reWgQOBR8hnZ1uwPQ+YJWmXump/yqWq31T/9YXLAh5C+abfur73hF4OKVZC0lXASGAgMB84C7gJuBbYDngGONJ2x4mV0cskfQCYBjzM8jrScZQ67vTfWk7SuykTe9alDLZca/tsSTuw/NJyDwKftv1q70UaKyNpJPDVelnA9F0bqP10Y326HjDV9gRJm5PPzrYgaThlwvLbgCeB46ifo3Sz/9o+4Y6IiIiIWJu1e0lJRERERMRaLQl3REREREQPSsIdEREREdGDknBHRERERPSgJNwREX2MpEX1ygg9fZxLJX2zp4+zpkk6VtLvejuOiOg71lv1SyIi1n71piBbAsuARcBvgTG2F/VmXD1N0j3AlbYva62zvfGaOLbtk9bEcSIi2l1GuCOiLzm0JpvDgT2Bsb0cT0RERBLuiOh76p3BbqUk3gBI2kDS+ZKekTS/lkP0q9sGSrpF0kuSXpA0TdI6ddtTksZK+pukFyVNkfT2RrsnSHqi7nezpMGNbZZ0kqTH676X1Dt2ImknSfdKelnSc5Kuaey3q6Tba5t/l3RUZ+9T0gTgg8CkWkYyqXHcnery5ZImS/pNfc3vJW0laWKN6TFJezbaHCzpeknPSpop6Ytdnefa9vi6PFLSbEmnSlogaa6k41ay77GSnpT0Sj3O6Ma24yXNqPHdKmloY9uwxrmZL2lco38nSppTHxMlbdCd2CRtXvtuoaT7gB0b2yTpwrrfy5IekrR7V+8rIqIzSbgjos+RNAQ4GHiisfo8YGdKEr4TsA1wZt12KjAbGEQpSxkHNO8KNho4iJKI7QycUY/zEeBc4Chga+Bpyp3/mkYBI4A96usOquu/A9wGbAYMAX5Q29wIuB2YCmwBfAqYLGlYx/dp+3TK3T/H2N7Y9pguTslRNeaBwKvAH4EH6vPrgAvqsdcBfgn8tZ6f/YFTJB3USZud2QrYtO77GeASSZt1fFF9jxcDB9vuD7wf+Evddjjl/H+M0h/TgKvqtv7AHZRyocGUfryzNns68F5K/+4B7F3fc3diuwRYQunD4+uj5UBgP0q/DwA+ATzfzfMREQEk4Y6IvuUmSa8As4AFwFlQRimBE4Av237B9ivAOcAn635LKcnWUNtLbU/zirfhnWR7Vr1t7wRKEgwlEf+p7QfqLbXHAu+TtH1j3+/afsn2M8DdLB91XwoMBQbbXmK7NUlvFPCU7Sm2X7P9AHA9cMT/cV5utH2/7SWUW0wvsX2F7WXANZTyGyhfDAbZPtv2f2w/Cfy4cZ5WZSlwdj2Hv6bU0u/SxWtfB3aX1M/2XNuP1vUnAufanmH7NUo/Da+j3KOAeba/X8/ZK7an1/1G12MvsP0s8G3g6FXFJmld4OPAmbYX234E+FmH/foDu1LuzjzD9txuno+ICCAJd0T0LYfXEdORlARpYF0/CNgQuL+WjbxEGSUdVLd/jzIaflstc/hGh3ZnNZafpoyuUv8+3dpQJ2g+TxlFbZnXWP4X0JrQ+HVAwH2SHpXUGlUdCuzTirPGOpoyQvtWzW8s/7uT562YhgKDOxx7HGXUvzuer0lyS/P9vsH2YspI8UnAXEm/krRrI4aLGsd/gXKetgG2Bf7RxbFX6AtW7KeVxTaIcgGBjn3civUuYBJlFHy+pB9J2qSLGCIiOpWEOyL6HNv3ApcD59dVz1ESy2G2B9THpq2redSR0lNt7wAcCnxF0v6NJrdtLG8HzKnLcygJIvBGqcTmwD+7EeM82yfYHkwZ1Z1c665nAfc24hxQy0U+31VTqzrWmzALmNnh2P1tH7IajwGA7VttH0D5ZeExykh6K4YTO8TQz/Yf6rYdu2hyhb5gxX5amWeB1/jfPm7GerHt9wDDKKUlX+tGuxERb0jCHRF91UTgAEnDbb9OSegulLQFgKRtWrXJkkbVSYwCFlIuLbis0dbJkoZIegdlxLc1wXEqcJyk4XWC3jnAdNtPrSo4SUfWWnOAFymJ8zLgFmBnSUdLWr8+RkjarYum5gOr65rb9wELJZ0mqZ+kdSXtLmnEamofAElbSjqsfkF5lVLe0TrflwJjWzXrkjaVdGTddguwlaRT6iTJ/pL2qduuAs6QNEjSQEp9/pWriqWW1dwAfEvShpLeBRzTiHWEpH0krQ8sptR6L+u8tYiIziXhjog+qdbxXgG0bsxyGqVs5E+SFlIm37Xqi99Zny+iTCicbPueRnNTKRMcn6yP8fUYd9b2rwfmUkZfu1vvPAKYLmkRcDPwJdsza335gbWdOZSSlPOADbpo5yLgiHpFj4u7eexO1eTzUEqd+UzKLwOXUSYbrk7rUCaqzqGUjHwI+EKN4UbK+7269tMjlAmw1HNzQI1xHvA48OHa5njgz8BDwMOUSaHjuxnPGEp5yTzKLyNTGts2oXxZe5FSavI8y385iYjoFq04LygiIppUbqjzWdt39HYsERHRnjLCHRERERHRg5JwR0RERET0oJSURERERET0oIxwR0RERET0oCTcERERERE9KAl3REREREQPSsIdEREREdGDknBHRERERPSgJNwRERERET3ov+NYPHRs4jU8AAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<Figure size 864x360 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig = plt.figure(figsize=(12,5))\n",
    "ax = fig.add_subplot(111)\n",
    "x_lim = 60\n",
    "mu = np.int(freq_results['x'])\n",
    "\n",
    "for i in np.arange(x_lim):\n",
    "    plt.bar(i, stats.poisson.pmf(mu, i), color=colors[3])\n",
    "\n",
    "_ = ax.set_xlim(0, x_lim)\n",
    "_ = ax.set_ylim(0, 0.1)\n",
    "_ = ax.set_xlabel('Response time in seconds')\n",
    "_ = ax.set_ylabel('Probability mass')\n",
    "_ = ax.set_title('Estimated Poisson distribution for Hangout chat response time')\n",
    "_ = plt.legend(['$lambda$ = %s' % mu])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "上述泊松分布模型和 μ 的估计表明，观测小于10 或大于 30 的可能性很小，绝大多数的概率分布在 10 和 30 之间。但是，这不能反映我们观测到的介于 0 到 60 之间的数据。"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### 贝叶斯方法估计μ\n",
    "\n",
    "<img src=\"assets/20201128203033.png\" width=\"30%\">\n",
    "\n",
    "<img src=\"assets/20201128203246.png\" width=\"30%\">"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "上述可解读如下（从下到上）：\n",
    "<ul>\n",
    "    <li>对每一个对话（i）观测计数数据（y）\n",
    "    <li>数据由一个随机过程产生，我们认为可以用泊松分布模拟\n",
    "    <li>泊松分布只有一个参数，介于 0 到 60 之间\n",
    "    <li>均匀分布的原因在于并没有提及任何条件"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**马尔可夫链蒙特卡洛方法MCMC**\n",
    "\n",
    "贝叶斯公式的只是一个参数，但如果我们的问题涉及到多个参数呢？分布的积分就应该改成多重积分，但是难点在于我们该怎么算，MCMC采样器从先验分布中选取参数值，计算从这些参数值决定的某个分布中得到观测数据的可能性。这个计算可以作为MCMC采样器的导引。从参数的先验分布中选取值，然后计算给定数据条件下这些参数值可能性——导引采样器到更高概率的区域。与上面讨论的频率论优化技术在概念上有相似之处，MCMC采样器向可能性最高的区域运动。但是，贝叶斯方法不关心寻找绝对最大值，而是遍历和收集概率最高区域附近的样本。所有收集到的样本都可认为是一个可信的参数\n",
    "\n",
    "**蒙特卡洛方法**\n",
    "\n",
    "是一系列应用非常广泛的算法，其思想是通过随机采样来计算或模拟给定过程。尽管很多问题都难以求解甚至没办法用公式表达，但我们可以通过采样或者模拟来有效地研究\n",
    "\n",
    "统计模拟中有一个重要的问题就是给定一个概率分布p(x)，如何在计算机中生成它的样本。其基本思想是通过大量取近似得到想要的答案。有一个经典的试验就是计算圆周率，在一个边上为1的正方形中画一个内切圆，现在在正方形内产生大量随机数，最后我们只需要计算圆内点的个数比上总体的个数，便得到了圆周率的值。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x2ed56e98ef0>"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# 每次结果会不一样，样本越多必然也会越准确，可以尝试把N值改小改大\n",
    "N = 10000\n",
    "\n",
    "x, y = np.random.uniform(-1,1,size=(2,N))\n",
    "inside = (x**2 + y**2) <= 1\n",
    "pi = inside.sum()* 4 / N\n",
    "error = abs((pi - np.pi) / pi) * 100\n",
    "\n",
    "outside = np.invert(inside)\n",
    "\n",
    "plt.plot(x[inside], y[inside], 'b.')\n",
    "plt.plot(x[outside], y[outside], 'r.')\n",
    "plt.plot(0,0,label='$\\hat \\pi$ = {:4.3f}\\nerror = {:4.3f}%'.format(pi, error), alpha=0)\n",
    "plt.axis('square')\n",
    "plt.legend(frameon=True, framealpha=0.9,fontsize=16)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### PYMC3概述\n",
    "**马氏链的平稳性**\n",
    "\n",
    "对于先验分布，如果能找到一个转移矩阵，那么在n步之后就会收敛到一个平稳分布，而这个分布就是我们要的后验分布。得到平稳分布后，根据平稳性，继续乘上这个转移概率矩阵，平稳分布依然不会改变，所以我们就从得到平稳分布开始每次对其进行抽样。\n",
    "\n",
    "<img src=\"assets/20201128211430.png\" width=\"30%\">\n",
    "<img src=\"assets/20201128211519.png\" width=\"30%\">\n",
    "越到后面几代人，值越平稳不变"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "\n",
       "    <div>\n",
       "        <style>\n",
       "            /* Turns off some styling */\n",
       "            progress {\n",
       "                /* gets rid of default border in Firefox and Opera. */\n",
       "                border: none;\n",
       "                /* Needs to be in here for Safari polyfill so background images work as expected. */\n",
       "                background-size: auto;\n",
       "            }\n",
       "            .progress-bar-interrupted, .progress-bar-interrupted::-webkit-progress-bar {\n",
       "                background: #F44336;\n",
       "            }\n",
       "        </style>\n",
       "      <progress value='6' class='' max='6' style='width:300px; height:20px; vertical-align: middle;'></progress>\n",
       "      100.00% [6/6 00:00<00:00 logp = -3,398.7, ||grad|| = 1,989]\n",
       "    </div>\n",
       "    "
      ],
      "text/plain": [
       "<IPython.core.display.HTML object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Multiprocess sampling (2 chains in 2 jobs)\n",
      "Metropolis: [mu]\n"
     ]
    },
    {
     "data": {
      "text/html": [
       "\n",
       "    <div>\n",
       "        <style>\n",
       "            /* Turns off some styling */\n",
       "            progress {\n",
       "                /* gets rid of default border in Firefox and Opera. */\n",
       "                border: none;\n",
       "                /* Needs to be in here for Safari polyfill so background images work as expected. */\n",
       "                background-size: auto;\n",
       "            }\n",
       "            .progress-bar-interrupted, .progress-bar-interrupted::-webkit-progress-bar {\n",
       "                background: #F44336;\n",
       "            }\n",
       "        </style>\n",
       "      <progress value='6000' class='' max='6000' style='width:300px; height:20px; vertical-align: middle;'></progress>\n",
       "      100.00% [6000/6000 00:56<00:00 Sampling 2 chains, 0 divergences]\n",
       "    </div>\n",
       "    "
      ],
      "text/plain": [
       "<IPython.core.display.HTML object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Sampling 2 chains for 1_000 tune and 2_000 draw iterations (2_000 + 4_000 draws total) took 64 seconds.\n",
      "The number of effective samples is smaller than 25% for some parameters.\n"
     ]
    }
   ],
   "source": [
    "with pm.Model() as model:  # 构造模型\n",
    "    mu = pm.Uniform('mu', lower=0, upper=60)  # 指定一个均值，服从正态分布且是0-60之间\n",
    "    # 指定泊松分布，并把数据放进去\n",
    "    likelihood = pm.Poisson('likelihood', mu=mu, observed=messages['time_delay_seconds'].values)\n",
    "\n",
    "    start = pm.find_MAP()\n",
    "    step = pm.Metropolis()\n",
    "    trace = pm.sample(2000, step, start=start, progressbar=True)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "上面的代码通过遍历 μ 的后验分布的高概率区域，收集了 200,000 个 μ 的可信样本。下图（左）显示这些值的分布，平均值与频率论的估值（红线）几乎一样。但是，我们同时也得到了不确定度，μ 值介于 17 到 19 之间都是可信的。我们稍后会看到这个不确定度很有价值。\n",
    "\n",
    "<img src=\"assets/20201128211719.png\" width=\"50%\">"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### PyMC3概述\n",
    "PyMC3是一个用于概率编程的Python库，提供了一套非常简洁直观的语法，非常接近统计学中描述概率模型的语法，可读性很高。其核心计算部分基于NumPy和Theano。Theano是用于深度学习的Python库，可以高效地定义、优化和求解多维数组的数学表达式。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[0 1 0 0 0 0 0 0 0 0 0 1 0 1 0 1 0 0 0 0 1 1 0 1 1 1 0 0 0 1 0 0 1 0 1 0 1\n",
      " 1 0 1 1 1 0 1 0 0 1 0 0 0 0 1 0 0 0 0 0 0 0 1 0 0 1 0 0 0 1 0 1 0 1 0 0 1\n",
      " 0 0 1 0 1 1 1 0 1 0 0 1 0 1 1 0 0 1 0 0 0 0 1 0 0 0]\n"
     ]
    }
   ],
   "source": [
    "# 定义抛硬币问题，假设知道真实的参数θ，用theta_real来表示\n",
    "np.random.seed(1)\n",
    "n_experiments = 100\n",
    "theta_real = 0.35\n",
    "data = stats.bernoulli.rvs(p=theta_real, size=n_experiments)\n",
    "print(data)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "现在有了数据，需要再指定模型。前面我们通过似然和先验的概率分布完成。对于似然可以用二项分布来描述，对于先验可以用参数为α=β=1的beta分布描述。这个beta分布再[0,1]区间内均匀分布是一样的。可以用数学表达式描述如下：\n",
    "<img src=\"assets/20201128213453.png\" width=\"30%\">"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "\n",
       "    <div>\n",
       "        <style>\n",
       "            /* Turns off some styling */\n",
       "            progress {\n",
       "                /* gets rid of default border in Firefox and Opera. */\n",
       "                border: none;\n",
       "                /* Needs to be in here for Safari polyfill so background images work as expected. */\n",
       "                background-size: auto;\n",
       "            }\n",
       "            .progress-bar-interrupted, .progress-bar-interrupted::-webkit-progress-bar {\n",
       "                background: #F44336;\n",
       "            }\n",
       "        </style>\n",
       "      <progress value='6' class='' max='6' style='width:300px; height:20px; vertical-align: middle;'></progress>\n",
       "      100.00% [6/6 00:00<00:00 logp = -69.315, ||grad|| = 14]\n",
       "    </div>\n",
       "    "
      ],
      "text/plain": [
       "<IPython.core.display.HTML object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Multiprocess sampling (2 chains in 2 jobs)\n",
      "Metropolis: [theta]\n"
     ]
    },
    {
     "data": {
      "text/html": [
       "\n",
       "    <div>\n",
       "        <style>\n",
       "            /* Turns off some styling */\n",
       "            progress {\n",
       "                /* gets rid of default border in Firefox and Opera. */\n",
       "                border: none;\n",
       "                /* Needs to be in here for Safari polyfill so background images work as expected. */\n",
       "                background-size: auto;\n",
       "            }\n",
       "            .progress-bar-interrupted, .progress-bar-interrupted::-webkit-progress-bar {\n",
       "                background: #F44336;\n",
       "            }\n",
       "        </style>\n",
       "      <progress value='4000' class='' max='4000' style='width:300px; height:20px; vertical-align: middle;'></progress>\n",
       "      100.00% [4000/4000 00:04<00:00 Sampling 2 chains, 0 divergences]\n",
       "    </div>\n",
       "    "
      ],
      "text/plain": [
       "<IPython.core.display.HTML object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Sampling 2 chains for 1_000 tune and 1_000 draw iterations (2_000 + 2_000 draws total) took 12 seconds.\n",
      "The number of effective samples is smaller than 25% for some parameters.\n"
     ]
    }
   ],
   "source": [
    "with pm.Model() as our_first_model:  # 构造模型\n",
    "    theta = pm.Beta('theta', alpha=1, beta=1)  # 指定先验\n",
    "    y = pm.Bernoulli('y', p=theta, observed=data)  # 用和先验相同的语法描述似然，唯一不同的是用observed变量传递观测到的数据\n",
    "\n",
    "    start = pm.find_MAP()  # 返回最大后验，为采样方法提供一个初始点\n",
    "    step = pm.Metropolis()  # 定义采样方法，用Metropolis-Hastings算法，PyMC3也会根据不同参数的特征自动赋予一个采样器\n",
    "    trace = pm.sample(1000, step=step, start=start)  # 执行推断，其中第一个参数是采样次数，2、3分别是采样方法和初始点"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**诊断采样过程**\n",
    "\n",
    "现在我们根据有限数量的样本对后验做出近似，接下来就是坚持我们的近似是否合理。我们可以做一些测试，可视化、定量等。这些测试会尝试从样本中发现问题，但并不能证明我们得到的分布是正确的，我们只能提供证据证明样本看起来是合理的。如果我们通过样本发现问题，解决办法有如下几种。\n",
    "<ul>\n",
    "    <li>增加样本次数。\n",
    "    <li>从样本链的前面部分去掉一定数量的样本，称为老化（Burn-in）\n",
    "    <li>重新参数化模型，也就是换一种不同但却等价的方式描述模型。\n",
    "</ul>\n",
    "\n",
    "**收敛性**\n",
    "\n",
    "通常，我们要做的第一件事就是查看结果长什么样，利用traceplot函数"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "D:\\Anaconda3\\lib\\site-packages\\arviz\\data\\io_pymc3.py:91: FutureWarning: Using `from_pymc3` without the model will be deprecated in a future release. Not using the model will return less accurate and less useful results. Make sure you use the model argument or call from_pymc3 within a model context.\n",
      "  FutureWarning,\n",
      "D:\\Anaconda3\\lib\\site-packages\\arviz\\plots\\backends\\matplotlib\\traceplot.py:214: UserWarning: A valid var_name should be provided, found {'t'} expected from {'theta'}\n",
      "  invalid_var_names, all_var_names\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "array([[<matplotlib.axes._subplots.AxesSubplot object at 0x000002ED583FFB70>,\n",
       "        <matplotlib.axes._subplots.AxesSubplot object at 0x000002ED58783668>]],\n",
       "      dtype=object)"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
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\n",
      "text/plain": [
       "<Figure size 864x144 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "burnin = 100  # 指定老化，前100个\n",
    "chain = trace[burnin:]\n",
    "pm.traceplot(chain, lines={'theta':theta_real})"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "对于未观測到的变量，我们得到了两幅图。左图是一个核密度估计( Kernel Density Estimation,KDE)图。右图描绘的是每一步采样过程中得到的采样值。注意图中红色的线表示变量 theta real的值。\n",
    "\n",
    "在得到这些图之后，我们需要观察什么呢? 首先，KDE图看起来应该是光滑的曲线。通常，随着数据的增加，根据中心极限定理，参数的分布会趋近于高斯分布。右侧的图看起来应该像白噪声，也就是说有很好的混合度( mixing)，我们看不到任何可以识别的模式，也看不到向上或者向下的曲线，相反，我们希望看到曲线在某个值附近震荡。对于多峰分布或者离散分布，我们希望曲线不要在某个值或区域停留过多时间，我们希望看到采样值在多个区间自由移动。此外，我们希望迹表现出稳定的相似性，也就是说，前10%看起来跟后50%或者10%差不多。再次强调，我们不希望看到规律的模式,相反我们期望看到的是噪声。下图展示了一些迹呈现较好混合度(右侧)与较差混合度(左侧)的对比。\n",
    "\n",
    "<img src=\"assets/20201128215037.png\" width=\"50%\">\n",
    "\n",
    "如果迹的前面部分跟其他部分看起来不太一样，那就意味着需要进行老化处理，如果其他部分没有呈现稳定的相似性或者可以看到某种模式，那这意味着需要更多的采样，或者需要更换采样方法或者参数化方法。对于一些复杂的模型,我们可能需要结合使用前面所有的策略。"
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    "### 模型决策\n",
    "\n",
    "一种定量地检测收敛性的方法是 Gelman- Rubin检验。该检验的思想是比较不同迹之间的差异和迹内部的差异，因此，需要多组迹来进行该检验。理想状态下，我们希望得到R=1，根据经验，如果得到的值低于1.1，那么可以认为是收敛的了，更高的值则意味着没有收敛。\n",
    "\n",
    "pycm3模块中gelman_rubin 因为Gelman＆Rubin（1992）论文是BDA3方程，与gelman_rubin的BDA2不同，所以改名了，且换了模块，绘图和诊断都迁移到arviz了"
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  {
   "cell_type": "code",
   "execution_count": 20,
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       "    theta    float64 1.011</pre><div class='xr-wrap' hidden><div class='xr-header'><div class='xr-obj-type'>xarray.Dataset</div></div><ul class='xr-sections'><li class='xr-section-item'><input id='section-15845eb7-09ca-4831-8b26-9fa7bd7c1ad1' class='xr-section-summary-in' type='checkbox' disabled ><label for='section-15845eb7-09ca-4831-8b26-9fa7bd7c1ad1' class='xr-section-summary'  title='Expand/collapse section'>Dimensions:</label><div class='xr-section-inline-details'></div><div class='xr-section-details'></div></li><li class='xr-section-item'><input id='section-b872a9a6-a44f-46fa-81af-1ee352d98e75' class='xr-section-summary-in' type='checkbox' disabled ><label for='section-b872a9a6-a44f-46fa-81af-1ee352d98e75' class='xr-section-summary'  title='Expand/collapse section'>Coordinates: <span>(0)</span></label><div class='xr-section-inline-details'></div><div class='xr-section-details'><ul class='xr-var-list'></ul></div></li><li class='xr-section-item'><input id='section-9cff1f91-78c6-4722-8984-b1188f4195c0' class='xr-section-summary-in' type='checkbox'  checked><label for='section-9cff1f91-78c6-4722-8984-b1188f4195c0' class='xr-section-summary' >Data variables: <span>(1)</span></label><div class='xr-section-inline-details'></div><div class='xr-section-details'><ul class='xr-var-list'><li class='xr-var-item'><div class='xr-var-name'><span>theta</span></div><div class='xr-var-dims'>()</div><div class='xr-var-dtype'>float64</div><div class='xr-var-preview xr-preview'>1.011</div><input id='attrs-1d8e0dfd-59e3-439b-b8b9-5c4994e50c95' class='xr-var-attrs-in' type='checkbox' disabled><label for='attrs-1d8e0dfd-59e3-439b-b8b9-5c4994e50c95' title='Show/Hide attributes'><svg class='icon xr-icon-file-text2'><use xlink:href='#icon-file-text2'></use></svg></label><input id='data-7220298d-73fa-42c8-b9c1-a3ec45869c94' class='xr-var-data-in' type='checkbox'><label for='data-7220298d-73fa-42c8-b9c1-a3ec45869c94' title='Show/Hide data repr'><svg class='icon xr-icon-database'><use xlink:href='#icon-database'></use></svg></label><div class='xr-var-attrs'><dl class='xr-attrs'></dl></div><div class='xr-var-data'><pre>array(1.0110859)</pre></div></li></ul></div></li><li class='xr-section-item'><input id='section-73e4597d-9d73-46a4-a9ab-8e593cb19c97' class='xr-section-summary-in' type='checkbox' disabled ><label for='section-73e4597d-9d73-46a4-a9ab-8e593cb19c97' class='xr-section-summary'  title='Expand/collapse section'>Attributes: <span>(0)</span></label><div class='xr-section-inline-details'></div><div class='xr-section-details'><dl class='xr-attrs'></dl></div></li></ul></div></div>"
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      ]
     },
     "execution_count": 20,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "import arviz\n",
    "arviz.rhat(chain)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "函数 summary提供了对后验的文字描述，它可以提供后验的均值、标准差和HPD区间(最大后验密度可信区间)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
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   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "D:\\Anaconda3\\lib\\site-packages\\arviz\\data\\io_pymc3.py:91: FutureWarning: Using `from_pymc3` without the model will be deprecated in a future release. Not using the model will return less accurate and less useful results. Make sure you use the model argument or call from_pymc3 within a model context.\n",
      "  FutureWarning,\n"
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       "      <td>0.36</td>\n",
       "      <td>0.05</td>\n",
       "      <td>0.269</td>\n",
       "      <td>0.447</td>\n",
       "      <td>0.003</td>\n",
       "      <td>0.002</td>\n",
       "      <td>309.0</td>\n",
       "      <td>299.0</td>\n",
       "      <td>318.0</td>\n",
       "      <td>267.0</td>\n",
       "      <td>1.01</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "       mean    sd  hdi_3%  hdi_97%  mcse_mean  mcse_sd  ess_mean  ess_sd  \\\n",
       "theta  0.36  0.05   0.269    0.447      0.003    0.002     309.0   299.0   \n",
       "\n",
       "       ess_bulk  ess_tail  r_hat  \n",
       "theta     318.0     267.0   1.01  "
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "pm.summary(chain)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "其中,返回值之一是 mc_error，这是对采样引入误差的估计值，该值考虑的是所有的采样值并非真的彼此独立。 mc error是迹中不同块的均值的标准差，每一块是迹中的一部分。"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**自相关**\n",
    "\n",
    "最理想的采样应该不会是自相关的，也就是说，某一点的值应该与其他点的值是相互独立的。由于参数之间的相互依赖关系，可能模型会导致更多的自相关采样。PyMC3有一个很方便的函数用来描述自相关。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 48,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "D:\\Anaconda3\\lib\\site-packages\\arviz\\data\\io_pymc3.py:91: FutureWarning: Using `from_pymc3` without the model will be deprecated in a future release. Not using the model will return less accurate and less useful results. Make sure you use the model argument or call from_pymc3 within a model context.\n",
      "  FutureWarning,\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "array([<matplotlib.axes._subplots.AxesSubplot object at 0x000002444A3F0518>,\n",
       "       <matplotlib.axes._subplots.AxesSubplot object at 0x000002444A403240>],\n",
       "      dtype=object)"
      ]
     },
     "execution_count": 48,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 993.6x331.2 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "pm.autocorrplot(chain)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "该图显示了采样值与相邻连续点(最多100个)之间的平均相关性。理想状态下，我们不会看到自相关性，实际中我们希望看到自相关性降低到较低水平。参数越自相关，要达到指定精度的采样次数就需要越多，也就是说，自相关性不利于降低采样次数。"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**有效采样大小**\n",
    "\n",
    "一个有自相关性的采样要比没有自相关性的采样所包含的信息量更少，因此，给定采样大小和采样的自相关性之后，我们可以尝试估计出该采样的大小为多少时，该采样没有自相关性而且包含的信息量不变，该值称为有效采样大小。理想情况下，两个值是一模一样的；二者越接近，我们的采样效率越高。有效采样大小可以作为我们的一个参考，如果我们想要估计出一个分布的均值，我们需要的最小采样数至少为100；如果想要估计出依赖于尾部分布的量，比如可信区间的边界，那么我们可能需要1000到10000次采样。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [
    {
     "ename": "AttributeError",
     "evalue": "module 'pymc3' has no attribute 'effective_n'",
     "output_type": "error",
     "traceback": [
      "\u001b[1;31m---------------------------------------------------------------------------\u001b[0m",
      "\u001b[1;31mAttributeError\u001b[0m                            Traceback (most recent call last)",
      "\u001b[1;32m<ipython-input-26-46d9a79a77f4>\u001b[0m in \u001b[0;36m<module>\u001b[1;34m\u001b[0m\n\u001b[1;32m----> 1\u001b[1;33m \u001b[0mpm\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0meffective_n\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mchain\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m[\u001b[0m\u001b[1;34m'theta'\u001b[0m\u001b[1;33m]\u001b[0m  \u001b[1;31m# 可以查看有效采样数644.0，这个api已经迁移，至今我都没找到替代的\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m",
      "\u001b[1;31mAttributeError\u001b[0m: module 'pymc3' has no attribute 'effective_n'"
     ]
    }
   ],
   "source": [
    "pm.effective_n(chain)['theta']  # 可以查看有效采样数644.0，这个api已经迁移，至今我都没找到替代的"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "显然，提高采样效率的一个方法是换一个更好的采样方法；另一个办法是转换数据或者对模型重新设计参数。\n",
    "\n",
    "目前为止，所有的诊断测试都是经验性而非绝对的。实际使用中，我们会先运行一些测试，如果看起来没什么问题，我们就继续往下分析。如果发现了一些问题，就需要回过头解决它们，这也是建模过程的一部分。要知道，进行收敛性检查并非贝叶斯理论的一部分，由于我们是用数值的方式在计算后验，因而这只是贝叶斯实践过程中的一部分."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**总结后验**\n",
    "\n",
    "我们已经知道，贝叶斯分析的结果是后验分布，其包含了在已有数据和模型下，参数的所有信息。我们可以使用PyMc3中的 plot_posterior函数对后验分布进行可视化总结，这个函数的核心参数是一个PyMc3的迹和或者一个 Numpy的数组，默认情况下，该函数会画出参数的直方图以及分布的均值,此外图像的底端还有个黑色的粗线用来表示95% HPD区间。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.axes._subplots.AxesSubplot at 0x2ed59fc6d30>"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "pm.plot_posterior(chain)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**基于后验的决策**\n",
    "\n",
    "有时候，仅仅描述后验还不够，我们还需要根据推断结果做决策，即将连续的估计值收敛到一个二值化结果上: 是或不是、受污染了还是安全的等等。回到拋硬币问题上，我们需要回答硬币是不是公平的。一枚公平的硬币是指θ的值为0.5，严格来说，出现这种情况的概率是0，因而，实际中我们会对定义稍稍放松，假如枚硬币的θ值在0.5左右，我们就认为这枚硬币是公平的。这里左右\"的具体含义依赖于具体的问题，并没有一个满足所有问题的普适准则。因此决策也是偏主观的，我们的任务就是根据我们的目标做出最可能的决策。\n",
    "\n",
    "直观上，一个明智的做法是将HPD区间与我们感兴趣的值进行比较，在我们的例子中，该值是0.5。前面的图中可以看出HPD的范围是006~0.71，包含05这个值，不过根据后验分布来看，硬币似乎倾向于反面朝上，我们无法就此裁定一个硬币是公平的。或许,我们需要收集更多的数据来降低数据的分散程度，从而得到一个更确定的决策；又或者是因为我们漏掉了某些关键信息,以至我们没能找到更完备的先验。"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**实用等价区间**\n",
    "基于后验做决策的一种方案是实用等价区间( Region Of Practical Equivalence,ROPE)，其实就是在感兴趣值附近的一个区间，例如我们可以说[045,0.55]是0.5的一个实用性等价区间。同样，R◎PE是根据实际情况决定的。接下来我们可以将ROPE与HPD对比，结果至少有以下3种情况：\n",
    "<ul>\n",
    "    <li>RPE与HPD区间没有重叠,因此我们可以说硬币是不公平的。\n",
    "    <li>ROPE包含整个HPD区间,我们可以认为硬币是公平的。\n",
    "    <li>ROPE与HPD区间部分重叠,此时我们不能判断硬币是否公平\n",
    "</ul>\n",
    "\n",
    "当然，如果选择区间[0,1]作为ROPE，那么不管结果怎样我们都会说这枚硬币是公平的，不过恐怕没人会同意我们对ROPE的定义。 plot_posterio函数可以用来画ROPE。从图中可以看到,ROPE是一段较宽的半透明的红色线段，同时上面有两个数值表示ROPE的两个端点。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.axes._subplots.AxesSubplot at 0x2ed56790240>"
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "pm.plot_posterior(chain, rope=[0.45,0.55])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.7.3"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}