From 1903ee13d3d4f809cad3e1eb15320e0b0f84a368 Mon Sep 17 00:00:00 2001 From: benjas <909336740@qq.com> Date: Sat, 28 Nov 2020 19:05:41 +0800 Subject: [PATCH] =?UTF-8?q?Add=20=E8=B4=9D=E5=8F=B6=E6=96=AF=E5=BB=BA?= =?UTF-8?q?=E6=A8=A1=E6=B1=82=E8=A7=A3?= MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8 Content-Transfer-Encoding: 8bit --- .../贝叶斯建模-checkpoint.ipynb | 282 +++++++++++++++ .../贝叶斯分析/assets/20201128183746.png | Bin 0 -> 9247 bytes .../贝叶斯分析/hangout_chat_data.csv | 339 ++++++++++++++++++ .../贝叶斯分析/贝叶斯建模.ipynb | 282 +++++++++++++++ 4 files changed, 903 insertions(+) create mode 100644 notebook_必备数学基础/贝叶斯分析/.ipynb_checkpoints/贝叶斯建模-checkpoint.ipynb create mode 100644 notebook_必备数学基础/贝叶斯分析/assets/20201128183746.png create mode 100644 notebook_必备数学基础/贝叶斯分析/hangout_chat_data.csv create mode 100644 notebook_必备数学基础/贝叶斯分析/贝叶斯建模.ipynb diff --git a/notebook_必备数学基础/贝叶斯分析/.ipynb_checkpoints/贝叶斯建模-checkpoint.ipynb b/notebook_必备数学基础/贝叶斯分析/.ipynb_checkpoints/贝叶斯建模-checkpoint.ipynb new file mode 100644 index 0000000..eb153e1 --- /dev/null +++ b/notebook_必备数学基础/贝叶斯分析/.ipynb_checkpoints/贝叶斯建模-checkpoint.ipynb @@ -0,0 +1,282 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## 估计模型参数" + ] + }, + { + "cell_type": "code", + "execution_count": 10, + "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", + "" + ] + }, + { + "cell_type": "code", + "execution_count": 14, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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\n", + "text/plain": [ + "
" + ] + }, + "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": 15, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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P38H2Q7P/9XnV8x6yANXYER4repyJJueix5loUszFW5qb2LVrV90lWMVZ3dN1l2Az8FjR40w0ORc9zkSTYi5umptYs2ZN3SVYxa1jbXWXYDPwWNHjTDQ5Fz3ORJNiLm6am1Cc7mSpW9d5uO4SbAYeK3qciSbnoseZaFLMxU1zEwcPHqy7BKtY3ZF1l2Az8FjR40w0ORc9zkSTYi5umptQnCNwqduy18euKvJY0eNMNDkXPc5Ek2IubpqbUJwjcKk7f/VU3SXYDDxW9DgTTc5FjzPRpJiLm+Ymli9fXncJVrF3MuouwWbgsaLHmWhyLnqciSbFXNw0N9HV1VV3CVaxa8IfWUUeK3qciSbnoseZaFLMxR1IE3v27Km7BKs4Y6XnaVbksaLHmWhyLnqciSbFXNw0N7Fu3bq6S7CKm0c9T7MijxU9zkSTc9HjTDQp5uKmuYnR0dG6S7CKjV2ep1mRx4oeZ6LJuehxJpoUc3HT3MTExETdJVhFd7vnaVbksaLHmWhyLnqciSbFXNw0N6E4R+BS53maNXms6HEmmpyLHmeiSTEXN81NKM4RuNR5nmZNHit6nIkm56LHmWhSzMVNcxOK050sdZ5yTpPHih5nosm56HEmmhRzcQfSRGdnZ90lWMXolE9uoshjRY8z0eRc9DgTTYq5uGluYmRkpO4SrOL0FZ6nWZHHih5nosm56HEmmhRzcdPcRF9fX90lWMWNoz4QUJHHih5nosm56HEmmhRzcdPchOJfOUvdad7SLMljRY8z0eRc9DgTTYq5uGluYnJysu4SrGJFm+dpVuSxoseZaHIuepyJJsVc3DQ3oThH4FLneZo1eazocSaanIseZ6JJMRc3zU0ozhG41HmeZk0eK3qciSbnoseZaFLMxU1zEytXrqy7BKsYOuSPrCKPFT3ORJNz0eNMNCnm4g6kiba2trpLsIrJw3VXYDPxWNHjTDQ5Fz3ORJNiLgvSNEfEqRHxpYi4MSJ+EBEvKm9/VUTcERHXlZcnL0Q9rdq3b1/dJVjFKV3umhV5rOhxJpqcix5nokkxl4U6qmoKeHFmbo2IbmBLRFxdLntjZr5+geo4Lv39/XWXYBU37POBgIo8VvQ4E03ORY8z0aSYy4Jsac7M7Zm5tfx5FLgROHkhXvue2L17d90lWMWZqzxPsyKPFT3ORJNz0eNMNCnmsuCb7SLidOAhwDeBRwOXRsSzgO9QbI3e03j/HTt2cPHFF9Pe3s709DQXXXQRl1xyCYODg6xcuZK2tjb27dtHf38/u3fvJjPp7+9naGiIVatWAbB//37Wr1/Pzp07iQjWrl3Lzp076enpYXp6mrGxMTZs2MDg4CAdHR309vYyPDzMxMQEO3bsYHx8/Ojyzs5Ouru72bVrF2vWrGF8fJyDBw8eXb58+XK6urrYs2cP69atY3R0lImJiaPLu7q66OzsZGRkhL6+PkZGRpicnDy6fL7Xqbe3l4mJiRN2nVa0HeaCvgkOTAcDB9o4u3uK2w600d2erOs8zJa97Zy/eort27efMOu0GHLas2cPK1euXFTrdKLntGfPHvr6+hbVOi2GnKamphgYGFhU63Si53TgwAEGBgYW1Tothpz27NlDf3//gq9T0x42c+FOFhERq4CvAK/JzCsiYj0wDCTwN8DGzHxu42Ouvfba3LRp04LV2OjgwYMsX768lte2mf3W5VsYmZz9C5KrnveQBajGjvBY0eNMNDkXPc5EU125bN26dcvmzZsfNtOyBZs9IyI6gI8B/5qZVwBk5lBmTmfmYeCdwMMXqp5WDA0N1V2CVZzX63maFXms6HEmmpyLHmeiSTGXhZo9I4B3Azdm5hsabt/YcLenATcsRD2tOrK533RsP+hZEhV5rOhxJpqcix5nokkxl4Xap/nRwDOB6yPiuvK2VwBPj4jzKHbPuA34gwWqx8zMzMysZQvSNGfm14CYYdGVC/H6P6/9+/ezbt26usuwBhuXH+bm/XVXYVUeK3qciSbnoseZaFLMxd91N7F+/fq6S7CK60Y8T7MijxU9zkSTc9HjTDQp5uKmuYmdO3fWXYJVnNvjAwEVeazocSaanIseZ6JJMRc3zU0Uxy+akql0Joo8VvQ4E03ORY8z0aSYi5vmJtauXVt3CVZxy/62ukuwGXis6HEmmpyLHmeiSTEXN81NKH41sNSd490zJHms6HEmmpyLHmeiSTEXN81N9PT01F2CVWwb90dWkceKHmeiybnocSaaFHNxB9LE9PR03SVYRYc/sZI8VvQ4E03ORY8z0aSYi1uQJsbGxuouwSrWn3S47hJsBh4repyJJueix5loUszFTXMTGzZsqLsEq9iy1/M0K/JY0eNMNDkXPc5Ek2IubpqbGBwcrLsEqzh/tQ8EVOSxoseZaHIuepyJJsVc3DQ30dHRUXcJVnFgWm/eRvNYUeRMNDkXPc5Ek2Iubpqb6O3trbsEqxg44HmaFXms6HEmmpyLHmeiSTEXN81NDA8P112CVZzd7d0zFHms6HEmmpyLHmeiSTEXN81NKP6Vs9Td5i3NkjxW9DgTTc5FjzPRpJiLm+YmJiYm6i7BKrrbs+4SbAYeK3qciSbnoseZaFLMxU1zE+Pj43WXYBXrOj1PsyKPFT3ORJNz0eNMNCnm4qa5CcU5Apc6z9OsyWNFjzPR5Fz0OBNNirm4aW5CcY7Apc7zNGvyWNHjTDQ5Fz3ORJNiLm6am+js7Ky7BKsYnfI8zYo8VvQ4E03ORY8z0aSYi5vmJrq7u+suwSq2j/sjq8hjRY8z0eRc9DgTTYq5uANpYteuXXWXYBVndU/XXYLNwGNFjzPR5Fz0OBNNirm4aW5izZo1dZdgFbeOeZ5mRR4repyJJueix5loUszFTXMTitOdLHWeck6Tx4oeZ6LJuehxJpoUc3HT3MTBgwfrLsEqVnf45CaKPFb0OBNNzkWPM9GkmIub5iYU5whc6jxPsyaPFT3ORJNz0eNMNCnm4qa5CcU5Apc6z9OsyWNFjzPR5Fz0OBNNirm4aW5i+fLldZdgFXsnPU+zIo8VPc5Ek3PR40w0KebS0nfdEfFAYFdmDkXEKuAlwDTw+sw8MJ8F1qmrq6vuEqxi14T/zlPksaLHmWhyLnqciSbFXFrtQD4IrC5/fj3wWOBRwDvmoygVe/bsqbsEqzhjpedpVuSxoseZaHIuepyJJsVcWj2q6vTM/GFEBPA04EHAOPCTeatMwLp16+ouwSpuHvU8zYo8VvQ4E03ORY8z0aSYS6tbmg9FRDfwcOD2zBwGDgF6O5zModHR0bpLsIqNXZ6nWZHHih5nosm56HEmmhRzaXVL8weBLwLdwFvK2x7KIt/SPDExUXcJVtHd7nmaFXms6HEmmpyLHmeiSTGXlprmzPyTiLgQmMzML5U3Hwb+ZN4qE6A4R+BS53maNXms6HEmmpyLHmeiSTGXlqciyMyrgB9FxCPL69/JzC/OW2UCFOcIXOo8T7MmjxU9zkSTc9HjTDQp5tJS0xwR94mIrwM3AZ8vb/vNiHjXfBZXN8XpTpY6TzmnyWNFjzPR5Fz0OBNNirm02oG8A/gMxT7Nk+VtVwO/NB9Fqejs7Ky7BKsYnfLJTRR5rOhxJpqcix5nokkxl1ab5ocDr83Mw0ACZOYI0DtfhSkYGRmpuwSrOH2F52lW5LGix5loci56nIkmxVxabZqHgPs33lCeJfCnrTw4Ik6NiC9FxI0R8YOIeFF5+9qIuDoibin/XXNc1c+zvr6+ukuwihtHfSCgIo8VPc5Ek3PR40w0KebSatP8euDTEfEcoD0ing58BHhdi4+fAl6cmWcDjwQuKZvulwFfyMwzgS+U12Uo/pWz1J3mLc2SPFb0OBNNzkWPM9GkmEurU869JyJ2Ay8AbgeeDfxlZn6ixcdvB7aXP49GxI3AycBTgceVd7sc+DLw0uOof15NTk7OfidbUCvaPE+zIo8VPc5Ek3PR40w0KebS8nfdZYPcUpPcTEScDjwE+CawvmyoycztEXGv6v137NjBxRdfTHt7O9PT01x00UVccsklDA4OsnLlStra2ti3bx/9/f3s3r2bzKS/v5+hoSFWrVoFwP79+1m/fj07d+4kIli7di07d+6kp6eH6elpxsbG2LBhA4ODg3R0dNDb28vw8DArVqxgx44djI+PH13e2dlJd3c3u3btYs2aNYyPj3Pw4MGjy5cvX05XVxd79uxh3bp1jI6OMjExcXR5V1cXnZ2djIyM0NfXx8jICJOTk0eXz/c69fb2MjExccKu002jbVzQN8GB6WDgQBtnd09x24E2utuTdZ2H2bK3nfNXT7F9+/YTZp0WQ07T09Ps2bNnUa3TiZ7T9PQ0Bw8eXFTrtBhyWrNmDQMDA4tqnU70nLq6uhgYGFhU67QYcpqenubQoUMLvk5Ne9jM2bfcRcRzj7HoELAN+EZmHmrheVYBXwFek5lXRMTezFzdsHxPZv7Mfs3XXnttbtq0adYa58PAwACnnXZaLa9tM3vNJ77JV4ZnP6L2quc9ZAGqsSM8VvQ4E03ORY8z0VRXLlu3bt2yefPmh820rNUtzc8CHkVxQOA24BRgPfAd4HSAiHhqZn7nWE8QER3Ax4B/zcwrypuHImJjuZV5I7CjxXoWxMqVK+suwSqGDnmeZkUeK3qciSbnoseZaFLMpdUO5AfASzLzPpn5/2XmfYAXA9+laKD/GXjzsR4cEQG8G7gxM9/QsOhTFPtHU/77yeOsf161tbXVXYJVTB6uuwKbiceKHmeiybnocSaaFHNptWn+XeAtldv+GXhGFvt3/CPwwCaPfzTwTOAJEXFdeXky8FrglyLiFooTpbz2uKqfZ/v27au7BKs4pctdsyKPFT3ORJNz0eNMNCnm0uruGUPAr/OzW4J/lbt2p1jOXWcKvJvM/BpwrFO5bW6xhgXX399fdwlWccM+z9OsyGNFjzPR5Fz0OBNNirm0uqX5j4D3RcTXI+LDEfF14P3A/yqXP4Imu2ecqHbv3l13CVZx5irP06zIY0WPM9HkXPQ4E02KubQ6T/NVEXE/4MnAvYErgc9k5q4jy4Gr5q3KmrQys4gtrPZwJoo8VvQ4E03ORY8z0aSYy/HM07yLYuvykqH41cBSd713z5DksaLHmWhyLnqciSbFXFraPSMi2iPijyLiYxHxlYi45shlvgus09DQUN0lWMV5vVN1l2Az8FjR40w0ORc9zkSTYi6t7tP8RuAPgGuA8ynmW74X8MV5qkvCkTPMmI7tBz1PsyKPFT3ORJNz0eNMNCnm0moHchHwK5n5T8BU+e9vAI+ft8rMzMzMzES02jSvAG4vfx6PiBWZeROwqM9VvH///rpLsIqNyz1PsyKPFT3ORJNz0eNMNCnm0upRVTcCvwh8i+LU2a+KiH3AHfNVmIL169fXXYJVXDfiAwEVeazocSaanIseZ6JJMZdWtzS/CDhyBNafAg+lONnJC+ajKBU7d+6suwSrOLfHBwIq8ljR40w0ORc9zkSTYi6tztP87YafbwGeOG8VCYk41kkMrS5T6UwUeazocSaanIseZ6JJMZdWp5x7fETct/x5Y0RcHhHvjogN81tevdauXVt3CVZxy/62ukuwGXis6HEmmpyLHmeiSTGXVnfPeBtw5PzF/wfoKH/+lzmvSIjiVwNL3TnePUOSx4oeZ6LJuehxJpoUc2n1qKqTM/OnEdEO/DJwGjAB3DlvlQno6empuwSr2DbueZoVeazocSaanIseZ6JJMZdWm+Z9EbEeOAf4r8zcHxGd3LXFeVGanp6e/U6LzIXv+m5L97vqefXMNtjhnlnSUhwr6pyJJueix5loUsyl1RbkzcC3gX8F3lre9mjgpvkoSsXY2FjdJVjF+pM8T7MijxU9zkSTc9HjTDQp5tLq7Bmvi4iPA9OZeWt58x3A8+atMgEbNizq4xxPSFv2ep5mRR4repyJJueix5loUsyl5S+7M/PmIw1zRDwe2JCZ189bZQIGBwfrLsEqzl/tAwEVeazocSaanIseZ6JJMZdWp5z7SkQ8uvz5pcCHgQ9FxCvms7i6dXQs6l22T0gHpvXmbTSPFUXORJNz0eNMNCnm0uqW5nOAb5Q/Px94HPBI4IXzUJOM3t7eukuwioEDntUE1sIAACAASURBVKdZkceKHmeiybnocSaaFHNptWleBmREnAFEZt6YmbcDa+avtPoNDw/XXYJVnN3t3TMUeazocSaanIseZ6JJMZdWj6r6GvAWYCPwcYCygdZbozmk+FfOUnebtzRL8ljR40w0ORc9zkSTYi6tbmn+fWAv8H3gVeVtm4B/mvuSdExMTNRdglV0t2fdJdgMPFb0OBNNzkWPM9GkmEurU87tAl5Rue0z81KRkPHx8bpLOOHN9clS1nV6nmZFHit6nIkm56LHmWhSzKXV2TNOiojXRMSPI2KkvO3CiLh0fsurl+IcgUud52nW5LGix5loci56nIkmxVxa3T3jjRQzaDwDOPL9+A+AP5yPolQozhG41HmeZk0eK3qciSbnoseZaFLMpdXNdk8D7p+ZYxFxGCAz74iIk+evtPp1dnbWXYJVjE55nmZFHit6nIkm56LHmWhSzKXVLc0TVBrsiOgHds15RUK6u7vrLsEqto+3fBJLW0AeK3qciSbnoseZaFLMpdUO5N+ByyPivgARsZFiCroPz1dhCnbtWtR/E5yQzuqerrsEm4HHih5nosm56HEmmhRzabVpfgVwG3A9sBq4BbgTePX8lKVhzZpFfe6WE9KtY56nWZHHih5nosm56HEmmhRzaalpzsyJzPzjzFwFrAe6M/NPMvPQ/JZXL8XpTpY6TzmnyWNFjzPR5Fz0OBNNirm0PH9XRKwA7g+sAs6MKA7Iysz/nJ/S6nfw4MG6S7CK1R0+uYkijxU9zkSTc9HjTDQp5tJS0xwRz6LYh3kCaGz9E7jPPNQlQXGOwKXO8zRr8ljR40w0ORc9zkSTYi6t7tP8D8B/z8y+zDy14bJoG2bQnCNwqfM8zZo8VvQ4E03ORY8z0aSYy/FMOffleaxD0vLly+suwSr2TnqeZkUeK3qciSbnoseZaFLMpdWm+S+BN0RE33wWo6arq6vuEqxi14TnaVbksaLHmWhyLnqciSbFXFrtQG4GngIMRcR0eTkcEYt60tw9e/bUXYJVnLFyUX/kTlgeK3qciSbnoseZaFLMpdWjqt4PvA/4CD97IOCitm7durpLsIqbRz1PsyKPFT3ORJNz0eNMNCnm0uqW5nXAX2XmDZl5a+OllQdHxHsiYkdE3NBw26si4o6IuK68PPnnWYH5NDo6WncJVrGxy/M0K/JY0eNMNDkXPc5Ek2IurTbN7wWeeQ9e5zLgSTPc/sbMPK+8XHkPnn9eTExM1F2CVXS3e55mRR4repyJJueix5loUsyl1d0zHg5cGhF/Dgw1LsjMx8724My8JiJOP+7qaqY4R+BS53maNXms6HEmmpyLHmeiSTGXVrc0vxN4PvB3wLsrl3vi0oj4frn7htxJxhXnCFzqPE+zJo8VPc5Ek3PR40w0KebS0ma7zLx8Hl77n4G/oTir4N8A/wd4bvVOO3bs4OKLL6a9vZ3p6WkuuugiLrnkEgYHB1m5ciVtbW3s27eP/v5+du/eTWbS39/P0NAQq1atAmD//v2sX7+enTt3EhGsXbuWnTt30tPTw/T0NGNjY2zYsIHBwUE6Ojro7e1leHiYzGTHjh2Mj48fXd7Z2Ul3dze7du1izZo1jI+Pc/DgwaPLly9fTldXF3v27GHdunWMjo4yMTFxdHlXVxednZ2MjIzQ19fHyMgIk5OTR5fP9zr19vYyMTFxzHU6pWuadZ2HWd2RbNnbzvmrp9g7GeyaWMYZK6e5ebSNjV2HGRgYaGmdLuibYOjQMiYPwyldh7lhXztnrpqmPZLr97VzXu8U2w8u49IPf5uNyw9z3Ug75/ZMMZXBLfvbOKdnim3jy+hYButPOszYVHBB3wQHpoOBA22c3T3FbQfa6G5P1nUePlrz9u3bF3VOaus0NjbGnj17FtU6neg5jY2NcfDgwUW1Toshp/b2dgYGBhbVOp3oOR0+XPyftpjWaTHkNDY2xqFDhxZ8nZqJzIXZR7TcPePTmXnO8Sy79tprc9OmTfNd3oz27t3L6tWra3ntulz4ru+2dL+rnveQOX2+Vp22YpqBA7PPoNFqfTY3luJYUedMNDkXPc5EU125bN26dcvmzZsfNtOy2s4UEREbG64+DbjhWPety8jISN0lWMXpKzxPsyKPFT3ORJNz0eNMNCnmsiBHVUXEh4DHAX0RsQ14JfC4iDiPYveM24A/WIhajkdf35I6AeIJ4cZRHwioyGNFjzPR5Fz0OBNNirkcc0tzRHyj4edX3pMXycynZ+bGzOzIzFMy892Z+czMPDczfyEzn5KZ2+/Ja8wHxb9ylrrTvKVZkseKHmeiybnocSaaFHNptnvGWRGxvPz5xQtRjJrJycm6S7CKFW2ep1mRx4oeZ6LJuehxJpoUc2n2XfcngZsj4jagKyKumelOrczTfKJSnCNwqfM8zZo8VvQ4E03ORY8z0aSYyzG3NGfmc4DfBf4FmOLu8zPPxTzN0hTnCFzqPE+zJo8VPc5Ek3PR40w0KebSdLNdZn4N+FpEdM7TXM3SVq5cWXcJVjF0qLYJX6wJjxU9zkSTc9HjTDQp5tLqyU3eExGPB54JnAzcAXwgM784n8XVra1t9vmAbWFNHq67ApuJx4oeZ6LJuehxJpoUc2lps11EPA/4CDAIXAFsBz4YEc+fx9pqt2/fvrpLsIpTutw1K/JY0eNMNDkXPc5Ek2IurR5V9WfAL2Xm947cEBEfAT4GvHM+ClPQ399fdwlWccM+HwioyGNFjzPR5Fz0OBNNirm0uoPoOuC/Krf9EFg7t+Vo2b17d90lWMWZqzxPsyKPFT3ORJNz0eNMNCnm0mrT/DXgDRGxAiAiVgL/CPznfBWmINNzAqtpD2eiyGNFjzPR5Fz0OBNNirm02jS/EPgFYCQihoC9wIMRPPX1XFL8amCpu967Z0jyWNHjTDQ5Fz3ORJNiLi01zZm5PTMvAO4L/Dpw38y8IDPvnNfqajY0NFR3CVZxXq/naVbksaLHmWhyLnqciSbFXI5rs11mbgO2zVMtclatWlV3CVax/aDnaVbksaLHmWhyLnqciSbFXNyBmJmZmZnNwk1zE/v376+7BKvYuNzzNCvyWNHjTDQ5Fz3ORJNiLrM2zRGxLCKeEBGdC1GQkvXr19ddglVcN+IDARV5rOhxJpqcix5nokkxl1mb5sw8DHwyMycWoB4pO3furLsEqzi3xwcCKvJY0eNMNDkXPc5Ek2Iure6ecU1EPHJeKxEUEXWXYBVT6UwUeazocSaanIseZ6JJMZdWv+seAD4bEZ8EbgeOzjidmX81H4UpWLt2UZ/w8IR0y/62ukuwGXis6HEmmpyLHmeiSTGXVrc0dwGfoGiWTwFObbgsWopfDSx153j3DEkeK3qciSbnoseZaFLMpaUtzZn5nPkuRFFPT0/dJVjFtnFP+KLIY0WPM9HkXPQ4E02KubQ8FUFEnA38JrA+My+NiAcAJ2Xm9+etuppNT0/XXYJVdLhnluSxoseZaHIuepyJJsVcWmpBIuK3gGuAk4FnlTd3A2+Yp7okjI2N1V2CVaw/yfM0K/JY0eNMNDkXPc5Ek2IurW5pfjXwS5l5XUT8j/K27wEPnp+yNGzYsKGW173wXd+d8+e86nkPmfPnrMOWvZ6nWVFdY8WOzZloci56nIkmxVxa/bL7XhRNMtw1c0Y2/LwoDQ4O1l2CVZy/2gcCKvJY0eNMNDkXPc5Ek2IurTbNW4BnVm77HeBbc1uOlo6OjrpLsIoD03rzNprHiiJnosm56HEmmhRzafW77j8CroqIi4GVEfE54CzgwnmrTEBvb2/dJVjFwAHP06zIY0WPM9HkXPQ4E02KubS0pTkzbwI2AW8F/gJ4L3BuZt4yj7XVbnh4uO4SrOLsbu+eochjRY8z0eRc9DgTTYq5tHxUVWYeiIivAz8B7szM/fNXlgbFv3KWutu8pVmSx4oeZ6LJuehxJpoUc2l1yrn7RMRXgduAzwC3RcTXIuK0+SyubhMTE3WXYBXd7Yv62NMTlseKHmeiybnocSaaFHNp9UDAyykOBlydmfcC1gDfLm9ftMbHx+suwSrWdXqeZkUeK3qciSbnoseZaFLMpdXdM84HLszMSYDM3B8RLwV2zVtlAhTnCFzqPE+zJo8VPc5Ek3PR40w0KebS6pbmbwAPr9z2MODauS1Hi+IcgUud52nW5LGix5loci56nIkmxVyOudkuIl7dcPVW4MqI+AxwO3Aq8GTgg/NbXr06OzvrLsEqRqfmfp7mVs/AuFjOqghzv851jZX5yG6xfB78+0uTc9HjTDQp5tLsu+5TK9evKP+9F3AI+DiwfD6KUtHd3V13CVaxfbzVL0dsIXms6HEmmpyLHmeiSTGXYzbNmfmchSxE0a5du1i1alXdZViDs7qn2X7I086p8VjR40w0ORc9zkSTYi4tH1UVESuA+wM/swaZ+Z9zXZSKNWvW1F2CVdw65oZZkceKHmeiybnocSaaFHNpdZ7mZwGDwBeBjzRcPjx/pdVPcbqTpc5TzmnyWNHjTDQ5Fz3ORJNiLq1uaf4H4L9n5tXzWYyagwcP1l2CVazu8MlNFHms6HEmmpyLHmeiSTGXVo+qmgC+/PO+SES8JyJ2RMQNDbetjYirI+KW8l+57fCKcwQudZ6nWZPHih5nosm56HEmmhRzabVp/kvgDRHR93O+zmXAkyq3vQz4QmaeCXyhvC5FcY7Apc7zNGvyWNHjTDQ5Fz3ORJNiLq02zTcDTwGGImK6vByOiOlWHpyZ1wC7Kzc/lbtOw3058Bst1rJgli9f1DPqnZD2Ts79PM12z3ms6HEmmpyLHmeiSTGXVr/rfj/wPoqD/+Zqz+z1mbkdIDO3R8S9ZrrTjh07uPjii2lvb2d6epqLLrqISy65hMHBQVauXElbWxv79u2jv7+f3bt3k5n09/czNDR0dKqS/fv3s379enbu3ElEsHbtWnbu3ElPTw/T09OMjY2xYcMGBgcH6ejooLe3l+HhYTo6OtixYwfj4+NHl3d2dtLd3c2uXbtYs2YN4+PjHDx48Ojy5cuX09XVxZ49e1i3bh2jo6NMTEywYcMGXv/Z69g1sYzRqeD0FdPcONrOaSumWdGWbNnbzvmrpxg6tIwzVsIpXYe5YV87Z66apj2S6/e1c17vFNsPFn/nbFx+mOtG2jm3Z4qpDG7Z38Y5PVNsG19GxzJYf9Lho895YDoYGxtjeHiY3t5eJiYmjrlOp3RNs67zMKs77qpp72Swa2IZZ6yc5ubRNjZ2HWZgYODo47u6uujs7GRkZIS+vj5GRkaYnJxkw4YNXNA3wdChZUwenpt1uvPgMi7om+DAdDBwoI2zu6e47UAb3e3Jus671vllH/0W28eXcVb3NLeOtTVdp40nFevU3X7X8plyalzn+f7szZbT8X72qjnd66TDM372qjndfvvtLa3TyMgInZ2dC75O5/RMzTqeJg/DwMBAyzk9cu3krONp4EAbAwMD855TdTwdz2dvZGSE3t5euc/ePVkn1fF0POvU1dXFwMDAolqnEz2nqamp4/odcSKs02LIaf/+/axevXrB16mZyJz9wKqI2AOszVbufOznOB34dGaeU17fm5mrG18jM++2X/O1116bmzZt+nlf9h4ZGBjgtNNOm7Pna/VMY/Oh1bOXzfXZ0OZ6nS/om+Arw/WcJUj9DHDHY65znuux0iqfEfDY6srEmnMuepyJprpy2bp165bNmzc/bKZlre6e8V7gmXNXElDs6rERoPx3xxw//z22bt26ukuwiptHPU+zIo8VPc5Ek3PR40w0KebSatP8cOBdEfHDiLim8XIPXvtTwLPLn58NfPIePNe8GB0drbsEq9jY5XmaFXms6HEmmpyLHmeiSTGXVvdpfmd5+blExIeAxwF9EbENeCXwWuDfIuJi4KfAb/28zz9fJiYm6i7BKrrbPU+zIo8VPc5Ek3PR40w0KebSUtOcmZfPfq+mj3/6MRZtvifPO98U5whc6jxPsyaPFT3ORJNz0eNMNCnm0upptJ97rMt8F1gnxTkClzrP06zJY0WPM9HkXPQ4E02KubS62a56EOAG4Azg68B75rQiIV1dXXWXYBW7JlrdDd8WkseKHmeiybnocSaaFHNpdfeMx1dvK7cynz3nFQnp7KxnajM7ttEpn9xEkceKHmeiybnocSaaFHO5JzuIXgYMAy+Zm1L0jIyMsHr16tnvaAvm9BXTDByoZ9q5xTJ/73zwWNHjTDQ5Fz3ORJNiLi01zRFR/U58BfB7wN45r0hIX19f3SVYxY2jPhBQkceKHmeiybnocSaaFHNpdQfRKWCy4TICvAL4w3mqS8LIyEjdJVjFaSum6y7BZuCxoseZaHIuepyJJsVcWt1sd9/K9bHMHJ7rYtRMTk7WXYJVrGjzPM2KPFb0OBNNzkWPM9GkmEurBwIOzHchihTnCFzqPE+zJo8VPc5Ek3PR40w0KebSdPeMiPhSRHyxyeULC1VoHRTnCFzqPE+zJo8VPc5Ek3PR40w0KeYy22a7Dxzj9pOBP6I4IHDRWrlyZd0lWMXQIc/TrMhjRY8z0eRc9DgTTYq5NG2aM/PdjdcjYh3wcuD5wEeAV89fafVra6tnajM7tsnDdVdgM/FY0eNMNDkXPc5Ek2IurZ5Guyci/gb4EbAeeGhmviAzt81rdTXbt29f3SVYxSld7poVeazocSaanIseZ6JJMZemW5ojogv4Y+DFwJeBx2TmDxagLgn9/f11l2AVN+zTPxBwrk+C0urz1cljRY8z0eRc9DgTTYq5zNaB/ARoA/4B+A6wPiLWN94hM784T7XVbvfu3axYsah32z7hnLlqml27vV+zGo8VPc5Ek3PR40w0KeYyW9N8EEiOfRKTBO43pxUJyfScwGraw5ko8ljR40w0ORc9zkSTYi6zHQh4+gLVIUnxq4Gl7voTYPeMpchjRY8z0eRc9DgTTYq5+HvuJoaGhuouwSrO6/U8zYo8VvQ4E03ORY8z0aSYi5vmJlatWlV3CVax/aA/soo8VvQ4E03ORY8z0aSYizsQMzMzM7NZuGluYv/+/XWXYBUbl3ueZkUeK3qciSbnoseZaFLMxU1zE+vXr5/9TragrhvxgYCKPFb0OBNNzkWPM9GkmIub5iZ27txZdwlWcW6PDwRU5LGix5loci56nIkmxVy82a6Jd357O9/43HDdZViDqYy6S5gzJ8KZ/lqt8T1P0psaaKmLaG2sHM/nsNWzWNqxtZqLLRxnokkxF29pbuKW/W11l2AVzkTT2rVr6y7BKpyJJueix5loUszFTXMT53hXADnORJPi12hLnTPR5Fz0OBNNirm4aW5i27jfHjXORFNPT0/dJViFM9HkXPQ4E02KubgDaaLD744cZ6Jpenq67hKswploci56nIkmxVzcgjSx/iTPCazGmWgaGxuruwSrcCaanIseZ6JJMRc3zU1s2evJRdQ4E00bNmyouwSrcCaanIseZ6JJMRc3zU2cv9oHnalxJpoGBwfrLsEqnIkm56LHmWhSzMVNcxMHpvXmCFzqnImmjo6OukuwCmeiybnocSaaFHPxd91NDBzwnMBqnImm3t7elu7X6ok05vokGnWeSGauX7vV96bVTOZDXTmfCOrMxWbmTDQp5uItzU2c3e1dAdQ4E03Dwz5zphpnosm56HEmmhRzcdPcxG3eqinHmWhS3CKw1DkTTc5FjzPRpJiLm+Ymutuz7hKswplompiYqLsEq3AmmpyLHmeiSTEXN81NrOv0nMBqnImm8fHxukuwCmeiybnocSaaFHNx09yE5wTW40w0Kc6nudQ5E03ORY8z0aSYS+1Nc0TcFhHXR8R1EfGduutp5DmB9TgTTYrzaS51zkSTc9HjTDQp5qKy2e7xmSl3mOTolOcEVuNMNHV2dtZdglU4E03ORY8z0aSYS+1bmpVtH/fbo8aZaOru7q67BKtwJpqcix5nokkxF4UtzQlcFREJvCMz/6Vx4Y4dO7j44otpb29nenqaiy66iEsuuYTBwUFWrlxJW1sb+/bto7+/n927d5OZ9Pf3MzQ0xKpVqwDYv38/69evZ+fOnUQEa9euZefOnfT09DA9Pc3Y2BgbNmxgcHCQjo4Oent7GR4e5hfXTvLjsWRd52G27G3n/NVTjE4F28eXcVb3NLeOtbGu8zCrO/Lo8r2Twa6JZZyxcpqbR9vY2HWY7va7lu+aWMboVHD6imluHG3ntBXTrGi7a/nQoWVMHoZTug5zw752zlw1TXsk1+9r57zeKbYfLJrGjcsPc91IO+f2TDGVwS372zinZ4pt48voWAbrT7qr5gPTwdjYGMPDw/T29jIxMcH4+PjRde7s7KS7u5tdu3ZxStd0S+s0MDBw9PFdXV10dnYyMjJCX18fIyMjTE5OsmHDBi7om5jTdepclpx1eJoD08HAgTbO7p7itgNtdLcvjpxO1HX68Y9/zKmnntp0PPX29nJOz1RL63To0CEGBwdZvnw5XV1d7Nmzh3Xr1jE6OsrExMTR5z+nZ6q2nAYGBmYdT2vWrOHBvZNzmtPw8HBLv/c+u+WHfHL7SbOu0wV9rX/2BgYGWLNmDePj4xw8ePDoOldzeujqyZbW6aLLtrSU0wv/2/3v0e/yVnKabZ2qn71mv/ea/f80MTHBrl277vH/T0rrNFf/59a1TsPDw3R1dS2qdVoMOQ0PD/OABzxgwdepmcisdwqviLh3Zt4ZEfcCrgb+V2Zec2T5tddem5s2baqltuf+63fYNr445gVu9cxbc30mr7k+G9opXdOLJpPF5KO/fQY9PT2z3k/983U86qqx1dedj99f6ut8Iti3b19LY8UWjjPRVFcuW7du3bJ58+aHzbSs9u+6M/PO8t8dwMeBh9db0V08vZkeZ6JJcWqgpc5jRZPHih5nokkxl1qb5ohYGRHdR34GLgRuqLOmRqs7fCINNc5E08GDB+suwSo8VjR5rOhxJpoUc6l7n+b1wMcj4kgtH8zM/6i3pLt4TmA9zkST4nyaS53HiiaPFT3ORJNiLrVuac7MH2fmg8vLgzLzNXXWU+U5gfU4E02K82kudR4rmjxW9DgTTYq51L5Ps7K9k54TWI0z0bR8+fK6S7AKjxVNHit6nIkmxVzcNDexa8Jvjxpnoqmrq6vuEqzCY0WTx4oeZ6JJMRf/Vm3ijJXTdZdgFc5E0549e+ouwSo8VjR5rOhxJpoUc/GRIk3cPLp45gOe63lT65ofdzFlspisW7duTp+vzvmXFwuPlWOb6/nCj8dcj5UTQZ3vdyuWYiYnAsVcvKW5iY1dnudUjTPRNDo6WncJVuGxosljRY8z0aSYi5vmJrrbPc+pGmeiaWJiou4SrMJjRZPHih5nokkxFzfNTXieUz3ORJPifJpLnceKJo8VPc5Ek2Iubpqb8DynepyJJsX5NJc6jxVNHit6nIkmxVzcNDfhKZv0OBNNilMDLXUeK5o8VvQ4E02Kufi3ahOjUz45gBpnoqmzs7PuEqzCY0WTx4oeZ6JJMRc3zU2cvsLznKpxJppGRkbqLsEqPFY0eazocSaaFHNx09zEjaM+kEaNM9HU19dXdwlW4bGiyWNFjzPRpJiLm+YmTvOWGjnORJPiFoGlzmNFk8eKHmeiSTEXb4poYkWb5zlV40w0TU5O1l3CglM/a+FiGivqZ5Q7HupjZTG9161Sz+R4LKb8FHPxluYmPM+pHmeiSXE+zaXOY0WTx4oeZ6JJMRc3zU14nlM9zkST4nyaS53HiiaPFT3ORJNiLm6amxg65LdHjTPRtHLlyrpLsAqPFU0eK3qciSbFXPxbtYnJw3VXYFXORFNbW1vdJViFx4omjxU9zkSTYi5umps4pcv/66hxJpr27dtXdwlW4bGiyWNFjzPRpJiLm+YmbtjnA2nUOBNN/f39dZdgFR4rmjxW9DgTTYq5uGlu4sxVnudUjTPRtHv37rpLsAqPFU0eK3qciSbFXNw0N9Eei2ee08XCmWjKdC5qPFY0eazocSaaFHPx93dNXO+vN+U4E01/+sUdjEwO113GktDqyQt6OzxWFNU1Vk6Ek1nM9Yk5Wh8rh1vKpM73UP1kSvNxUhXvnnGCOa/X85yqcSaanIseZ6LJuehxJpqGhobqLuFu3DQ3sf2g3x41zkSTc9HjTDQ5Fz3ORNOqVavqLuFu/EkxMzMzM5uFm+YmNi73PKdqnIkm56LHmWhyLnqciab9+/fXXcLduGlu4roRH0ijxploci56nIkm56LHmWhav3593SXcjZvmJs7t8cEBapyJJueix5loci56nImmnTt31l3C3bhpbmIqo+4SrMKZaHIuepyJJueix5loitDLxU1zE7fsb6u7BKtwJpqcix5nosm56HEmmtauXVt3CXcTimdcaXTttdfmpk2bannt13zim3xluLOW17aZXdA34UwEORc9zkSTc9HjTBbO8ZzcZGBggNNOO20eq5nZ1q1bt2zevPlhMy3zluYmto377VHjTDQ5Fz3ORJNz0eNMNPX09NRdwt34k9JEh98dOc5Ek3PR40w0ORc9zkTT9PR03SXcjT8qTaw/yXM3qnEmmpyLHmeiybnocSaaxsbG6i7hbtw0N7Flr+duVONMNDkXPc5Ek3PR40w0bdiwoe4S7sZNcxPnr/bcjWqciSbnoseZaHIuepyJpsHBwbpLuJvam+aIeFJE/DAifhQRL6u7nkbf+dJn6y7BKpyJJueix5loci56nImmT3ziE3WXcDe1Ns0R0Qa8FfgV4IHA0yPigXXW1Oi7X/ZAUuNMNDkXPc5Ek3PR40w0XXHFFXWXcDd1b2l+OPCjzPxxZk4AHwaeWnNNR3XV/e7Y3TgTTc5FjzPR5Fz0OBNNU1N6u83UenKTiPhN4EmZ+bzy+jOBR2TmpUfuc+WVV45u37796Ee6p6dn59q1a4cXor7du3f3LdRrWWuciSbnoseZaHIuepyJphpzOW3z5s39DgM+kgAACzpJREFUMy2o+5DRmU4s/jNd/JOf/OTuBarFzMzMzGxGdX8psQ04teH6KcCdNdViZmZmZjajupvmbwNnRsR9I6IT+B3gUzXXZGZmZmb2M2rdPSMzpyLiUuBzQBvwnsz8QZ01mZmZmZlV1b2lmcy8MjPPyswzMvM1ddcD2nNHLyUR8Z6I2BERNzTctjYiro6IW8p/19RZ41ITEadGxJci4saI+EFEvKi83bnUKCKWR8S3IuJ7ZS5/Xd5+34j4ZpnLR8pv9GwBRURbRHw3Ij5dXncmNYuI2yLi+oi4LiK+U97m32E1iojVEfHRiLip/P/lUYqZ1N40q1GfO3qJuQx4UuW2lwFfyMwzgS+U123hTAEvzsyzgUcCl5Tjw7nU6xDwhMx8MHAe8KSIeCTwOuCNZS57gItrrHGpehFwY8N1Z6Lh8Zl5XmY+rLzu32H1+ifgPzJzE/BgijEjl4mb5ruTnjt6KcnMa4DdlZufClxe/nw58BsLWtQSl5nbM3Nr+fMoxS+2k3EutcrC/vJqR3lJ4AnAR8vbncsCi4hTgF8F3lVeD5yJKv8Oq0lE9ACPBd4NkJkTmbkXwUzcNN/dycDtDde3lbeZhvWZuR2KBg64V831LFkRcTrwEOCbOJfalbsBXAfsAK4GbgX2ZuaRMwT4d9nCexPwZ8Dh8vo6nImCBK6KiC0R8YLyNv8Oq8/9gJ3Ae8tdmd4VESsRzMRN893NOne02VIXEauAjwF/nJn76q7HIDOnM/M8iqk7Hw6cPdPdFraqpSsifg3YkZlbGm+e4a7OZOE9OjMfSrEb5iUR8di6C1ri2oGHAv+cmQ8BxhDYFWMmbprvznNHaxuKiI0A5b87aq5nyYmIDoqG+V8z84ryZuciovxa88sU+5yvjogjsyT5d9nCejTwlIi4jWI3vydQbHl2JjXLzDvLf3cAH6f4I9O/w+qzDdiWmd8sr3+UoomWy8RN89157mhtnwKeXf78bOCTNday5JT7ZL4buDEz39CwyLnUKCL6I2J1+XMX8ESK/c2/BPxmeTfnsoAy8+WZeUpmnk7x/8gXM/MZOJNaRcTKiOg+8jNwIXAD/h1Wm8wcBG6PiAeUN20G/gvBTCLT3wxVRcSTKbYIHJk7WmIqvKUmIj4EPA7oA4aAVwKfAP4NuA/wU+C3MrN6sKDNk4h4DPBV4Hru2k/zFRT7NTuXmkTEL1AcKNNGsTHk3zLz1RFxP4qtnGuB7wK/l5mH6qt0aYqIxwH/OzN/zZnUq3z/P15ebQc+mJmviYh1+HdYbSLiPIoDZjuBHwPPofxdhlAmbprNzMzMzGbh3TPMzMzMzGbhptnMzMzMbBZums3MzMzMZuGm2czMzMxsFm6azcxOQBGxv5wJYCFe68KI+MRCvNY9FRGXRcTftnC/b0XEgxaiJjNbHNw0m9kJIyJui4jxsmEcLBukVXXXNd8i4ssR8bzG2zJzVWb+eIFK+DvgtQv0Wgvl9cCr6y7CzE4cbprN7ETz65m5CjgPeAjw8prrWdQi4heB3sz8Rt21zLFPAY8/csYxM7PZuGk2sxNSeRapz1E0zwBExEkR8fqI+GlEDEXE28sz5BERfRHx6YjYGxG7I+KrEbGsXHZbRLw8Iv4rIvZExHsjYnnD8z4/In5UPu5TEXHvhmUZES+MiFvKx761PHMiEXH/iPhKRIxExHBEfKThcZsi4uryOX8YEb8903pGxGuA/wa8pdzC/paG171/+fNlEfG2iPhseZ+vR8SGiHhTWdNNEfGQhue8d0R8LCJ2RsRPIuKPmrzVvwJ8peGxERFvjIgd5Xp9PyLOme39L5c/NSKui4h9EXFrRDypoZ5Ple/FjyLi+Q2PeVVE/FtEvC8iRiPiBxHxsIblD4mIreWyjwCNuR0z88w8CGyhOCOcmdms3DSb2QkpIk6haOh+1HDz64CzKBrp+wMnA39VLnsxsA3oB9ZTnMmw8exOzwB+GTijfI6/KF/nCcDfA78NbAQGKM7o1ujXgF8EHlze75fL2/8GuApYA5wCvLl8zpXA1cAHgXsBTwfeNtM+tpn55xRnYby03CXj0mO8Jb9d1twHHAKuBbaW1z8KvKF87WXA/wO+V74/m4E/johfnuE5Ac4Ffthw/ULgseV7tBr4H8Cuctkx3/+IeDjwPuAl5eMeC9xWPu5DFNncm+IU038XEZsbXvMpFO/5aootxEf+cOikOEvo+ynOsPfvwH9veNxsmd9IkZmZ2azcNJvZieYTETEK3A7soDi9OuXW3ecDf5KZuzNzlGJf3N8pHzdJ0fSelpmTmfnV/NlTor4lM28vT9P6GopGFopm+j2ZubU83fHLgUdFxOkNj31tZu7NzJ8CX+Kurd+TwGnAvTPzYGZ+rbz914DbMvO9mTmVmVuBj1E0jD+vj2fmlnIL6seBg5n5vsycBj5CsSsLFM19f2a+OjMnyv2i39nwPlWtBkYbrk8C3cAmirPK3piZ21t4/y+meB+vzszDmXlHZt4UEacCjwFeWr5H11GcTveZDa/5tcy8slyX93NXo/tIoAN4U5npR4FvV2ptlvlouX5mZrNy02xmJ5rfyMxu4HEUjVtfeXs/sALYUn4dvxf4j/J2gH+k2Cp9VUT8OCJeVnne2xt+HqDY6kn578CRBZm5n2LL6skN9x9s+PkAcOTgxD8DAvhWuVvBc8vbTwMecaTOstZnABtafA9mMtTw8/gM14/UdBpw78prv4JiS+xM9lA0yQBk5hcptvS+FRiKiH+JiB5mf/9PBW6d4fnvDRxpso8YoPn7uzwi2svH3lFphAcafp4t825g7zHW28zsZ7hpNrMTUmZ+BbiMYhYEgGGK5vBBmbm6vPSWBw2SmaOZ+eLMvB/w68CfVnYBOLXh5/sAd5Y/30nRaAJHd61YB9zRQo2Dmfn8zLw38AcUu2Dcn6JB/0pDnavLXS/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" + ] + }, + "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", + "