From f66da8998056de33580c5b0d0d38227b722ea3ce Mon Sep 17 00:00:00 2001 From: ss <13998040+zhushanshan0717@user.noreply.gitee.com> Date: Mon, 14 Oct 2024 12:42:14 +0800 Subject: [PATCH] added lec6 --- Lecture6.ipynb | 1 + 1 file changed, 1 insertion(+) create mode 100644 Lecture6.ipynb diff --git a/Lecture6.ipynb b/Lecture6.ipynb new file mode 100644 index 0000000..e2ddd81 --- /dev/null +++ b/Lecture6.ipynb @@ -0,0 +1 @@ +{"cells":[{"cell_type":"markdown","metadata":{"id":"22B733A3BFE049CCA72BE2F628394282","jupyter":{},"notebookId":"6536255793c31faf0a5a8dc8","runtime":{"execution_status":null,"is_visible":false,"status":"default"},"scrolled":false,"slideshow":{"slide_type":"slide"},"tags":[]},"source":[" #
Lecture 6 : Approximating the Posterior
\n"," \n","##
Instructor: Dr. Hu Chuan-Peng
\n"]},{"cell_type":"markdown","metadata":{},"source":["在 lec5 中我们简单地介绍了如何使用 pymc 软件包实现 MCMC 算法。 \n","\n","然而，MCMC 算法中看似随机的采样过程为何会让我们得到后验分布的样本？🤔 \n","\n","我们将在这节课揭露 MCMC 算法背后的秘密。😎 "]},{"cell_type":"markdown","metadata":{},"source":["## 什么是 MCMC？\n","\n","MCMC（马尔可夫链蒙特卡洛）是一类用于从复杂概率分布中抽样的算法。\n","\n","虽然实现过程有所不同，但常用的 MCMC 算法，如 **吉布斯采样**、**差分进化算法** 以及 PyMC 默认使用的 **NUTS**（No-U-Turn Sampler），都是 **Metropolis-Hastings** 算法的变种。 \n"," \n"," \n"," \n"," \n"," \n"," \n"," \n"," \n"," \n"," \n"," \n"," \n","
\"\"\"\"\"\"
吉布斯采样算法差分进化算法汉密尔顿算法
\n","\n","\n","通过这些算法，我们可以对难以直接求解的后验分布进行近似。\n"]},{"cell_type":"markdown","metadata":{},"source":["我们将在本节课重点讨论 Metropolis-Hastings (MH) 算法，而不是研究所有的变种。 \n","\n","- 虽然实现该算法需要计算机编程技能，而这些技能并不在本课程的范围之内（例如编写函数和 for 循环）， \n","- 😜ps. 即使没有学会 MH 算法的实现，也不妨碍我们通过 pymc 来实现各种 MCMC 算法。 \n","\n","🎯Goals \n","- 从概念上深刻理解马尔科夫链算法的**工作原理**。 \n","- 探索基础 **Metropolis-Hastings** 算法。 \n","- 在**normal-normal**和**beta-binormal**例子中了解 Metropolis-Hastings 算法的运行原理"]},{"cell_type":"markdown","metadata":{},"source":["## Normal-Normal 模型的后验分布 \n","\n","首先，是我们习以为常的 Normal-Normal 模型的例子。 \n","\n","\n","1. **似然模型**：假设我们从一个平均值为$\\mu$，标准差为0.75的正态分布中获取了一个$Y=6.25$的数据： \n"," $$ \n"," Y|\\mu \\sim \\ N(\\mu, 0.75^2) \n"," $$ \n","\n","2. **先验模型**：该正态分布群的平均值满足： \n"," $$ \n"," \\mu \\sim \\ N(0, 1^2) \n"," $$ \n","\n"," *可以简单理解成我们一开始对$\\mu$的信念，为$\\mu$在平均值为0，标准差为1的正态分布中波动* \n","\n","3. **后验分布**：那么在$Y=6.25$这个结果下，结合先验，更新后的$\\mu$是怎样的？ \n","\n"," $$\\mu | (Y = 6.25) \\sim \\text{N}(?,?)$$ \n"]},{"cell_type":"markdown","metadata":{},"source":["**🎯目标：使用MCMC来近似 Normal-Normal 模型的后验分布** \n","\n","之前的课程(lec5)告诉我们，有些时候我们无法直接计算后验分布，但我们可以使用MCMC对后验进行近似。 \n","\n","虽然这里的后验分布可以轻松的计算，但为了能更好地理解 MCMC的原理，我们就从这个简单的例子开始吧 🍻。 \n","\n","假设我们使用MCMC进行了 N=5000次 的采样，那么我们可以得到这样一条马尔科夫链 $\\left\\lbrace \\mu^{(1)}, \\mu^{(2)}, \\ldots, \\mu^{(N)} \\right\\rbrace$ \n","\n","* 左图展示了每一次采样的结果，而通过右图我们可以知道采样结果的分布如何（即哪些值出现的频率更高） \n","\n","❓那么这些采样值是怎么得到的？ \n","\n","> 我们以这个Normal-Normal 模型为例，来详细介绍采样的规则 \n","\n","![Image Name](https://www.bayesrulesbook.com/bookdown_files/figure-html/ch-7-mcmc-goal-1.png)"]},{"cell_type":"markdown","metadata":{},"source":["**1. 后验分布模型 vs. 后验分布采样** \n","\n","📍需要注意的是，我们现在已经通过公式推导获得了后验分布模型： \n","\n","$$ \n","\\begin{align*} \n","\\mu | (Y = 6.25) & \\sim \\text{N}(4, 0.6^2) \\\\ \n","&\\propto \\exp\\left(-\\frac{1}{2}\\left(\\frac{(\\mu-\\mu_0)^2}{\\sigma_0^2} + \\frac{(Y-\\mu)^2}{\\sigma^2}\\right)\\right) \\\\ \n","&\\propto \\exp\\left(-\\frac{1}{2}\\left(\\frac{\\mu^2 - 2\\mu\\mu_0 + \\mu_0^2}{\\sigma_0^2} + \\frac{Y^2 - 2Y\\mu + \\mu^2}{\\sigma^2}\\right)\\right) \\\\ \n","&\\propto \\exp\\left(-\\frac{1}{2}\\left(\\frac{\\mu^2(\\frac{1}{\\sigma_0^2} + \\frac{1}{\\sigma^2}) - 2\\mu(\\frac{\\mu_0}{\\sigma_0^2} + \\frac{Y}{\\sigma^2}) + (\\frac{\\mu_0^2}{\\sigma_0^2} + \\frac{Y^2}{\\sigma^2})}{1}\\right)\\right) \\\\ \n","&\\propto \\exp\\left(-\\frac{1}{2}\\left(\\frac{\\mu^2 - 2\\mu(\\frac{\\mu_0\\sigma^2 + Y\\sigma_0^2}{\\sigma_0^2\\sigma^2}) + (\\frac{\\mu_0^2\\sigma^2 + Y^2\\sigma_0^2}{\\sigma_0^2\\sigma^2})}{1}\\right)\\right) \n","\\end{align*} \n","$$ \n","\n","然而，**后验分布模型不等于后验分布采样** \n","- 换句话说，我们不能直接从上面的后验分布的公式中，得到参数的采样$\\left\\lbrace \\mu^{(1)}, \\mu^{(2)}, \\ldots, \\mu^{(N)} \\right\\rbrace$。 \n","- 一个类似但不太正规的例子是， \n"," - 当我们知道线性模型 $f(\\mu|Y=6.25, \\sigma = 0.75) = 6.25 * \\mu + 0.75$， \n"," - 并且我们想采样很多个 $\\mu$， \n"," - 但$\\mu$ 的数量受到 $f(\\mu)$的影响，即$f(\\mu)$越大时保留的 $\\mu$ 的越多， \n"," - 那么我们如何采样 $\\mu$ 呢？ \n","\n","显然，我们无法直接采样得到 $\\mu$，**要获得后验分布的采样 $\\mu$，我们需要计算后验模型 $f(\\mu)$ 的值**。"]},{"cell_type":"code","execution_count":1,"metadata":{},"outputs":[],"source":["import plotly.graph_objects as go\n","import numpy as np\n","from scipy.stats import norm"]},{"cell_type":"code","execution_count":6,"metadata":{},"outputs":[{"data":{"application/vnd.plotly.v1+json":{"config":{"plotlyServerURL":"https://plot.ly"},"data":[{"mode":"lines","name":"Regression 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Line and Normal Distribution"},"xaxis":{"title":{"text":"X"}},"yaxis":{"title":{"text":"Y"}}}}},"metadata":{},"output_type":"display_data"}],"source":["x_range = np.linspace(2, 10, 1000) # 设置 x 的范围为 [1,10]\n","y_reg = 6.25 * x_range + 0.75 # 设置回归模型\n","y_norm = norm.pdf(x_range, 6.25, 0.75)\n","\n","# 使用Plotly绘制回归线\n","fig = go.Figure()\n","\n","# 绘制回归线\n","fig.add_trace(go.Scatter(\n"," x=x_range,\n"," y=y_reg,\n"," mode='lines',\n"," name='Regression Line'\n","))\n","\n","# 绘制正态分布曲线\n","fig.add_trace(go.Scatter(\n"," x=x_range, \n"," y=y_norm * 100, # 扩大 100 倍保持和回归模型的 y 轴单位相似\n"," mode='lines',\n"," name='Normal Line'\n","))\n","\n","\n","# 设置图表布局\n","fig.update_layout(\n"," title='Regression Line and Normal Distribution',\n"," xaxis_title='X',\n"," yaxis_title='Y'\n",")\n","\n","# 显示图表\n","fig.show()"]},{"cell_type":"markdown","metadata":{},"source":["**2. 未归一化的后验分布(unnormalized posterior pdf)** \n","\n","❓但是当分母太过复杂时，我们无法计算后验模型 $f(\\mu)$，有什么替代的方法吗？ \n","\n","但通过贝叶斯公式我们知道： \n","\n","$$f(\\mu | y=6.25) \\propto f(\\mu)L(\\mu|y=6.25).$$ \n","\n","- 尽管未归一化的分布并不是真正的后验分布，但这二者的形状、集中趋势、变异性是一样的 \n","- 可以看到，真实的后验分布和未归一化后验分布，处理在 y 轴上的单位不一样，但他们的形状、集中趋势、变异性是一样的 \n","- 重要的是，两个分布中，$\\mu$ 的结果主要集中在 2-6 之间 \n","\n","因此，当进行采样时，我们可以使用**未归一化的后验分布** 的结果来替代计算真实的后验分布 $f(\\mu)$ \n","\n","![Image Name](https://cdn.kesci.com/upload/s2ty9jty8t.png?imageView2/0/w/960/h/960) \n"]},{"cell_type":"markdown","metadata":{},"source":["## Metropolis-Hastings(MH)算法 \n","\n","在刚才的例子中，我们已经涉及到 MH 算法最朴素的思想： \n","\n","- 后验分布模型可以通过公式进行推导得到，然而无法对它进行直接采样。 \n","- 我们可以根据后验模型 y 轴的大小来决定 x 轴参数的数量。 \n"," - 例如，我们均匀的从参数的范围(x~[0,1])中抽取 10000个参数样本 $\\mu_i$。 \n"," - 然后我们计算对于每个 $\\mu_i$ 的 $f(\\mu_i)$ 的大小，$f(\\mu_i)$ 越大那么 $\\mu_i$ 被保留的可能性越高。 \n"," - 最后，我们可能保留5000个参数。而此时，这 5000 个参数将不再是 \n"," 均匀的分布在[0,1]中，而更接近于后验分布的形状。 \n","- 正如之前提到，计算 $f(\\mu_i)$ 是比较困难的，我们可以计算非标准化的 $f(\\mu_i)$。 \n","- 此外，直接在[0,1]中均匀的采样效率太低，我们在接下来会利用 MCMC 状态转移的性质来提高采样效率。 \n","\n","现在我们就来体验这个奇妙的过程"]},{"cell_type":"markdown","metadata":{},"source":["### 建议分布(proposed distribution) \n","\n","为了提高采样效率，我们**不会**直接从一个分布中进行大量采样，再进行筛选(也被称为拒绝)。 \n","\n","在 MCMC 中，我们会构造一个建议分布 (proposed distribution) $q(x)$，然后利用 MCMC 状态转移的性质来进行采样。 \n","\n"," \n"," \n"," \n"," \n","
\"图片1\"
\n","\n","首先复习一下MCMC的状态转移的性质： \n","- 假如不同的情绪对应一种状态，也就是参数可能的取值。 \n"," - 例如，冷静是 $\\theta_1=0.5$; 悲伤是 $\\theta_2=0.3$；开心是$\\theta_3=0.7$； 以此类推.....。 \n"," - 这样，我们可以确定参数选择的范围 $\\theta_{k} \\sim [0,1]$，参数是离散变量，每一个值对应一种心情，值越大开心程度越强。 \n"," - 注意，我们用下标 k 来表示不同的心情以及对应的参数值。 \n","- 每一天我们的心情都会发生变化或者不变，代表一次采样，即一次状态的转移。 \n"," - 常年内月的记录心情的变化，我们获得了马尔科夫链 $\\left\\lbrace \\theta^{(1)}, \\theta^{(2)}, \\ldots, \\theta^{(n)} \\right\\rbrace$。 \n"," - 注意，我们用上标 n 表示不同的天数。也就是说每一天的心情\\theta^{(n)} 对应了一个具体的心情参数值 $\\theta_{k}$ \n","- 根据 MCMC 的状态转移的性质，今天的心情只依赖于上一天的心情。 \n"," - 比如，第一天的心情为开心 $\\theta^{(n-1)}_{3}$，那么下一天心情开心 $\\theta^{(n)}_{3}$的概率为 0.5，冷箭 $\\theta^{(n)}_{2}$ 或悲伤 $\\theta^{(n)}_{1}$的概率为0.25。 \n"]},{"cell_type":"markdown","metadata":{},"source":["这样我们能构建一个状态转移表： \n","\n","| 心情 | 开心$\\theta^{(n-1)}_{1}$ | 冷静$\\theta^{(n-1)}_{2}$ | 悲伤$\\theta^{(n-1)}_{3}$ | ... | \n","| :----: | :----: | :----: | :----: | :----: | \n","| 开心$\\theta^{(n)}_{1}$ | 0.5 | 0.25 | 0.25 | ... | \n","| 冷静$\\theta^{(n)}_{2}$ | 0.5 | 0 | 0.5 | ... | \n","| 悲伤$\\theta^{(n)}_{3}$ | 0.25 | 0.25 | 0.5 | ... | \n","| ... | ... | ... | ... | ... | \n","\n","- 每一行代表：当日心情(n)受到上一天心情(n-1)的影响。 \n","- 可以写成服从概率分布的形式：$choice(n) \\sim Distribution(n-1)$。 \n","- 这里的 **Distribution 就是建议分布**。 \n"," - 它为第二天的心情变化提供了建议，所以被称为建议分布 $q(x)$。 \n"," - 它形式化了 MCMC 的性质。当前状态依赖于上一次选择。"]},{"cell_type":"markdown","metadata":{},"source":["**在真实的MH算法中** \n","\n","为了求解一个不常见的分布$p(x)$，先构造一个常见的分布$q(x)$进行采样，其中$q(x)$叫做建议分布(proposal distribution) \n","\n","在这个Normal-Normal 模型例子中，我们使用正态分布作为建议分布： \n","- 也就是说我们将 $choice(n) \\sim Distribution(n-1)$ 具体化为 $\\theta^{n} \\sim Normal(\\theta^{n-1}_{k},\\sigma)$ \n","- 需要注意的是，之前的例子中，$\\theta_{k}$ 为离散值，每一参数代表一种心情，而心情本质可以是连续的，所以我们可以将$\\theta_{k}$变为连续变量。 \n","- 大家可以把 $\\theta$ 看作开心程度，其值越高，代表个体越开心。 \n","\n","> 🤔思考, 如果你昨天的心情系数(开心程度)为 3 (我们用 $\\theta_{n-1}$ 表示)， 那么你今天开心程度为 2 或 4($\\theta_{n}$) 的可能性有多大？那么根据建议分布，今天心情 $\\theta^{n}$ 最大可能对应的值是哪些？ \n","> \n","![Image Name](https://www.bayesrulesbook.com/bookdown_files/figure-html/ch-7-mh-proposal-1.png)"]},{"cell_type":"markdown","metadata":{},"source":["\n","我们已经了解了建议分布的思想。 \n","\n","接下来，我们需要了解**如何根据建议分布进行采样**，以及如何从 **建议分布 $q(x)$ 得到后验分布 $p(x)$** 。"]},{"cell_type":"markdown","metadata":{},"source":["### 接受率 (acceptance probability) \n","\n","虽然我们了解了当前样本可以根据上一次的样本从建议分布中进行采样 $\\theta^{n} \\sim Normal(\\theta^{n-1}_{k},\\sigma)$。 \n","\n","然而，我们如何判断这个采样是否合理呢？换句话说，我们需要思考是否保留或拒绝这个采样。 \n","- 假设上一次采样的参数值为 $\\theta^{n-1} = 3$， 根据建议分布$q(\\theta) = Normal(0.1,1)$ 我们采样得到参数值 $\\theta^{n} = 1$。 \n","- 而实际上，我们后验分布(或者未标准化的后验分布)为 $p(\\theta) = Normal(5,1)$。 \n","- 显然，$\\theta^{n} = 1$ 在 $p(\\theta)$ 的边缘。那我们是否要保留该采样呢？"]},{"cell_type":"code","execution_count":7,"metadata":{},"outputs":[],"source":["def plot_example():\n"," # 准备数据\n"," posterior_mean = 5\n"," posterior_std = 1\n"," proposal_means = [3, 4, 8]\n","\n"," # 生成后验分布的数据\n"," x = np.linspace(0, 10, 1000)\n"," y_posterior = norm.pdf(x, posterior_mean, posterior_std)\n","\n"," # 生成建议分布的数据\n"," y_proposals = [norm.pdf(x, mean, posterior_std) for mean in proposal_means]\n","\n"," # 使用Plotly绘制后验分布和建议分布\n"," fig = go.Figure()\n","\n"," # 绘制后验分布\n"," fig.add_trace(go.Scatter(\n"," x=x,\n"," y=y_posterior,\n"," mode='lines',\n"," name='Posterior Distribution',\n"," line=dict(color='black', width=8)\n"," ))\n","\n"," # 绘制建议分布\n"," for i, y_proposal in enumerate(y_proposals):\n"," fig.add_trace(go.Scatter(\n"," x=x,\n"," y=y_proposal,\n"," mode='lines',\n"," line=dict(width=1),\n"," name=f'Proposal Distribution {i+1}'\n"," ))\n","\n"," # 设置图表布局\n"," fig.update_layout(\n"," title='Posterior and Proposal Distributions',\n"," xaxis_title=\"θ\",\n"," yaxis_title='Probability Density'\n"," )\n","\n"," # 显示图表\n"," fig.show()"]},{"cell_type":"code","execution_count":8,"metadata":{},"outputs":[{"data":{"application/vnd.plotly.v1+json":{"config":{"plotlyServerURL":"https://plot.ly"},"data":[{"line":{"color":"black","width":8},"mode":"lines","name":"Posterior 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and Proposal Distributions"},"xaxis":{"title":{"text":"θ"}},"yaxis":{"title":{"text":"Probability Density"}}}}},"metadata":{},"output_type":"display_data"}],"source":["plot_example()"]},{"cell_type":"markdown","metadata":{},"source":["**不同接受策略的影响** \n","\n","* 我们可以考虑三种接受建议的情况： \n","\n"," 1：始终不接受提议。 \n","\n"," 2：始终接受提议。 \n","\n"," 3：只有当提议(n+1)的后验可能性大于当前(n)值的后验可能性时，才接受提议 \n","\n","* 我们来看看这三种情况对应生成的trace plot \n","![Image Name](https://www.bayesrulesbook.com/bookdown_files/figure-html/ch7-bad-step2-1.png) \n","\n"," 1. 使得马尔科夫链在采样时一直停在同一个值 \n","\n"," 2. 马尔科夫链的采样并不会稳定在某一个范围内 \n"," \n"," 3. 采样只停留在$\\mu = 4$附近(只能采到一部分值) \n","\n","* 因此我们知道，尽管采样应该更多地停留在“高后验可能性的值”，但也不能只取到这附近的值。 \n"]},{"cell_type":"markdown","metadata":{},"source":["**接受率 (acceptance probability)** \n","\n","可见，选择一个合适的接受策略非常重要。而接受率 ($\\alpha$, acceptance probability)就是为了解决这个问题。 \n","\n","- 首先，我们将从建议模型中抽取一个新的参数 $\\theta^{n+1}$ 的概率为 $q(\\theta^{n+1}|\\theta^{n})$ \n","- 对于是否接受 $\\theta^{n+1}$，我们定义接受概率$\\alpha$ \n","$$ \n"," \\alpha = \\min\\left\\lbrace 1, \\; \\frac{f(\\theta^{n+1})L(\\theta^{n+1}|y)}{f(\\theta^{n})L(\\theta^{n}|y)} \\times \\frac{q(\\theta^{n}|\\theta^{n+1})}{q(\\theta^{n+1}|\\theta^{n})} \\right\\rbrace. \n","$$ \n","- 别看这公式很复杂，其实很简单。 \n","- 分数的上下分别代表下一个参数$\\theta^{n+1}$和当前参数$\\theta^{n}$的非标准化后验。即我们之前提到，要通过非标准化后验来判断是否接受一个参数。 \n"," - 其中，$f(\\theta)L(\\theta|y)$ 为非标准化后验 \n"," - $q(\\theta^{n}|\\theta^{n+1})$ 部分代表了从建议分布中采样新参数的过程。 \n","- 可以想象，$\\frac{f(\\theta^{n+1})L(\\theta^{n+1}|y)}{f(\\theta^{n})L(\\theta^{n}|y)}$ 大于1且其值越大，表明下一个参数$\\theta^{n+1}$的后验概率越大，因此它越有可能被接受。 \n","- 如果$\\frac{f(\\theta^{n+1})L(\\theta^{n+1}|y)}{f(\\theta^{n})L(\\theta^{n}|y)}$小于1，则代表下一个参数$\\theta^{n+1}$的后验概率过小，因此我们要舍弃它。 \n","\n","所以，对于是否接受或拒绝新的参数 $\\theta^{n+1}$，则有： \n","$$ \n","\\theta^{(n+1)} = \n"," \\begin{cases} \n"," \\theta^{(n+1)} & \\text{ with probability } \\alpha \\\\ \n"," \\theta^{(n)} & \\text{ with probability } 1- \\alpha. \\\\ \n"," \\end{cases} \n"," $$ \n","- 也就是如果我们不接受新的参数，那我们用原来的参数替代现在的参数。 \n","- 这样避免了参数采样被浪费，并且使得概率更大的参数被更多的采样。"]},{"cell_type":"markdown","metadata":{},"source":["总的来说，MH 算法包含两个关键思想和两个关键步骤： \n","\n","两个关键思想 \n","- 根据非标准化的后验进行参数的接受或拒绝 \n","- 根据 MCMC 的特性设置建议分布来完成状态转移 \n","\n","两个关键步骤 \n","- 设定建议分布 \n","- 根据建议分布的参数、未标准化后验计算接受率"]},{"cell_type":"markdown","metadata":{},"source":["### 代码示例 \n","\n","我们使用代码感受一下这个过程"]},{"cell_type":"code","execution_count":10,"metadata":{},"outputs":[],"source":["import numpy as np\n","import scipy.stats as st\n","import pandas as pd\n","import seaborn as sns"]},{"cell_type":"markdown","metadata":{},"source":["首先，我们假设当前的参数值 $\\theta^{n} = 3$，然后我们根据该参数设定建议分布，并进行一次新的采样。 \n","\n","- 注意，为了方便演示，我们将建议分布(正态分布)的 $\\sigma$ 固定为1。"]},{"cell_type":"code","execution_count":11,"metadata":{},"outputs":[{"name":"stdout","output_type":"stream","text":["从建议分布中新采样 θ(n+1)为： 3.711673530262846\n"]}],"source":["np.random.seed(2023)\n","\n","current = 3 # 假设theta(n)为3\n","\n","proposal = st.norm(current, 1).rvs() # 从当前正态分布中抽出一个样本\n","\n","print(\"从建议分布中新采样 θ(n+1)为：\",proposal)"]},{"cell_type":"markdown","metadata":{},"source":["接着，我们根据新采样得到的参数计算其相关的接受率。 \n","- 注意，我们假设先验正态分布的参数为：mean = 3, sigma = 1 \n","- 另外，我们假设似然模型仅包含一个数据：Y = 6"]},{"cell_type":"code","execution_count":12,"metadata":{},"outputs":[{"name":"stdout","output_type":"stream","text":["后验比为： 22.024353294942063 , alpha为: 1\n"]}],"source":["# 设置先验\n","prior = st.norm(loc = 3, scale = 1)\n","def likelihood(theta):\n"," Y = 6 # 假设数据 Y 为 6\n"," return st.norm(loc = theta, scale = 0.75).pdf(Y) # 注意：这里为方便演示固定 scale = 0.75\n"," \n","\n","# 计算建议位置(n+1)的未归一化的后验概率值（先验*似然）\n","proposal_posterior = prior.pdf(proposal) * likelihood(proposal)\n","\n","# 计算当前位置(n)的未归一化的后验概率值（先验*似然）\n","current_posterior = prior.pdf(current) * likelihood(current)\n","\n","# 计算接受概率α，为两者概率值之比\n","alpha = min(1,proposal_posterior/current_posterior)\n","\n","# 打印出接受概率α\n","print(\"后验比为：\", proposal_posterior/current_posterior, \", alpha为:\", alpha)"]},{"cell_type":"markdown","metadata":{},"source":["最后，我们根据接受率 $\\alpha$来决定是否接受建议分布的参数作为新的采样值。"]},{"cell_type":"code","execution_count":13,"metadata":{},"outputs":[{"data":{"text/plain":["3.711673530262846"]},"execution_count":13,"metadata":{},"output_type":"execute_result"}],"source":["# 根据接受概率α进行抽样，抽样内容为建议位置和当前位置\n","next_stop = np.random.choice([proposal, current], 1, p=[alpha,1-alpha])\n","\n","# 打印出下一个位置的值\n","next_stop[0]\n","\n","#从第一段代码我们可以看到此时的接受概率α=1，因此接受了建议值作为我们的下一个值"]},{"cell_type":"markdown","metadata":{},"source":["在这个例子中，我们可以看到只有建议参数的后验值大于之前参数的后验值就会选择它作为新的参数 (因为接受概率α=1)。 \n","- 然而当建议参数的后验值小于之前参数的后验值时，例如 α=0.1。 我们任然有小部分几率接受它作为新的参数。 \n","- 这种随机性的引入，使得采样过程更加灵活，减少了样本之间的相关性，不容易陷入到某些局部最优中。 \n","\n","![Image Name](https://cdn.kesci.com/upload/s2le9nbz6q.png?imageView2/0/w/450/h/450) "]},{"cell_type":"markdown","metadata":{},"source":["**定义单次采样函数** \n","\n","我们可以直接定义一个函数，将刚刚的操作全都结合在一起，这样当我们想进行抽样的时候，不用重复写代码"]},{"cell_type":"code","execution_count":14,"metadata":{},"outputs":[{"data":{"text/html":["
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proposalalphanext_stop
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"],"text/plain":[" proposal alpha next_stop\n","0 3.091205 1 3.091205"]},"execution_count":14,"metadata":{},"output_type":"execute_result"}],"source":["def one_mh_iteration(current, sigma = 1):\n","\n"," \"\"\"\n"," def后面为函数值，current为输入值，作为建议分布(正态分布)的均值\n"," \n"," 接下来的代码和之前一样\n","\n"," return 则是该函数返回的值，我们将建议值，接受概率，和下一个位置这三个值组成了一个数据框进行返回\n"," \"\"\"\n"," proposal = st.norm(current, sigma).rvs()\n","\n"," prior = st.norm(loc = 3, scale = 1)\n"," def likelihood(theta):\n"," # 假设数据 Y 为 6\n"," Y = 6\n"," return st.norm(loc = theta, scale = 0.75).pdf(Y)\n"," \n"," proposal_posterior = prior.pdf(proposal) * likelihood(proposal)\n"," current_posterior = prior.pdf(current) * likelihood(current)\n"," alpha = min(1,proposal_posterior/current_posterior)\n"," next_stop = np.random.choice([proposal, current], 1, p=[alpha,1-alpha])\n"," return pd.DataFrame({\"proposal\":[proposal],\n"," \"alpha\":[alpha], \n"," \"next_stop\":[next_stop[0]]})\n","np.random.seed(8)\n","one_mh_iteration(current=3)"]},{"cell_type":"code","execution_count":15,"metadata":{},"outputs":[{"data":{"text/html":["
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proposalalphanext_stop
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"],"text/plain":[" proposal alpha next_stop\n","0 3.849313 1 3.849313"]},"execution_count":15,"metadata":{},"output_type":"execute_result"}],"source":["# 变换不同的随机数种子，其实也是生成不同的建议值\n","np.random.seed(83)\n","one_mh_iteration(current=3)"]},{"cell_type":"markdown","metadata":{},"source":["**多次采样** \n","\n","上述函数只进行了一次采样，即当前位置为3时，下一个可能采样的结果 \n","\n","基于当前位置，提出下一个采样值，接受或拒绝它。那么新的采样值就变成了当前位置，我们需要不断重复这个过程"]},{"cell_type":"code","execution_count":16,"metadata":{},"outputs":[],"source":["def mh_tour(N, sigma = 1):\n","\n"," \"\"\"\n"," N为迭代次数，w为均匀分布的一半宽度\n","\n"," 我们在单次采样函数的基础上叠加了一个循环\n"," 将每次的采样结果存在mu[i]中，\n"," 在每次采样结束后，将采样结果替换为当前位置\n","\n"," 返回值为迭代次数，和每次采样得到的结果\n"," \"\"\"\n"," current = 3\n"," mu = np.zeros(N)\n","\n"," for i in range(N):\n"," sim = one_mh_iteration(current,sigma)\n"," mu[i] = sim[\"next_stop\"][0]\n"," current = sim[\"next_stop\"][0]\n"," \n"," return pd.DataFrame({\"iteration\": range(1,N+1),\n"," 'mu': mu})"]},{"cell_type":"code","execution_count":17,"metadata":{},"outputs":[{"data":{"text/html":["
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iterationmu
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\n","
"],"text/plain":[" iteration mu\n","4995 4996 4.528634\n","4996 4997 4.528634\n","4997 4998 4.745413\n","4998 4999 5.847077\n","4999 5000 5.847077"]},"execution_count":17,"metadata":{},"output_type":"execute_result"}],"source":["# 调用定义好的函数，将采样次数设为5000，均匀分布的一半宽度设为1\n","np.random.seed(84735)\n","mh_simulation = mh_tour(N=5000)\n","mh_simulation.tail()"]},{"cell_type":"markdown","metadata":{},"source":["**采样结果图示**"]},{"cell_type":"code","execution_count":18,"metadata":{},"outputs":[{"data":{"text/plain":["[]"]},"execution_count":18,"metadata":{},"output_type":"execute_result"},{"data":{"image/png":"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"]},"metadata":{},"output_type":"display_data"}],"source":["import matplotlib.pyplot as plt\n","\n","#生成一行两列的画布\n","fig, axs = plt.subplots(1, 2, figsize=(20, 5))\n","\n","#trace plot：在第一列绘制出每一次的采样结果\n","axs[0].plot(mh_simulation[\"iteration\"], mh_simulation[\"mu\"],\n"," color=\"grey\",)\n","axs[0].set_xlabel(\"iteration\", fontsize=16)\n","axs[0].set_ylabel(\"mu\", fontsize=16)\n","\n","#density plot：在第二列绘制出采样结果的分布\n","axs[1].hist(mh_simulation[\"mu\"], \n"," edgecolor = \"white\",\n"," color=\"grey\",\n"," alpha = 0.7,\n"," bins = 20,\n"," density = True)\n","axs[1].set_xlabel(\"mu\", fontsize=16)\n","axs[1].set_ylabel(\"density\", fontsize=16)\n","\n","# 绘制分布外围线条\n","x_norm = np.linspace(2,10,10000) \n","y_norm = st.norm.pdf(x_norm, loc=mh_simulation[\"mu\"].mean(), scale=mh_simulation[\"mu\"].std())\n","\n","axs[1].plot(x_norm, y_norm, color='blue')"]},{"cell_type":"markdown","metadata":{},"source":["我们可以使用 arviz 简化这个绘图的过程"]},{"cell_type":"code","execution_count":19,"metadata":{},"outputs":[{"data":{"text/plain":["array([[, ]],\n"," dtype=object)"]},"execution_count":19,"metadata":{},"output_type":"execute_result"},{"data":{"image/png":"iVBORw0KGgoAAAANSUhEUgAAA7YAAADaCAYAAACSJN4kAAAAOXRFWHRTb2Z0d2FyZQBNYXRwbG90bGliIHZlcnNpb24zLjguNCwgaHR0cHM6Ly9tYXRwbG90bGliLm9yZy8fJSN1AAAACXBIWXMAAA9hAAAPYQGoP6dpAABo4ElEQVR4nO3dd5wb5Z0/8M+orLZre/Oud9e994JtWjA1QJwCF4gh5Ai5kIMAx+X3y0HufpCGSXLJJblcnEAIgSPAhSOUkNjGFJtqXNdt3ds2b+9FfX5/7EpWmZFGo5FG2v28X6992asdjb4ajaTnO8/zfB9BFEURRERERERERCnKoHcARERERERERLFgYktEREREREQpjYktERERERERpTQmtkRERERERJTSmNgSERERERFRSmNiS0RERERERCmNiS0RERERERGlNCa2RERERERElNKY2BIREREREVFKY2JLREREREREKY2JLREREREREaU0JrZERERERESU0pjYEmng0UcfhSAIOHbsGNauXYvMzExUV1fjD3/4AwDgmWeewcyZM5GdnY21a9fi3LlzvvsKgoBHH300YH/btm2DIAjYtm1b4p4EERERyeJ3PVFyY2JLpKGbb74Zn/vc5/Daa69hyZIluPPOO/HQQw/hySefxI9//GP8/ve/x5EjR7B+/Xq9QyUiIiIV+F1PlJxMegdANJ48/PDDuOWWWwAAy5YtQ3FxMX73u9/h9OnTyMnJAQC0trbi/vvvR3NzMyZNmqRnuERERBQlftcTJSf22BJp6JprrvH9Pz8/HyUlJVi9erXviw4AZs2aBQBobGxMeHxEREQUG37XEyUnJrZEGsrPzw/4PS0tTfI2ALDZbAmLi4iIiLTB73qi5MTElkhnFosFDocj4Lauri6doiEiIiKt8bueKP6Y2BLpbPLkyaivrw+4bfPmzTpFQ0RERFrjdz1R/LF4FJHOvvjFL2LDhg14/PHHsXTpUmzevBlvv/223mERERGRRvhdTxR/TGyJdPbwww+jq6sL//Ef/wG73Y6bbroJv/zlL3HjjTfqHRoRERFpgN/1RPEniKIo6h0EERERERERkVqcY0tEREREREQpjYktERERERERpTQmtkRERERERJTSmNgSERERERFRSmNiS0RERERERCmNiS0RERERERGlNEXr2Ho8HrS0tCAnJweCIMQ7JiIioohEUcTAwAAqKipgMPA6baz4XU9ERMkmmu96RYltS0sLqqqqNAmOiIhIS42NjaisrNQ7jJTH73oiIkpWSr7rFSW2OTk5vh3m5ubGHhkREVGM+vv7UVVV5fuOotjwu56IiJJNNN/1ihJb75Ck3NxcftkREVFS4bBZbfC7noiIkpWS73pOSiIiIiIiIqKUxsSWiIiIiIiIUhoTWyIiIiIiIkppiubYElFkLb0jeOdoO/Iz03DN3FKYjLxuRERE0em3OSF6AGumWe9QiIhSChNbIg1sOnge//zSfgw73ACAxZPz8N9fXYlsC99iRESk3LtH2wEA6xZN0jkSIqLUwi4lohi9e6wd976wD3PKc/Huty7Hf966GAeb+vB//3c/RFHUOzwiIiIionGP3UlEMTjZPoj7nh9Nap/96gpkpplQW5SF830jeOxvR7HlcCuunVeud5hEREREROMae2yJVOobduIfnt0Ni9mIJ768FJlpF64TffXiKZhZmoP/2HoCHg97bYmIiGh8EUWRI9MoqTCxJVLB5fbg3hf2oqlnBL+9fQnKrRkBfzcaBNxzxTQcaxvA1iNtOkVJRBNJTU0NBEEI+bnnnnv0Do2IxqE369uw+VCr3mEQ+XAoMpGMfpsTb+w/j9a+EZRa01GZn4nK/AwM29147G9H8PHpLvzkpgVYWl0gef/r55fjP7Yex6/eOYmr55RCEIQEPwMimkh27doFt9vt+/3QoUO46qqrcPPNN+sYFRGNVzanO/JGRAnExJZIwvsnOvDAi3XoGnJAEIDgkTY56Sb89OaF+MLSStl9GA0C7r5sCr798kHsOdeDZTXSCTARkRaKi4sDfn/88ccxdepUXHbZZTpFRERElDhMbImC7D7bja89uxu1Rdl45s4VmFOei85BOxp7RtDUMwxRBC6fWYy8zLSI+1q3aBI2bDqKZz4+x8SWiBLG4XDgueeew4MPPsjRIkRENCEwsSXyc75vBHf+YRcq8zPxx7tWoiBrNHktyU1HSW46llbnR7W/dLMRX1xWhac+OIP262ejJDc9HmETEQV49dVX0dvbi6985Suy29jtdtjtdt/v/f39CYiMiIgoPlg8imiMKIr4ziuH4PKIePory31Jbaxuu6gablHEHz9p0GR/RESRPPXUU7juuutQUVEhu82GDRtgtVp9P1VVVQmMkIiISFtMbInGvL6/Be8cbce3r52FqoJMzfZbVZCJtbNK8PzOBjhcHs32S0Qk5dy5c3jrrbdw1113hd3uoYceQl9fn++nsbExQRESERFpj4ktEYCuQTu++5d6LKvOx+0XVWu+/y+vqkHHgB2bD7MsPhHF19NPP42SkhJcf/31YbezWCzIzc0N+CEiIkpVTGyJAHzvjXoM2lx4/AsLYDBoX2jl4mlFmFKUhWc+Oqv5vomIvDweD55++mnccccdMJn0LaPR3DuC7iGHrjEQEdHEwcSWUs77Jzpw7c/fw5d/vxPn+0Zi3t87R9vwWl0L7ls7DdNKsjWIMJTBIOCO1TXYc64Hu892x+UxiIjeeustNDQ04M4779Q7FOw+2433T3ToHQYREU0QTGwppZzrGsLXnt2NvhEn9pztxl3P7I5p3uqAzYnvvHIIs8py8PXLpmoYaagvLq9CUbYFv3znZFwfh4gmrquvvhqiKGLGjBl6h5I0GrqG4fGIkTckIqKUxsSWUspP3zwOgyDgtXvW4Je3Lsbhln784aMzqvf3/Tfq0dZvw4++sABmY3zfDulmI/7h0lq8d7wDdY29cX0sIiIaHQ69r7EHx9sHdI3D4fIwuSYiijMmtpQy2gds+OvB87hjdQ1KctOxdnYpPjWzGBu3ncKQ3RX1/l7Y2YA/7W7CN6+YjoVVedoHLGH9ymoUZafhsb8egSiykUNEFE8u9+iIHr0r0m853IqdnIZCRBRXTGwpZby2rwVuj4i/W3ZhrcUHrpyBnmEnXtod3TIV+xp68Mhrh/GpmcW4f+10rUOVlWUx4f9eOws7z3bjtbqWhD0uEdFEpvd1RI8ooq3fpm8QRETjHBNbShlb69uwsNKK2qIs320Lq/KwoqYAv//wLNwKh3l1DNjxjef2ojwvHT//4uK4VEEO56YllVhUlYcf/PUI2gfY0CEiihcBoZ/vTrcHh5r7ODSYiGicYWJLKWHQ7sLehh5cOqM45G9fvaQWDd3D2FrfFnE/LrcH9z6/F30jTvzmtqWwZprjEW5YBoOAH9+0AEN2F+794z443foOkSMimkiOnh/AqY5BNPXEXlWfiGiiau4dUTUVMJ6Y2FJK+OR0F1weEWumFYX87crZpaguzMRTH5yOuJ/HNx3FJ2e68fgX5mN2eW48QlVkRmkOfnzTAuw8241/+p862F1u3WIhIhrv/PtmPWPjkkWwx5Zi43B50G9z6h0GkS52n+3GtmPJtaQbE1tKCR+c7ESG2Yglk/ND/mY0CLhzTS12ne0JW234tbpm/O6DM7hzTS3WLZoUx2iVuXFhBf71+tl448B53PH7nZx/RUSUQFLDlImisetsN9492q53GES6cXmSa9ShSe8AiJT44EQnVk4pQJpJ+lrMTUsr8dM3j+GpD87gP29dHPL3wy19+PbLB3DRlAI89OlZ8Q5XsbsumYLiHAv+5eWDuPTH7+LmZZVYXJWPLIsRpzqGcOR8P5p7R1CcbcEXl1dh7exSvUMmIiJS5WT7ICrzM5BuNuodiiY6B+16h0AqHWruQ9eQA5dJTHGj1MXElpJee78NJ9oH8cXlVbLbZFlM+NLKajz5/mk8cOV0TC3O9v2ta9COf3h2DwqzLPivLy2J+3q10Vq3aBIWV+Vj4/ZT+NPuJjy3o8H3t+rCTEwuyMThln589ZnduG/tdDx41QwdoyUiSh0CO2WTRr/NicMtfWjvt2G1xLQiokQ61TGodwgUB0xsKentOdcDAFhRWxB2u69dUosXdjbg4T8fxB/vWgmT0YDeYQduf2onuobs+N+7V6Mw25KIkKM2uTATGz4/H99bNxctvSMYdrhRVZCJbMvoW9Tl9uBfXz2EX759AgsmWXHlHPbcEhGF0zfsxN6G0e8PrhseqqV3BOf7bFhaHTrFJx7EsRGLTpXVqO0uNzoHHZiUl6FhVNoQRRECr6IQ6S65uq6IJOxt6IHFZIhY7Kkw24LvfmYuPjnTjX/84168vKcJf/fbj3GqYxBP3bEc8yZZExSxemajAdWFWZhdnutLagHAZDTge+vmYU55Lh55/TBGHCw2RUQUztmuIcnbmeKO2nW2G009wwl/XLXp384z3dh9thsOV2xz+t6qb8PJdvbWxVPPkAPvn+hQvAwjkVaY2FLS29fQiwWVVkVDiD+7eBL+3w1zsO14B/75pf0YtLnw9FeWS1ZTTjVpJgO+u24umntH8PzOhsh3ICIiGie8F3Q9Mfa+DzlcONzSp0VIPmpDau+34XjbgKaxJIODzX3oHnJg0JZcS8HQ+MehyJTUHC4PDjT34e9X1yi+z50X1+LmZZVo67ejpjATpiSbUxuL5TUFWFlbgN9/cAZfWV0Do4FDn4iIInG62XMUzqDdhbePtOGS6cUoyEqLy2NM1OWVuoccsJgMyLKENrk/Pt0FYHQJQArldHtgFAQY2NYhhcZPi5/GpSPn++FwebB4cl5U98tJN2NaSfa4Smq9/n5NDZp7R/DxqS69QyEiSglOd+jwVT2nRDZ0DWPzofP6BRCkc2C0um9L70jcH0vtcddiDmvw0Ni6xt6495i+f6IDbx1pi+tjaEkURc2GEMd6MePtI+3YebY75ji6Bu042toPl8TnAI0v46/VT+OKt/CH1Pq1E9WnZpXAmmHGn/c16R0KEVFKSLbaUQeae2F3eZKuqFWShRPAm9YGx3iua0hx3YngJPZc1+iyerFK4sMWtUPN/XjjQEtM56ZWF43sLjfa+m0x72d/Uy+OtQ6ge8ihQVSJ1TFgT7rPiXgZdrhgd8VWQ4aJLSW1vQ29mJSXgZLcdL1DSRoWkxHXLyjHlkOtGHZw/goRpRa7y41dZ7vRMZC4NUDdGjQMnW5PzI2uYMnQXh2t6Dv2/xRL0ZxuD+oae7HjtLIRTC4OSY+ooXu0oFg052ZXFOv5atkjrJTDNfp4qfbqtw/Y8NGpzglT7GxrfRu2HI5tdAMTW0pq+xp6oh6GPBF8bvEkDDnc2FqfOsObiIgAoH/EhZbeERxtjb2nTKne4dh7arYcbsXmQ61R30+qt0VQXRt44nC6PQGvm1Ty7T20Wl9wiNZ46lFTc3GjrV95Ynvk/ADeONACjw4Vk1PtZfKMjZw+0yld4X08ivW9xMSWklb7gA1NPSMchixh6eR8VFjTselg9I0sIqJEOtYaOPzT23DWayUQqYaTzenGnnM9YRMkLXuZLiRp6jR2D2u67Js30Y5nwz/afdc19mL78Q7f8/QdM7/9SN0WTjItNZvIXkub040BmzNhj+cl9bp4e4RdCf0ASJ6MNpqEPt08mqaZjEl04iY5JraUtPY19AIAe2wlGAwCrpxTivdOdMDm5Jq2RJS8Qnpmk6eN6XO2awhNPcNo7ol/8aRYeTwi9jb04MOTnZrsL9G9WEp7q71D1V0e+YI/3tj1PqXUPP7pjsQNL32zvg3vHG3XbH99I06cbL9wwSq4lzfca5yqw961IIoiNh1qxaHm6JabSrWeZi053R4cbOpVvD0TW0pae871wGIyYE5Frt6hJKW1s0sx7HArnltERETSEj330tvsd3tE7Djdhaae4aj3YXdpV+E11h7kSOpb+tEZxTxMQL4xf0JivmEqNvwH7YmrkSE1SmHI7lLda/ze8Q4cboltKoEer5neybTbI8Ll8eBUlBc1UvH81srpjiFfL78STGwpae06242FVXmwmIx6h5KULppSgKw0I94+ot1VWCKiePO20ZJpcJ1nrOVokBmrGq/5gCPO0aqv+xuj68FR68OTnb7VBhLpRPsA6qOsPuxNQi6cL6OvzbmuIYltkqPlf7CpD33Dyob8arF8USzeOtKGT850oX3AFvW8Rk/Q9nJ3l7pZrrp1PCVLYpgkYaSUaN/bTGwpKY043DjU3IflNZxfK8diMuLSGcV4+0jbuCpcQUTqNTc347bbbkNhYSEyMzOxaNEi7NmzR++wAiTq40pp3tDYPewrziKX2H5yRv1amlLP1+FdT3Psb+GG24bsb+xfNXlR56AdjUG9H/7hBX+X9I048f6JjoRXsQWUzcH2DUVOQHjtAza0D0gvPSOKo0MmT3cO4qNTyoaI+798kb7DG7qGZR87Fh0Ddnx8qiugOJGezYn3jnfgk3E8Ck3tsU3ESzJkdyV0eHy8MLGlpLS/qRdOt4jlNQV6h5LU1s4uRUufLeor4UQ0/vT09GDNmjUwm83YtGkT6uvr8dOf/hR5eXl6hxbQcNeid83jEXG6Y1CTi3oH/ea7ySWL/knFsMOl2VJFydDT6L9OaHA0h5v70D3k0KSqtJfShNz72ip5iRNxFD8+1YWPT8knXdFeZ/A/DpGe477GnrCPHavhMIXImntH8MnpLvQOO3wjFyL1Nof7s+j71/v6ithzrht9w070DDvQKrFu7YDNiXYN1rOV4nB5FPeyxyra9/uFCzfxP8M/ONmJg2Pv92TqLIk2FFN8wiCKze6z3RAEYEk1e2zD+dTMYhgE4K36dsytsOodDhHp6Ec/+hGqqqrw9NNP+26rqanRJRYlDSOlCY7L7cGJ9kHUFmUh3Tw6NeVUxyDqz/fDaBBQXZgVXWxBv/sPq1QS09tH2uERRaxbNCmqx5WMJSgYPXpGB2wuZFlkpvyMHY9YwtJ7KR4l2vttyLSY0DvsQGV+ZtT3H01YxipLR9j2dMcgcjPMAQWWkieNCHWibQB9I0609ttQU5iFhVV5EKA+5uDPhhGnG009I+gZkk8uvYWvYn3PSX0sfXSqE30jTk3ez2oeP1k4xubsv3+iAwsq81BbFP5zNdxnvPcCiMGQ+OH27LGlpLTrbA9mleUiN92sdyhJrTDbgiWT8/H2Ua5nSzTRvf7661i2bBluvvlmlJSUYPHixXjyySf1DitEtI27jkE7jrcNYOeZbrxW14wznUO+obxaLxkiNxTZX/D8wlgE72n32chDnrXuTQnXc+g9HiJE9Aw54HRHX7AqeLmnqIWZlK1Vj9bHp7vw9pE27DnXg36Vy+IonTN7sLkPH57sDDru2r6mHo+IUx2DeK2uGX0joc9HyeN5tzAbL6QK3pEKwU81mvC9Rc+899FjTWf/1SSkjo+UvmHpYfmJWJlC7vDWNfbigxPqqqO7PWJA7QD/xxi0xVbY7K0jbfjLgZaY9qEWE1tKOg6XB7vPdmMF59cqcuWcUhxo6gsYTkZEE8/p06exceNGTJ8+HVu2bMHdd9+N++67D88++6zk9na7Hf39/QE/4fQOOxT3vgU3dP1/D9cG7ht2hjS6vb/2jA2HPdk+6Ncojp1/wzoe9XzCPd/g59o1FHnIr9adPgLkkzLfrSLw3omOqKvw/+3g+YD5m8E8QY3rZCBqV2xa+WNqvL/68/2+JWWUDOH1T86UxKI0GQ0+v21Oty5Fs4Kfk5r20qGW0GH5jd3D2HK4FT0K3rdADHNsZe53rmsIXUPqpkW8caAFb9Zf6BTR8uLKiI7LUDKxpaTzyZkuDDncuHxWid6hpIQrZ48eJ1ZHJprYPB4PlixZgsceewyLFy/G17/+dXzta1/Dxo0bJbffsGEDrFar76eqqirs/rcf78B7x0N7Bxq6hnE2KHlR00TqHnJg2/H2kKUw4tUO9u5X5+K0AaIpKKRV2IIg/1jeJMSbe3YrbMB7SfXw+sf99tH2mHp23EkytjPWMNTev3fYgRNtoT3iA349blLnd/DjNfeORL0cU8D+FLzjz3UNYcvh1pBzLd5LTfnzPoaSkRly/BNz7/tBaS9/Msyp9yd3oVLrOEVRTEjPNsDElpLQ20fakWE2YtWUQr1DSQlTi7NRW5SFN+tb9Q6FiHRUXl6OOXPmBNw2e/ZsNDQ0SG7/0EMPoa+vz/fT2NgY8TGGHaFD1PY19mB/U6/iOL0N2+BeH+9V/r6R8MPgRFG80GOrQVYaj7zW5nRLVhi1Od0BPT62oLVolTwd7XM5+R5r7+9aDr8ecbp9DWqp8ylYuEZ2POYkx9qoV3qo/JOr4Mc81NynqGDX9uMdmhWP7A8akhvuIkak81Tqz5ES52QqWCRFKrxoP3781y5WMvpFeqBw/Gn9UhxvG8SWw60YCVOkTCtMbCmpiKKIt4+2Yc20Il+REApPEARcM7cMH57sVD03iIhS35o1a3Ds2LGA244fP47q6mrJ7S0WC3JzcwN+lHApmGcZMpw44G8R7x3wW7hhj96/2F1u1DX2BiQ6wTlPNFV2B2xOvFbXjAGVn6k7TnfhYHNfSC/Fm/Vt2H68w/e7/5za4CQtUe18//ouwUfaEIfEdtDuwuZDyi/Ebj/egSG7dAIcTTLkdHtCRgPEg5rE2P9puMfmx354MrHL3gRHLbVsUSxnQVPPiGb7ilYsp68oir7CSkDwqIro9n+q/cLIls2HWkOW3pKPQdn+4+FE2wAONoWusx1NTN6q8tEWknO4PDguMSIhHCa2lFROtg+isXsEa2dzGHI0rp1XBqdbxLtHORyZaKL6p3/6J+zYsQOPPfYYTp48ieeffx5PPPEE7rnnnpj37QmTMMab5FBKiAF/O9E2iHNdQ2jwayie6woaHi0Td/D+3zzc6qvCer5PXe0Cp1v6wcIlYm8caPEV1gGAo60DksP3tB4mKAhCmEbqWPEoib8faOpF37ATLrcHr9U1o6FLWSPdK5olhOoaeyUvb0TTuE5EUhuNiL2eMQwl8L/vkF3qHAoVayGu7iFHSLEqtWeqxyMmTTXtE+2D2HTovGQ8Z7vk548rEcvw73DqWy7Msfanpvhb/fl+nO6M7b0jhPkcCUfJiI5gTGwpqWw+1ApBAK7g/NqoLJhkRbk1Paqr4EQ0vixfvhyvvPIKXnjhBcybNw/f//738fOf/xzr16+Ped8BPa4KmqtqGrTRtOODG0jehny4oalKYhLFwMIn6ou9iJL/lyM1pPpE+wBOd8g3nLWaG2w2hukR985/DHoKTrcHZzqH8PHpTvSOJTLRJo77JXqB5AzIVGmN5uXxxFAUKtJr6F8gy+0RZRMI//1IVaPuGXIEDFfVgtLkS+45KnkPDNpcON832iMbvMbzwaa+kItMko/j9//9Tb1xac+Eex3l/ua9uGVzjr6mUvO65fZqc7o1GWId7R5OtA+EvB/bB2z428HzipJpresOJHIeNRNbShoej4iX9jRhzdQilOam6x1OSjEYRocjbzvWkZA5DESUnG644QYcPHgQNpsNR44cwde+9jVN9huYqCnZPrb7R9z/2L/engCjwdsjIL/zIdmr//KtuHAVfaW43B44XB7NGnAuiWxMq2GJ3uk+aX7LuQQn2N7fwg1F/vCkuuVGlAxp99JiOcxYerojHfPg4ZJyxRz9r7ukmy5Mt/LG9t6JDmw7NnpfNb1rSkm9T+wu5VMMgl+OEac7cMrA2H93nO7C6c5B1DX2KorBq0HBEF1RFPHRqU7fMNew22rwjvTuQ+p8l3ouIw43thxuRf35/pjngmvxnu8aHB0hobSCsxaCe7kTMY+aiS0ljQ9OdqKhexg3L6vUO5SUdPXcUow43XjvREfkjYmIdCaXLIVbKsjL2wPkzcO8hXjCVcmVm6cZrnci2uGQn5zpxrvH2v2KW0V197DsLjdOtg9qVjBJSWjxXJolmp5JJVVs+0acYefjKW1T94+4QpYgUnJX/55+ufNG6kJFNLFpRWrt1ljmUcu9PkrOVbWnmNsjomPAjt1ne9TtIEikpx/u72e7hrDVb+kc4ML5cLJ9EG/IVP5W+v5Sm5j325yqhnRL1TUIHhZ8pDVy0TLverjevbHHliYMURTx620nUW5Nx3XzyvUOJyWtqClAfqaZw5GJSHPRNkiCG2JSQ5l7hh2Keu32NURuuPqKHEXRySXVqIy14dU5aA+YFytAiGmf/g3MM51DONzS51eER7uk83BLn+QeE1Wp1un2oK6xV7aX0mCQeb384nvveAeOhKkQrPSp7GvswYGg+YlKjsPOM5GLPQ3GOKRabTGzYFLrjCpdAqd7yAFHHHqToz3V1Fx0UXM6yyVl/ufEgM0Vkvglwypi7x5txzsaLQXZORDY03uyXX7qgfe1+cDbu53Ag8HElpLCpkOt2HG6G/94+VSkmXhaqmEyGnDN3DJsrW/jcGQi0ozHI+JvB8/7fo8l19l5pjtgWKJ/kSW5dmq4RrT3PkbD6PfGifaBsf0qH8Krts0Vfpiy9gmhfWyO31EFPSXREBF5GKqSZxNLVf4znUM41zUkO6c4XGVsr0g9jtH0evWMFbbyVdJWcB+5ecCBMYzKTDMF3N7SO4IthyNflPbO84wk0tGKpSf+falRYcmQxYWhqBK6fXSecFfQHNQL88wv7MTtESX32TFgD3sRJCfdJPs3KdFUcpfj/fyM5iW3u9y+3nZvzP6jDT44oW76QSKukzGDIN01dA3j4VcOYkGlFV9aWa13OCnts4snYdDuwtYjbZE3JiJS4HBLYCIVLkFo77dh08HzIY18by+mt8CMV7ihw73DDpxsDx1aKnWPjLH5ot4Gu9ScPjn+jXz/5XciOdDUK9vjnORLcgbYcTqxy8pIiXS85BrlURWPivI1OdzS56uOrfXrGfx0TrYPSlbAjhe1c5a1PAzefcV6bJ1uD5p6oqvILWXbsXbsPNN9oZcxjDcOtGBQYs7+R6c6cbxttCdT6pwtyraois0jigld57e5dwQfnxr9XPD25Lv83kBdQ4HJ/4GmXrSGqSDvq4qcgMHITGxJN6Io4p2jbfjCbz4CAPzq1iW+AiCkzoqaAkzKy8Cr+5r1DoWIUtTxtsBEtnckcAhauPZVU+8IHG5PyBw+uXlw4XrZth/vCEmqg3mT0tNBFUCHJUatxKNJZXN5cFai59bbSzLicEvGoka08feMLb/incsqFWc89I04Ax5XjeBYg4fJRlNYyeZ040TbAPol5pXKEkeTzUG7C/02p2YNcrnTPZ6FoqRY/ApXhaM2mVLSwy7xaBG3sLvcvmJR/rGFu5D19pG2mOYPyz0XueUVoznvozlKwSNXgkdInGwfUDQVTemR8Cav3s9Yl8wSZsDoiItPznThbOcQXG6P7HrYEEc/HxwKCpWpFV2fOJEGzveN4PW6FvxpdyNOdQxhekk2Nt62BJMLM/UOLeUZDAI+u7gCv9l+Gp2DdtVXB4lo4jrRNohl0y/8HtywC9cwirbhHlykJ1ojY70mHUHDB8OvkRr4mLFcTv3kdBcG7S6UWdN9VYb9bTse2/y2cMMHIw0tbO69sPxKtsWE/U29qh/PP4loH7AhPzNN/nHH5gCH68GJ9LjByYHJIMDpd67sPNONNdOKZGMN7IXvQdeQHVlpypu8/knDuc5hTC/N9v2+62w3si0mTCvJlrqrYmrOfLvLDZvTLXmuRUNpJ0Ki16yO5KNTXegfcWLdokkBt4dLpLVePkkvwfUDjgRd9It0EVB+vxGG8I+995UUAtvf1Bv2IoLd5cHHp7tQmpuOrDQTRIhYUJkXVbyRsMeWEqaxexh3//cerH78HWzYdBT5mWn4+RcX4a/3XYJpJTl6hzdufG5xJdweEX/ZL12Fj4goFuF7caSXA5G7x/bjHbJVOzPCNN69S9RE05gLjtvudKNvOLZiPPHseQgmd9y7Bu1hn4eaqqjB2vovXDjoH7mQKChZIkaN4Kc6aHcFXKy4MAc2/H4ONff5ep7kl3uKTkvvCI63DQTMO1fK2/OrdorrnnM92H5c/coHDpcHLb0jsn8Prs8RPPJC9r2vIgHedqwjqiWfgAvFt0QxvoNa/Y9xtK9VU88wBu0ulb3W8oKnbWhVsXzToVa8WS/f0+t91HDTRvw53WLAMbM53b5YvZ8Xbf02nO4c9NUpEEUxbDGqaDCxpYTYdqwdV//He3j/RAfuu2I63v+/n8L/fmM1Prt4EotFaWxaSTYWVFrxCocjE1EcON2jjZDgRq7HI/oq9h4MqiobzuZDrZJrUeZmmGMLNIKDzX0x96gmQ4fWByc7wz6PY63yS+AEk2uM+78+4Xr7RFH0LcUUi+C0RaqKrxKnOuQby9EMs9VseqPffg4o6EGXYvNbRsa3W4UBHjnfj11nu2V7MYMTnOD3sdyFDDVppiiK6A47skJ7Sl/H8CM+IpOrzi11nA409eK1usjtteAeU//ksa1f+eiIYC6PJ/wFqrGHVXqOBefbbx9p993mLUAV/BnSb3P5KrNH81hSmFFQ3L19pA1fe3Y3ppdm4+1/vhz/dNUMVBVw2HE8fX7xJBxo6ouqQUNEpMThlj4cbukL6MUDgDaJ5NQrUjtl77nekG2ULj+iVDxrryRDsajgIYX+h09Jw9lrxOFGY7d8MR5TmMT2VMdQTEvBHG3tR7/NGXEIrNa9YZFo3T+oxZxa/+TrLwcCe4/levN6x3pglU4BUDs3Velb1394rZLef288LVEMc08WB5tCL/YJQqTq6heEvL/9/h/u/Rqr4HM/0rkb/NK7PBfm3HrXEvf/bG8fsGl6hZCJLcXV2c4h3PfCPsypsOK5u1aizJqud0gTgrcn/IWdDXqHQkQpLriR6m3YBDd6Y0nupBrQrCUYKPgIBR+e9oGgZUpUJH+CMDpPbm9Dj+ww63BJixZLzTX3jCjusZFKOJWeh9Gcr2rP7eAkwG9xK3U7lBFtD5fSzZUmwIH7Ux5LuHWHw96vpR8dfue73DmpRaXpqIqOhXFWxUgGUeb/QPTL96jlf/FBFEVFQ/CDP3u8sQ7aR+NIN19IPw829YUMc47lu4SJLcXV996oh9Eg4Le3LUVuenyHldEFeZlpuH5+Of68t4lr2hKRptQ2OsLNR3V7RF+xIy/5QkbqHl+tcI17rWJR0kaN9FgiRLxW1+wbohqu4RuuEIy3J1CulzLc3D7/+8TS4Z4EHeAB1MRzvm/ENzTft58odyS13FUsvAmw4h5VhfG6PaJvDeloqE08RQC7z0lXWvcXvJSVmp53NSMQpF5njQegIM2ovIDY5kOtONcVfa/uqY5B39x0pUdOEOSfq/cCZnDxsw+DlliK5f3PxJbi5sOTnXjnaDvuWzudPbU6+NLKyei3uVQVuCAikuPfaPMv/hKuMWJ3ubHpkPxnkUcUfUVtvI0irYqjeHmXoQkuiBPJ0TBTOrwN5eD1efXknasW7vC9cSBycUG5JEwI8zf/RCiapMV/f4IQRQIos13fsBPdQ+HnSUbTeFZzgfhY60DMa4829sifV1onSlKGFRTcykozhcyBVhqa2ucgimLYIfFe0b7XtRScREcaQWF3uUMuovkvsdM/4gwYfm71q0GgZBi3mosIDUFDnJWdzqHP03s/99jzCd5PLMsxBeNyPxQXoihiw6YjmFyQidtXVesdzoS0rDof00qy8fzOBnxhaaXe4RDROPSxX49IrI34YOHm2Kp5JO/yMwO2wMZ6pH2NOCM37g8292FKcWzLv8hxuj043TGEkGWKgo6PVhWavY1krYZgqhHruRRrUTB/IkT1CZjEvoDEJKVS1CR6kXo5Y3kuai9ehYuouXd0KHvXoPSFjTOdQ7rUH5F6qv7J7uZDrSjOsWD11AvLWPmvz+tdrmt6SQ5mleUEvC6dQcudacX/MyCWt6R32Liv9zfoQlaw0fe/unODPbYUF3sbenCouR/3fmqa4oXASVuCIOBLKyZjz7keHG1VN4+FiCYmb8XWEYc7pNHkf3U9Uq9YLOQ6ZJxuT8DcxYBeY1GULaSitl0WLsFOxDqfh1v6cbS1P2RYazD/RrAWWvttkscsXC6ixcUNAUJMQxEP+VVXlVOSk658Hq+ovlEffL9kKDIGaBtHLIltbrpZk946t0eEZ+xn99lu7DnXIzun9UBTryZLYEVL6jAF94h3BM2TlxoGfaJ9AG/Wt8LpVnfc1M5rBpR9hgpC6HMNPkciveYcikxJ5/lPGpGTbsKNCyv0DmVC+8KSSmSlGfHEe6f1DoWIUsiZziEM2JzYfa5bdpuQ3iiNG+1yQ/eCG0VvHQnsndvbID33Tm0DOtzFWf/kKNz6oGqd6hhUVUG3e8ihqlfKfxkO+aHI4RL92E+CvhGn8gJQErcpqTJrNgoRLxT4P4baqshaz5HVSvB89ljEUqG6fcCGrfVtUd/P5nQHvC88oog361ux6ZD8eqxAYi8sBD+WVJLaGmGZHrmLL3aXxzcCRel9YqdwuZ8o9xQ8giZWTGxJc33DTrxxoAWfWzwJGWnsrdWTNdOM9RdV47W6lriWgyei8cfm9Ej2yCaqbai0J0hp74va9p7SOPYoKGajhlzCHC6sQ1GsIyxHLkm1Od043iadsLlU9iL5J47n+yJXRXZ5Yht23dw74hvaqUTvsLph2f5zHz0edelxNIlKc+8Idp/tjnjOSq0brVbwY+nVK213eWI+L7QiitKvdc+QdsP7ta4aH2lYeOegQ3E7MtL5F7HHllWRKZm8WtcMu8uDW5ZP1jsUAnDXxbUwCgJ++94pvUMhohQi1wxPluGUiaI0sU30vMkhhwtNPdINTbUNfP/XtqF7WLIhe6ilD6c6BiXv779sRzTnSXDvcqSeLDWPoda5rqGYhm96tWheYCz0hNt9thvNvSNxGT0gR6ookdLXL9GUFFnSQmu/TfKCm5KpG0pHaMid+vF6T9icbkUXg6QS5JDbIsQYy2oeTGxJU6Io4oWdDVhUlYc5Fbl6h0MASnLTceuKKryws5FzbYlIA6Otkt1n5YcpxyZeGaJ0aypS5VelQy21XsdXicMt0p/pSob3BVeyVSon3NJ9fk9DyZDg8Sy4Me9yi1EPEx29T+jtnYN22YsaieYKmmiuZnmcRImmDRTrkN62/tCCTl1DkYs87T6rbOSH1gmsVkOYpT4tg5f3ifR5d6C5V/XjM7ElTdU19uJo6wBuXVGldyjk58GrZiI/04x/feWQ4gXXiWhiU1ucRCvaN9zU3U/5mp+JP15q1wGNRbhlVvyPQCKOh9q5r3rwiNJJajhyvXf7GnpjDyiIXMXkaJsM3nWUU12sp2+4taLD6RtRVpBPLkneeiT6OctaC+4ZNxsDPzMG7eEvvHUPOTBgUzdsm4ktaeqFnQ3ItphwwwIWjUom1kwzvnP9bOw+14Mn3mchKSKKTK5HNlH5m9bDGdWGPRzDsLhUE+scxUTm9sEVZJOd/6FRekFCFKXP23hc0JBbMibSxfCSnHTNYxkP1F/YiW3Eih4Xu/xJXQg0GaJPN9UOG2diS5rptznxl/3nsW5RBbIsXCI52Xx20SR8ZmEFHt90FL/edlL11UQimtgSMdSwb8QZcYhwtNQ2NM/JLBsyHsU6fDiRPaip9h0Wv2q1o+I1rzbSaxrcGzdexPpqqR0dp3VRKCmJTn7VnPuDNpeqC2XMPkgzr9W1YMTpxq0rWDQqGQmCgJ/cvAAA8OPNx/DMR2dx8bRiFGWnITPNBGuGCTNKc7B4cj6rWROloEcffRTf/e53A24rLS1Fa2v4JTCSTVPPMHLS2TxJRYnssRUEIEmK4CriUbkerlRSYDQI8ARNFdgVpznvkeZrR6qmO1H1qKykrXbuezTeVLHEklJSNQnUfCz025ywZoSZzy+D3xykCVEU8fwnDVhQacW8SVa9wyEZFpMRv7hlEW5cWIFX65rxwckO9I+4Aj5Isy0mfGZRBf7P1TORn5WmY7REFK25c+firbfe8v1uNCbuIpWWSY0WVWiDTbRqzvES7jjyEF/QOxw4V1KPOdiJkIgeRj10DdpRkhvLMOvkfb3jOXpA6jxXc+6f6RxCZX5m1PdjYkuaONDUhyPn+/HY5+brHQpFIAgCrppTiqvmlPpu83hE9Aw7cLilH389cB7/u7sJ7xxpx6++tBjLagp0jJaIomEymVBWVqZ3GEkpeZuZqSVcZdd4D7f1JyC1XtPR+bLRRSxCRL+CCtekvY9Pd2Hdokmq7z9Or2NEJPm0VR6LM53RFyLjHFvSxAs7G5CZZsRnFrFoVCoyGAQUZltw6Yxi/OimBXj1njXItBhx+1M7seN0l97hEZFCJ06cQEVFBWpra3HLLbfg9OnEFYtL9gq1iUy6iIL1DDuiTnbcHhHvn+gIuT2Zen+VLodFE4PUuan2bG3qiX7eOBNbitmAzYnX97dg3aIKZLNo1LgwpyIXf/r6KkwuyMTfP70rLsMCiUhbK1euxLPPPostW7bgySefRGtrK1avXo2uLumLU3a7Hf39/QE/sUiitrYuCrMseoegO7WVTNWY4KcbJUAsawVP1PNTbt1lr4q8jLg+PhNbitnLe5ow7HDjSyuq9Q6FNFSUbcFzd62ENcOMbzy3R3aNOyJKDtdddx2+8IUvYP78+bjyyivx17/+FQDwzDPPSG6/YcMGWK1W309VVWzrj+9v6o3p/qlOTaGT8SaR1VZFMfV64bWKNsWedsrac65H9X0n6msU6T0Zbh1sLTCxpZi4PSKe/ugsltfkY34li0aNN8U5Fvz6tiVo7h3Bt17ar7p8PRElXlZWFubPn48TJ05I/v2hhx5CX1+f76exsTHBEepLzdqK4ST7UOxkE2sPd7Ie79qiLOk/aBhuMj1zFkWWlqznZ7xFaiZq/bkbjIktxeTtI2041zWMr15cq3coFCdLJufj326Yg631bfjNe6f0DoeIFLLb7Thy5AjKy8sl/26xWJCbmxvwM5HMLMvWO4QJrSIvloqzgFEQkrJXLDNNfkqWVj3MqdZTPRGNl36AvMzoVseQS+gLxlbZiPeFECa2pJooivjte6dRmZ+Bq+awCud4dvtF1fjsogr8+5Zj+PgUi0kRJaNvfetb2L59O86cOYNPPvkEN910E/r7+3HHHXfoHZquqgtletA0LnpzpnNI0/2Nd7Guf2oxG+FKoexBRHL1tFJ8qb34kGZMrtRs8eS8qLaXW1vakKCu/eQ6epRS3jnajj3nevDNK6bBOF4XMiMAow2Qxz4/H1OLs/HNF/ahvd+md0hEFKSpqQm33norZs6cic9//vNIS0vDjh07UF09sesfzCmfWD3RE4YIHEjKed1MX0k9h9sDl9uTsp0IchW7EzVknYktqeLxiPjJlmOYUpSFLyyp1DscSoDMNBM23rYUIw4X7n1+H1zuxFW/JKLIXnzxRbS0tMDhcKC5uRkvv/wy5syZo3dYukszsakzHqXaHMbOQTv6x1kRxhW1XOdeK1OLL0yNGHG60T6QHB0IqdZtxU97UuVPuxtxtHUAD149A6YkGzZB8TOtJBs/umkBdp7txk+2HNM7HCIi1Vj0JrUdbkm9ZegautUvH6M175xHtSrzM1Buje/SLROJeZy0peV6bIftoxXT4z09fHwcRUqozkE7Nmw6ilVTCnH9fOmiJDR+3bCgAl9ZXYPfvncaWw636h0OERElyNyK5BnW7b82ZjIRRWBhZR6qCjL1DiWsS6YXx3T/srGklheItDOjNAcA4EjgetBak5v2XmZVVixuQWVeTI/PxJai9v036jHicOMHn5sXc/EHSk0Pf3o2Fk/Owz//aT9OtA3oHQ4RJUBWmGqvNDFo9Z2fH2Wl1VQiAqgpykJmmlHvUOLKOHYuCGODVYuzY1u+iS6shf3ByU6dI7kg2ve83hW7mdhSVF7f34LX6lpw39ppAfMBaGJJMxnwm9uWIstixFef2Y2eIYfeIRFRksgda5wlO16WjZ5WlU0nF2SGHP9VUwo12Xey6Boc39+LmZagxD1Ob6hJeeN7uPNkv5798dBXJNdjy+JRlHSae0fwnVcOYnlNPr5x+TS9wyGdleam44nbl6Gt34Zv/HEPnCwmRUQAltewoEwquEhFIqnVAghSjdxo18tMVlIdVpZxWMAsNz3wApYQp8xWTfG3VOo9VtIjGut86FhE+6rK9djG6/wINv7eaRQXbo+If/qfOkAEfvZ3i7i8DwEAFlbl4Sc3L8SO09145PXDug9BIaL4UXLF3WIyINuSekOWi1KoIXzFrBJN9qOmsaxl4zQr6DyJpUcnGadFJWFIceF9nsnyfHPTzaou2ujN7REl31+zynJ9w75TgVwr0PsU4l3NnIktKfKb7aew80w3fvC5eUlfEIES6zMLK/DNK6bh+U8a8OzH5/QOh4h0FGtBGq0p7QUM7n3S06yy8AWacnSM1aCy1RiceAoQUJxjCUhAYqkKm0wNf2/D3aT2YKWoeL0C0Q5/77el5pJKbpkxvIKQWkuWecI8DyVi7SBJnSNFujnQ1Iv/2Hoc6xZVYN2iSXqHQ0non66cgWvmluJ7b9TjgxPJU/SAiLSjpGGi1RxMraQHNQiXTM73/T8Ze/kWVOahLFdZ9dBYqXn2ao+ZXGPVWywn1vMmmpw4U2ERtIunFamMZlQqJSNaiNf7qSo/+s4UPd7a6WZ1xcIyxu4nQpSMWwAwoywnhsgSq7Vfev1dDkWmpNA37MQ//nEvyqzp+N66eXqHQ0nKYBDws79bhBmlObjn+b042zmkd0hElORqi7IS/pjJnmzUFmXBmmlOinnKUr3vZpXTkIJ7Y70NeNPY/mJdwzMeSZXaOb/eHH6iTM2J91BkozH6HQefD59OwNKUat+z3reUKMpfbEo3pX6FbRaPIt15PCIe/FMd2vvt+PX6Jb4rq0RSsiwmPPnlpTAZBNz17G4MpOhwICJSL5rGy/xJ1vgFIsM/PP+hf/5xe9eSTKTLZ5TgUr9EsiIBlWAjJYNSc3CD58XKCV4aSi5xNRkNmFyQiSXVeYr2KyceQ5FjrSVSmHVh3nay5rhLJudjjYqeaalzJ/nGP1yQzLF5P4bkTuFEjCxJi/HCkhKJeg2Y2JKsjdtP4e2j7fh/N86JecFkmhgq8zOx8balONs5hPtfrJOdM0JEFE2DTbMhzn676RmWXo6lJCfxhaSsmWbkKyjmtLgqP+I28aT0dTAH9YyHu9fiyfkoyYlt+LXa0yPSfGY1vEns5MLkr0dSVZCpqnDapdNDk+EkHNnvIwhC0hY9LctNh8VkGB3BIhGi2yM9RFlLhQkonuf9vI90kSfWViMTW5L0Wl0zfrLlGD6/ZBLWr5ysdziUQlbUFuB76+bhnaPt+P4b9RNmOBbReBf8VpYaqhmvBphWPZj+87wS2cxNtrnHaoV7Gv49vME5RPD9tD4cg3ZX2L9PKcqWvD1SrqPmQoJ/1dfgnutkEcvyQxV5GQHvfS3nTkpVVNeiDWEQ5IszaUXtUUhPM+DaeeWyReHyM+M/WjIRH08ciky6eau+Dd96aT/WTCvE459fkJQFNii5fWnlZHz9sin4w0dn8Yu3T+gdDhHFQWlu6FV+tY1ci8wcsupCZfNwlTbU/b/OEjn0Lxl7i7SOyL8oU6IKxSiVaZE+vyK91mXW2HqSPzWrBNfNi//8Tim5YaaPGWOo2OxfgM2fxWTE5DCrZlw7ryzivl0aJp9Xz7nweNG+p9XM/1f7seE/jF7qfSP32aglb9JvNhqwsjb1lkryx8SWArxW14yvP7cH8ydZsfG2pUlfaIOS179cOwu3LK/Cz986gT98eEbvcIhIY1LVStV+Z8g1Cr0JaxxGIof85qVmHd5I99Grx1ZuGSO1ybvSu0XqoVX6+Ks0Wo9UrtNPy+sN3kTS/7GMBgFpJkOcV+6UFu7YxdILGnyRxuHyABhNjhbLJL1luekwK0impWq5qI00I019Qpio9+vlM0pgijC/1ZppVnWZaG6F8hoG3tfU6fYg3RwYj5Lj738RQY73mMb7vcCshQCMfsj9/oMzeOB/6nDRlAL891dXJtW6fpR6BEHADz83H9fOLcOjf6nH/+5p0jskItKQ0SAE9GzIDfdUolRmiRut25f+CZXcvtUk55HilCrEpEa0x2NhVZ70fiLcr0amp1yuJ3b0uEoX4wp3v0hKFC59FPlihNzamtJxragNrXC7dnapZG9WhtmIi6YUojpMb6UeEnUtxeUZTWzDFRidlK9sKkGGyiVzlIgmWY1lqHY0gpPvaF+zcL25xQmsFWAyCrg+QuVpb8+0J87T05jYEmxON7710gF87416XDevDE/dsVxx5UOicIwGAb+4dREunVGM//O/+/HnvUxuicYTuYTl4mlFuGxG6HIxwbLSTCi3ZmBBhArJWrXRE9VvGjwneFZ5YistZ6WZMG+SFQVZaZgpsQZmpEb+9NLoLlJcMaskoKcy5LwI/2vMlgUtteJNTLwXFOTmL8rFUW4dff38D1O2xSQ5NPmymcUozU1PqWlb8Ugt4jXcXqs8aEGl8h7MqcXZUffaxnP4vfy5FXhw/C8QBt8l3LrM0UYefKHObDREPP+9Hfb+owWmlYR+zsT6ejOxneC6hxy49ckd+PO+Jnzr6hn4ry8tUb3INJEUi8mIJ25fiounFeGfX9rPnluicUSUaSIXZlsC5lzKuXJOKVbUFsAQRaP48pklEbeRW4PUv7Ear46DnPTQ520QBN/xuHJ2ady/Z1dOKcDU4tFGY16GdJEvNXlYuPv493RH2rdJwdqklQp7+YDQ3sLLZ5agtigLK2oLsHZ2qeyIAC2GnAYnNFLnVSzDYoN5X9dIwiVawTGumqp+yHfw0718xoX3p3fJI0EQ4tKDbM0wqx4NEe61NxgEVCegqnU8p94H7zpch5UQ5eei1BrXkRh8PbYXbptbYcXSam0rvTOxncCae0fwhY0f4cj5fvz2tqW494rpKXXFkVJHutmIJ7+8DJdML8a3XtqPJ987rXdIRBSlSF8P8ah8K9U4z5VIHIPNkOtxlC0YFU1UkQU3Dv17KQyCgPIYixJFw7+X0duIVPt0wyUD/uv/Bm/n/c1iMmJRVZ6i5X2imSPob0pRNtLNRiyozIPFZAwZplwWplcLCFxfWerZzq0IXCLIu49wx3SJhss0zVOx/vM1c8PPgdRiHWDvLqx+VXzlLnxF2ocSRoOAqcXZYXsiA/Yd9AqtlBhurmg/slXnlO/DNNZ9GWl+bSQzwyxXFd1yauH/Hss0kwuPIb3cj9bzmZnYTlBt/TZ86ckd6Bq04/mvXYSrI3zoEcUq3WzE7768DJ9ZWIEf/u0IHvvbES4FRJTiwvUKadFckWoYC4KAy2eWYE65fKNOrqEeeLN2nz96VwEObsTKNWq9SV7EixRyc2nD3Me/F1quWJTRIIStdB2uqq6c4Cq9hdnhe/DmTcoNexymROgRnVaSE9DLFLwLqXPWmoAlW4KZ/XrFQ0cIBMYYvO6wGuG+zqXOm3WLJinbh8x+r59fjqqCzJBzPV9mtIZ3s4q8DCyuykdJbjpmluVIzqcejVnZe1rNkk6rpxZi9dTQhDzaJlG4ed3RfCKFS4KNgoCaoth7r71DkTnHljRnc7rxlad3oWvQgf/+6krZ0u1EWkszGfDzLy7CV1bX4In3TuPbLx+Ay+3ROywiUiDa5E2usZRuNob0evnzL1zokfl4sGaYo5rTt6gqL2xl1pgT0wh3T5ZLeN7nOTo0NPrnrLgqsszvkS5mylXVDSc/yqGogiD45txGOgZyfw+YTzy2jSHoXz0tmZwf9rmFjihQ/1hKn62S8y2aIfr++/M/5pGKvxkEYPLYMONZZbkhowekCoSlKehZDVxKLPxzNRkFyeJOcj3cSo+xf9IoF4JUIu7dtDjb4nsNphZnY3lNATLSjMhJN+OKWeGngESK0XsMg19jrd8urBA0AX3/jXocOd+PZ+5cIVsxkSheDAYBj9w4BwVZafjZ1uPoG3HiP29dwqWliJKdRg2QZdX5KMxWVrHTm4eaYxyyV12YherCLNicbgCjDU8tOw5Ceu3Gdj6lKBtNPcPISjP5btOiIZdtMWHQ7gp4fP+nE+khvH/Py0xDtsWIpp4R39+y0kyyc0LlGuwhiWwchqXLCd51uHPF26ieXZ6DnHQT8sJU8o328UutFlQPZ2FKcfRroI53wa+/3NBoqfNEyXDmtbNL0DFgR11jr2w1YO++w73vc9PNkgXCLGYDHGMX4U0GAU53bB8essv1xviZ1DFg9/0/+GJdmtGA/Mw0zCjNwSdnuiTvPyk/AxlpRlwztwwWU2BBqFgrVudlpmFZTQFKcyw41zUUZsvYDgJbkhPMGwda8MdPGvCPl09VVLGSKB4EQcB9a6fje+vmYsvhNnzrpf3waLgwO9FEt2HDBgiCgAceeEC3GORymWyZObK+okt+dyzNSceCyjzMDjPsOJoiQ/6xqfnECS6aUjm2lq9cwleaa8F188s1rxir+vt7LAxvD9dlM4p96xEX51gwt8KKtbOle2aULAHoTSplezqjjVeB4IeSS2xuWFCBq2aXAhitkjy7PDfi6xLNq+adPxypaNrS6nxcNy/80ijxFvw6eNculVrmpjQ3HRdptJ7whcczSv6u9l2SmWZCdWEWrplbFlBca0VtgW+udrQjFOR6YDPSjAFrBKu6aKPRG8H/sYNHXwbHZTAIuHRGsWTiHrxtutkYcrxinQ8MAJPyMjTZTzjssZ1AznUN4aGXD2JZdT4evGqG3uEQ4curauBwefCDvx5BuTUdD316tt4hEaW8Xbt24YknnsCCBQs03W+G2Yj+EWdM+5CaV+e1ZloRBmwuHGru892Wl2mOONQ03FqOctT2KAZvlpmmrkEea2+x2sahr9CRX8C5GWZkW0yYVpwddt1Y/8q5FpMRdpc7ZJu1s0vgdIs40TYQ+LjxXApF4b7VXFwQhNEe7Kpwcxmj3G2a0aD7CKXgkC0mI25cUIEBmwvbjrcH/M2aYUZpbjoWVuZhwOZCNLznudLXyC3xxojmvRKcMHuXbRqNQZqSyIK3KclNx9LqfAw73GjsHla8Hy+5XujgW73DpJWcY1UFmdjb0BNFFBKPPw76F9hjO0HYXW7c+/w+GI0Cfnnr4rhfMSFS6q5LpuArq2vw2/dOY2t9m97hEKW0wcFBrF+/Hk8++STy89XVT5hanC3ZcxOpGqv/0FhgtIcgmuFrFpMRRdmWgEQ17DxBxXu+wLs7g0ZDkX0NdyH0Ni0VZ1tQU5gVsj6uV7SJuv/f081GrJ1dGjap9beitkC2x9hbhTi0mJWiXcdkyeT8sAXF1BAEAVfOKZVcC9h/GzWunF2Kq+aUyr6msbCY5dt4M0pzsFqikrDBIMCaaca186SHCdcUZWF+FGvBRsP7nnHFOMQ3HN9QZFX3DX2NK/MzMaM0R9W5LTdALfiz46Ip0VVu9l/mLJq49Cx+F2m5rGjfX8xuJogfbTqGg819+PebFsblQ5QoFg9/ejYWVFrxrZf2o63fpnc4RCnrnnvuwfXXX48rr7xS9T5KciySa2VmW0whQ4LNpguNDqmE7uq5ZZgU5XfO7HL5JEJelMMMEbmQkeT9gh7Gm0AEF5eZX2lFZX4GihTOJY7EYjZgYVWebK9j6PI6kYbYqm/IllszIq7LKtc5Gs0hV9qe9fZ+VhVkYnqpmnNHH1kWEzLTTFheo27ZmXDCLac0uzw3ZN3fePG+3EpfS6mKuUYFax4r4T3n1Vx48j+f7U7pinb+CVi4iIuzLbJzu4N7cqMtbuZflC/ce1yuEnQslxXidfHqUzOLcUkUUy+Y2E4AW+vb8PsPz+CrF9fiyjmleodDFCLNZMB/3roYdpcb3/tLvd7hEKWkF198EXv37sWGDRsUbW+329Hf3x/wE8mMoMRheklOwLqgUqJt8ERKmry8DdTRpC7a9TK1aYVNKcrCksn5IUNVM9NMWFpdAINMhqfXiD9vAq5mXnI0ghvVckuwKLEmzDqlOekmTeYvx1oYJypRhLuspkBRRd5k5U1UI1eKHt3Of+iwV266GctrCjC9JLaLFrLLz/rfLrON/4WAvDBLN+UoWGN7SXW+7OeClsK9L4KPczyS0pW1hbh8RvhKylJcQd3ZOelmRfP7vVL33UKKNPeO4Fsv7ceCSiu+fe0svcMhklVdmIX71k7HXw+ex7tH2yPfgYh8Ghsbcf/99+O5555DerqyIaUbNmyA1Wr1/VRVVfn+5m1aRGqoGQ2Cb91PJdVLlVDem6i+yrAgIGA9VbUNO0EQxtbSVHd/rSh9eIvJgGvnlWnesxnciPYejylF2bhmbhkq8kbPSal5uZH493qnGQ0hBby0oPZCR6SLOrFSMtphckGmqrVUlYppaL3v4pOyzfMyzZLz8CvyMjQvwOYlCELEZS/nT7L6LgaFi2PNtCJ8ym9ZHKn5/+FONbljrfT89G6VlRZ4wUdqaonUvtWMYpG78FJmTYc104xJeRm+InvSjx/4e6zD0ZnYjmMOlwfffH4vPB4Rv+JyKpQCvnbJFMwozcajfzmsqgFENFHt2bMH7e3tWLp0KUwmE0wmE7Zv345f/vKXMJlMcLtD308PPfQQ+vr6fD+NjY2+v3nbN+EaJFLzS+Np1dRCLKzMk3l8ZUFcKGYz2vDSek6mXpTOsRUEQVWxrXAunlYUUrTH20MnCKNzeLVqf6SnGVEQ5bq1ivYbZk5qOMnQrlo8OT9sr3a0tFqvGlDeY+v/vowXbwhmiaHN4XphRy9cCb5ezuC81v94WUzGgN5FuSG/crQayRE86uVTYdagXRthfVo5V84uxdrZpbhufvgK38tqCrC0Wnm9B6kCYtHQ/x1JcfPdvxzG3oZe/OTmhb7FqImSmdlowCM3zsW5rmE889FZvcMhShlr167FwYMHUVdX5/tZtmwZ1q9fj7q6OhiNocmMxWJBbm5uwA8AQBAU9b5KzYeLp5KcdNQUXehl9c3fi6I57G3cepccGgdFQMfEJyW4eo50ISF/UmsSe9cf9iY0kYeihkpEQZt0sxFLJufHZZ6rnHDPK9oaKN4kX+nw/UTzBEwXCHXN3DKsnV3qa6PGq1cWAAqzLJhdnitZCMw0dsLmWC70fHs/37zDkN0e7wiR2GIM9/rnhhkho2Skglxs4S5mZfk952g+D7MsJmT73VftcfHey2QwoCjbguklofUdosHlfsapP+1qxB8/acA9n5oqW+GOKBmtmVaEK2eX4j/fPonPL6nUrPgK0XiWk5ODefPmBdyWlZWFwsLCkNujEa6pYg4eghahVRSu99ef0rat97OhOMeCM51DAX/LHWuM1volwsBoA2/VlMKA6qHR0CrZUjLkb26FFZlpRuw6243JBVlht410zCryMtDSOxJNiADUJxre46T3EG0lvPOjr51Xpmt1WAC+BPu1umZF28djWLaWvMmhINON5u3pn1thxeyyXM3mvksxGoSQGgFeGWlGrJpaiAK/zwUxKCkP/j2Y1HvaP2lzeaSLTvnLSTfjkunFeP9ER8jfonkrekOZN8mKEYd2o99WTS2ULZ4VK5NR0GTkAXtsx6H9jb3411cP4dIZxXjwqpl6h0MUte9cPxs2lxs/23pc71CIJjSpNtzVc8pw7bwy3zDMyO2t0S3KrMrmIypNpgqy0rBu0SQUZKVheU1+QEGUdLMR6xZNklzCpiQ3PWQIaaSExn94YUhCH0SrjuxpJdmoyMvAukWTUJwjf4HPYjJEnDO7dHI+rpmbuIvcUuvlxoOWgwYsJu2GTOtpSlFsPV7Br5nSkRlSm4mKi0chYkElrebwyynJSQ9YCvPCMOrR373To4KjnFKcpekQf28vvNJRDpX5Gb5e6OB7TC3OjrhMG3DhtRuMsE5xSU562DWd/R9XL+yxHWc6B+24+7k9KLOm45e3LIrrsA6ieKktysIdq2rw+w/P4PaLqkOWGCGiyLZt26b6vpX5megecqDcmoHcDDMy/YrTyA17lGt2er+HlH4bqem1Kcy2oDDboriny0tpYuTf6L54epGmBe7UDNP1d+28cticbhxoCvMYBgHphugb3lonprH2yPWPODWKZPyK11qz0RAEAaIo+g1F1nb/3qHD8eRNbJ1jxYy81XqDL2xVF2ahKj9TMjG/sHauGHJbOJdOLw75nJW7+La0+sIwevPYhZlsBdWZ/XnnGGs1vURJMu2j8bmR+pemyMfp9uCeP+5F77ATv719qeqhVkTJ4JtrpyMvMw0P/fkgHK74DH0holACRtesXT21CFkWE0py0gPmUoVsH6GlNqc8FzNKc1CusMc2WRRmxX8axJLJ+bhhQfjiK0ooLR4VrXC909kWE2oKww+RjkUqDGNWY7w9r3BPR/lyP5HVFGahICsN18wtw/UavGci8V7MszlHe2q9z8UiUWhM6+V78rPSQgqyKeH93J4fTWKJC+ekJ76d4opdOVv90qRMbMeRDX87ik/OdONHNy1gDxelPGuGGY99bj7qGnvxky1H9Q6HiFRKMxkwuzy+8+diFRzatfPKsGpqYdwez7/9GI/jYtawR0tujde1s0uxsCov7H31nrMab8l8TmtFTSee96hEmpcajXSzEZdML1aV8KmROdZj6isaNfasTFEksVL3UX0kFN6xOMeieLSmd6meC+dxcmS2sYw25VDkceK1umb8/sMzuOviWnxmYYXe4RBp4tp5Zfj7NTV48v0zKM1Nx1cvrp0QDQkiPfEtFqaKqOZDczXaT1BgWvcg6a0wy4KuIbveYaQk7/zs1VOLFCUMwUmomrmtggBADJ2nqtRlM4qx/XhoAaVE8lb7Lh9bg3lGaTYEAahSWAQPGC2aNbfCitJcC96JcfqC1p/LV84uhckYOE1Ei5HI3sJ9Skld/Irm4kHIfVXfk5LG4ZY+fPvlA1g1pRD/ct0svcMh0tTDn56N9n47fvDXI9hyuBVLqwtgNgpo7hlBU88I+kacmFaSjavnluL6+eUBxR+IKP60bBQlmqpGuwaPm5+ZhsbuYWSljc9mmNbnwrKafGw53KrtTnUS7fkTS0Jz9ZwyX/ISrgBZwOMF/a7Faxltj20yTKXLtpiwbtEk3+8mo0HVaMhpQcvXJMvF+ayApXpG/431pb5kejGyLLH3qMfSwz8+P1EnkN5hB+5+bg8KMtPwqy8tZqOexh2z0YD/vHUxVk8rxDMfncXTH56ByyOiIi8dlXmZqCnKxJ5zPfjrwfP4/Ydn8dObF4Z8kRARSfEtSxNhu0jL8+RlRNcQry3KQnGOJezc5fEgZO6vyv3IzfWNdt3XVDG3wurr5YwlsVSzvm3wa6Y0UfG/SFRTmIVTHYO+39WMIFhRW5CSF8vixXsEqwuzcK5rKOy20coZq/pemhNbHQRvRedYxTLiZHx/oo5zbo+Ib76wD239dvzv3askF0knGg8MBgHrV1Zj/cpqiKIIUQz84BNFEZsOteLfXj2EL2z8CH+8a2V0VfmISLUk6YBQZUpxFmxON2qLslB/vj/k7wsq82BzunG+b3QNWKNBkExyM9KMuGZuGbYcblW8rJGWSa3/a5CoOYjRiOYcsZgMsLs8AUmNXDt3Vln4ZY7ixbv8k9Je0Gj5X5xNdEEf/x7F1VOLUJQdPlnx9vz5z8WeN8mKOeW5+MuBFtVx+C/fNZ6o/bjMSTdjyeR8lOama57YZltM42bEW+o/gwns3988hvdPdOKHn52HBZV5eodDlBCCIIRczRMEAZ+eX47X7l2D3AwT1v/uE5xsH9ApQqLUprbgT7zXmYwHs9GAhVV5sg262qIszC7P9S0vYjIIskMJ081GXD2nDHMrpIcrlo6tqRvvZfgumV4U1/0rEcu54D2+gUukSB8zvYZ1WjPN+PT8ckxS0WMcbcxaLcGiRnGOJWK8U4uzsHpqUcia0QaDgNqi+FXNTgVan51VBZlxW2tZr6RW67cwE9sU9beD57Fx2yncflE1bl5WpXc4REmhMj8TL/7DKqSZDPiH/96DARvXPCSi2K2oLcDCyjykm42+SqJSMtKMsonA/ElWXDO3LOwSOmola6e5mrhWTS3E9JIc+QJeSULL19EapuCON7GtLcpCVYHywkWJIgiCbM/1gsq8gHmqpI055bkoy02t5dP85WemxW05NQ5FTkH7G3vx4J/qsLwmH/92wxy9wyFKKpPyMvDr9Utw6xM78OCf9uO3ty0ddxVCiZJJtsUEgyBgRqk+w0ITId1sRM1Y75PaHhODQUC6IbmTtWSQm27GnIrQRC8/Mw0VYxVqPzWrJNFhxdVlM4ojzietLswKmwBrLRmT6FThvRjhP4y83JqB7iG7Jj2U01P8s/bSGcVx2zcT2xRzqmMQdz27GyU56fjNbUvjNiSBKJUtrynAv90wB4+8fhi/ee8U/vHyaXqHRJQystOjaxqYjAbcmCTLzFXkZaR0T0Y0lkzO9/0/WSqtegUnaVqsZ+vfGPbOcU1FUkdCEISICU8ir8/esKAioY833uRlpqF32BFw24raArg9YtK9V/UmdzRmluWEHR0jh4ltCjnRNoAv/e4TiCLw+68sZ7EoojC+vKoa+xp68NM3j2NZdQFW1BboHRJRSoj3HNB4Wl4zcd7nqdCjxja8djyeC/9PNxuRE+UFqGik8mdAUgm6wMPjqtyssuiXVgI4xzZlbK1vw+d+/REEAC/+w0VczoQoAkEQ8MPPzUd1YSa++cJedA3a9Q6JiIgmOLXJvsV8ocl+zdwyrJ6qf5Ewksb0VT9MbJOYKIrY29CDrz27G197djemlmTjtXvXMKklUijLYsKv1y9B77AT9z6/D3aXW++QiIg0l2wNabn5ouzBVS8Zl3EiipXWQ7M5FDnObE43OgbsGHa4YTQIMBsFmIwGmAwCRBHoHLSjfcCG9n47OgbsaB8Y+33AjqaeEXQM2JFjMeHb187CnRfXJH2VQKJkM6ssFz++aQHuf7EOD/5pP355y2IOByJKcstqCmA28n2qFAvkESWfVFwCTS9ujRZsZmIbJ3vO9eDJ907j7aNtcLqVv1gFWWkoybGgOMeCy2YUY/XUQlw1pxQ5KVwogUhv6xZNQuegA99/ox5Ddhd+ccvihFaXJKLoqFkfdKKbWpyNUx2DvjV39RTcCcOe2gu0KKRFyY3ne/S0Wj6Lia3GRFHEr7edwk+2HENRtgV3rKrBrPJcZFuMcHlEuNwinG4PXGNXJoqyLSjJsaAk14KibEtc1rcjIuCrF9cix2LCd149iLU/3Y47L67BRVMKkZ+ZhmGHCzanG3aXBx4PUJSThskFmchM40ckEaWGuRW5mFaSnVSrJURawoa0U5xjQfeQI/KGOqotykJ+ZpreYVAS8V4DSDczsU06oijiu3+pxx8+OovPL5mEH3x2HhvGREnk75ZXYXZ5Lv79zWP48eZjYbc1GgTMKc/Fspp8XD6zBCtrCzjHiYgAjBbvcbg9kTdMIEEQ+Bk1gaVCMakFlXl6h0BJxnvtS6uRDMy6NLRx+yn84aOz+IdLp+Ch62ZxrSqiJDS/0opn7lyBlt4RHG3tx4DNhcw0EzLMRqSZDDAIQMeAHUdaB7D3XA9e3NmIpz88i3SzARdPK8ZNSyuxdnYJR1cQTWDpZuOESSILsy1o6hmOqjbBpPwMHG8bQJl1YqwpHBU2Dcc9b5LGEQuRiWMHSasyAUxsNfLGgRb8ePMxfH7xJCa1RCmgIi8DFWHm8V03vxzAaAG4XWe78e7RDmw6dB5vHWlDUbYF/3j5VNx2UXVSDfsjItLa4qo8zCjNjupiXm66GesWTQq5nfNLaSJhXhuZ50KXrSbYItPArrPdePBP+7GitgAbvjCfSS3ROJJuNuKS6cX4fzfOwQffvgJ/+PvlmF2eg++9UY8b/vN9HDnfr3eIRERxYzAIMRewZKuIiMLR6qIXE9sYHWsdwFf/sAuTCzLxxO1LuRwP0ThmNAi4fGYJ/vurK/H0V5ajb8SJdf/1IX7/wRnfcBoiIiI57PsY/0pzLQCAjAkyXSEW3veDVksjMbGNwc4z3fjiEx8jM82EZ+5cgTxWeiOaMD41qwSb778Ul88oxvfeqMedf9iFzkG73mHRBLZx40YsWLAAubm5yM3NxapVq7Bp0ya9wyIimlCml+bg2nllyEhjYhuJdzpXrkbLmjKxjZIoijjTOYRHXjuE9b/bgaJsC166exXX3COagPKz0vDb25fiB5+dh49OdeG6X7yP94536B0WTVCVlZV4/PHHsXv3buzevRtXXHEF1q1bh8OHD+sdGk1w3ila7K2kiYIjOJXJTTfjkunFmFOeq8n+WDxKRseAHR+d6kT9+X609NrQ1mdD34gTnYN2dA05YDIIuGVFFf7P1bNgzdTmKgMRpR5BEHDbRdVYUVuAbz6/D1/+/U5cM7cU96+dgTkV2nxQEylx4403Bvz+wx/+EBs3bsSOHTswd+5cnaJKHVOKsmHRaC1FIjnM7YkCFWRpN+KVia0fm9ONN+vb8NLuRnxwshOiCFhMBkzKy0BpbjqmlmRhSXU+FlRacemMYvbSEpHPjNIcvHbvGjz1wRn8ZtspbDn8PhZW5eGq2SW4dEYxZpfncokgShi3242XXnoJQ0NDWLVqleQ2drsddvuF4fP9/RO7ENr8SqveIRARUQySNrF1uj1o6hnB+b4RiCKQn5mGKcVZmq8b5/aI2HW2G28caMHrdS3ot7lQVZCBB9bOwJVzSjC7LBcGrRZXIqJxLd1sxD2fmobbLqrGK3ub8EpdC3669Tj+/c3jSDMaMKMsG3PKc1GZn4nSXAtKc9NRmGVBfpYZhVkWzsehmB08eBCrVq2CzWZDdnY2XnnlFcyZM0dy2w0bNuC73/1ugiMkmphWTy1CQ/cQstKStulNlPIEUUEpz/7+flitVvT19SE3Nz5D6xwuDw619GHH6S7sON2N3We7MexwBwYrAJMLMrGoKg+Lq/KwaHI+5pTnKl5HctjhQnPPCJp6R3CqfRD7GnrxyZludA7akWE24tp5Zfi7ZVVYWVvAZJaINNE95MBHpzpxuKUf9S39ONraj/YBu+TC7elmAwoy05CflYaCrDTkZaYhL8OMvEwzrBlm5KabkWkxIstiQrbFhKy0sX8tRmSnmybcnJ5EfDelGofDgYaGBvT29uLll1/G7373O2zfvl0yuZXqsa2qquLxJM25PSLeONACs9GAT4+tEU7KNPeOYMDmxKwyvidpYormuz7hie2h5j7Ut/RjxOnGgM2Jhu5hnOkcwsHmPticHgDArLIcXDSlEAurrKiwZsBoENAxYMfJ9kEcbR1AXWMvmntHAIxW05qUl4HibAuy000wCKMfoEN2NwbtLgzaXRiyuzBgd8Hh8gTEMrkgE0ur83HVnFJ8amYJe0uIKCGcbg86Buxo7behZ8iB7iEHeoYd6B5yjv4+7PD92z/iRO+wEy5P5FL4xTkWVOVnoDI/E1UFY//mZ6IyPwMVeRmKLwJGw+HyYMDmhNN9IT7/AjH+lwg9IuDyeFCUbdFk9A0T28iuvPJKTJ06Fb/97W8jbsvjSfHCxJaI1Irmuynh4yH+evA8Nm475fu9LDcdkwszcftF1VhWU4DlNQWKJhG399uwr7EXdY29aOkdQXu/HV2DdogYbUhlp5tQmZmB7PTRHo1siwm5GWZMysvApPwMVBdkojDbEr8nSkQkw2w0oCJvNNlUQhRFDDncGLRduFg3NHbhbtgxehGvb8SJpp4RNPUM40BTLzYdOh+SbJbkWJCXkYacdBNy0kc/E3PSTTAbDTAKAoxGAUZBgMkgwOURYXN6MOJ0w+50j12MdGHA5sSAzYX+sf/bgy4YKvH811Zi9dSiqO9H0RNFMaBXlkgPXOebiBIh4Ynt1y+dgjtW1SDDbERGmlF1D0JJbjqumVuGa+aWaRwhEVFyEQTBd4FOKY9HRNuADY3do8luY/dozYJ+mxP9Iy50DzlwrmsY/TYXnG4PPB4RblGEyyPC7RFhNAhINxmQkWZEutmIDLMR2RYTCrLSUF2YNZYcjybGuUHDoP0XWvdvzwoCYDIYMK04W5PjQoEefvhhXHfddaiqqsLAwABefPFFbNu2DZs3b9Y7NJrgjGPTu2aW5egcCRGNZwlPbPMytSvpTERE0gwGAeXWDJRbM7CitkDvcCgB2tracPvtt+P8+fOwWq1YsGABNm/ejKuuukrv0GiCEwQB6xZN0jsMIhrnWJqNiIhoHHjqqaf0DoGIiEg3XFSRiIiIiIiIUhoTWyIiIiIiIkppTGyJiIiIiIgopSmaY+st097f3x/XYIiIiJTyfidxKRFt8LueiIiSTTTf9YoS24GBAQBAVVVVDGERERFpb2BgAFarVe8wUl5XVxcAftcTEVHyUfJdL4gK0l+Px4OWlhbk5ORAEATNAgynv78fVVVVaGxsRG5ubkIecyLh8Y0vHt/44bGNr1Q6vqIoYmBgABUVFTAYOLMmVr29vcjPz0dDQwMvFGgkld5PqYDHU3s8ptrjMdVWNN/1inpsDQYDKisrNQkuWrm5uTwp4ojHN754fOOHxza+UuX4MgHTjrfBYLVaU+K1TyWp8n5KFTye2uMx1R6PqXaUftfzEjcRERERERGlNCa2RERERERElNKSNrG1WCx45JFHYLFY9A5lXOLxjS8e3/jhsY0vHt+Ji6+99nhMtcXjqT0eU+3xmOpHUfEoIiIiIiIiomSVtD22REREREREREowsSUiIiIiIqKUxsSWiIiIiIiIUhoTWyIiIiIiIkppSZfYbty4EQsWLPAtarxq1Sps2rRJ77DGpQ0bNkAQBDzwwAN6hzIuPProoxAEIeCnrKxM77DGlebmZtx2220oLCxEZmYmFi1ahD179ugd1rhQU1MTcv4KgoB77rlH79AoQX7961+jtrYW6enpWLp0Kd5//329Q0oK7733Hm688UZUVFRAEAS8+uqrAX8XRRGPPvooKioqkJGRgcsvvxyHDx8O2MZut+Ob3/wmioqKkJWVhc985jNoamoK2Kanpwe33347rFYrrFYrbr/9dvT29sb52SXehg0bsHz5cuTk5KCkpASf/exncezYsYBteEyVi9Ru5rGMjVRbmcc0eSVdYltZWYnHH38cu3fvxu7du3HFFVdg3bp1IScMxWbXrl144oknsGDBAr1DGVfmzp2L8+fP+34OHjyod0jjRk9PD9asWQOz2YxNmzahvr4eP/3pT5GXl6d3aOPCrl27As7drVu3AgBuvvlmnSOjRPif//kfPPDAA/jOd76Dffv24ZJLLsF1112HhoYGvUPT3dDQEBYuXIhf/epXkn//8Y9/jJ/97Gf41a9+hV27dqGsrAxXXXUVBgYGfNs88MADeOWVV/Diiy/igw8+wODgIG644Qa43W7fNl/60pdQV1eHzZs3Y/Pmzairq8Ptt98e9+eXaNu3b8c999yDHTt2YOvWrXC5XLj66qsxNDTk24bHVLlI7WYeS/Xk2so8pklMTAH5+fni7373O73DGDcGBgbE6dOni1u3bhUvu+wy8f7779c7pHHhkUceERcuXKh3GOPWt7/9bfHiiy/WO4wJ4/777xenTp0qejwevUOhBFixYoV49913B9w2a9Ys8V/+5V90iig5ARBfeeUV3+8ej0csKysTH3/8cd9tNptNtFqt4m9+8xtRFEWxt7dXNJvN4osvvujbprm5WTQYDOLmzZtFURTF+vp6EYC4Y8cO3zYff/yxCEA8evRonJ+Vvtrb20UA4vbt20VR5DHVgrfdzGOpnlxbmcc0uSVdj60/t9uNF198EUNDQ1i1apXe4Ywb99xzD66//npceeWVeocy7pw4cQIVFRWora3FLbfcgtOnT+sd0rjx+uuvY9myZbj55ptRUlKCxYsX48knn9Q7rHHJ4XDgueeew5133glBEPQOh+LM4XBgz549uPrqqwNuv/rqq/HRRx/pFFVqOHPmDFpbWwOOncViwWWXXeY7dnv27IHT6QzYpqKiAvPmzfNt8/HHH8NqtWLlypW+bS666CJYrdZx/xr09fUBAAoKCgDwmMYiuN3MY6meXFuZxzS5mfQOQMrBgwexatUq2Gw2ZGdn45VXXsGcOXP0DmtcePHFF7F3717s2rVL71DGnZUrV+LZZ5/FjBkz0NbWhh/84AdYvXo1Dh8+jMLCQr3DS3mnT5/Gxo0b8eCDD+Lhhx/Gzp07cd9998FiseDLX/6y3uGNK6+++ip6e3vxla98Re9QKAE6OzvhdrtRWloacHtpaSlaW1t1iio1eI+P1LE7d+6cb5u0tDTk5+eHbOO9f2trK0pKSkL2X1JSMq5fA1EU8eCDD+Liiy/GvHnzAPCYqiHXbvYmSDyW0QnXVub5mdySMrGdOXMm6urq0Nvbi5dffhl33HEHtm/fzuQ2Ro2Njbj//vvx5ptvIj09Xe9wxp3rrrvO9//58+dj1apVmDp1Kp555hk8+OCDOkY2Png8HixbtgyPPfYYAGDx4sU4fPgwNm7cyMRWY0899RSuu+46VFRU6B0KJVBw77woiuyxV0jNsQveRmr78f4a3HvvvThw4AA++OCDkL/xmCon12724rFUTmlbmcc0OSXlUOS0tDRMmzYNy5Ytw4YNG7Bw4UL84he/0DuslLdnzx60t7dj6dKlMJlMMJlM2L59O375y1/CZDIFTGin2GVlZWH+/Pk4ceKE3qGMC+Xl5SEXt2bPns3iNho7d+4c3nrrLdx11116h0IJUlRUBKPRGNJL0N7eHtIrQYG8le/DHbuysjI4HA709PSE3aatrS1k/x0dHeP2NfjmN7+J119/He+++y4qKyt9t/OYRk+u3cxjGb1IbWXv8+UxTU5JmdgGE0URdrtd7zBS3tq1a3Hw4EHU1dX5fpYtW4b169ejrq4ORqNR7xDHFbvdjiNHjqC8vFzvUMaFNWvWhCwJcfz4cVRXV+sU0fj09NNPo6SkBNdff73eoVCCpKWlYenSpb5K2F5bt27F6tWrdYoqNdTW1qKsrCzg2DkcDmzfvt137JYuXQqz2Rywzfnz53Ho0CHfNqtWrUJfXx927tzp2+aTTz5BX1/fuHsNRFHEvffeiz//+c945513UFtbG/B3HtPYedvNPJbRi9RWnjJlCo9pMkt4uaoIHnroIfG9994Tz5w5Ix44cEB8+OGHRYPBIL755pt6hzYusSqydv75n/9Z3LZtm3j69Glxx44d4g033CDm5OSIZ8+e1Tu0cWHnzp2iyWQSf/jDH4onTpwQ//jHP4qZmZnic889p3do44bb7RYnT54sfvvb39Y7FEqwF198UTSbzeJTTz0l1tfXiw888ICYlZXFzy9xtDrqvn37xH379okAxJ/97Gfivn37xHPnzomiKIqPP/64aLVaxT//+c/iwYMHxVtvvVUsLy8X+/v7ffu4++67xcrKSvGtt94S9+7dK15xxRXiwoULRZfL5dvm2muvFRcsWCB+/PHH4scffyzOnz9fvOGGGxL+fOPtG9/4hmi1WsVt27aJ58+f9/0MDw/7tuExVS5Su5nHMnbBbWUe0+SVdIntnXfeKVZXV4tpaWlicXGxuHbtWia1ccTEVjtf/OIXxfLyctFsNosVFRXi5z//efHw4cN6hzWu/OUvfxHnzZsnWiwWcdasWeITTzyhd0jjypYtW0QA4rFjx/QOhXTwX//1X77v3yVLlviWX5no3n33XRFAyM8dd9whiuLo8h+PPPKIWFZWJlosFvHSSy8VDx48GLCPkZER8d577xULCgrEjIwM8YYbbhAbGhoCtunq6hLXr18v5uTkiDk5OeL69evFnp6eBD3LxJE6lgDEp59+2rcNj6lykdrNPJaxC24r85gmL0EURVGXrmIiIiIiIiIiDaTEHFsiIiIiIiIiOUxsiYiIiIiIKKUxsSUiIiIiIqKUxsSWiIiIiIiIUhoTWyIiIiIiIkppTGyJiIiIiIgopTGxJSIiIiIiopTGxJaIiIiIiIhSGhNbIiIiIiIiSmlMbImIiIiIiCilMbElIiIiIiKilMbEloiIiIiIiFLa/wfx/aPlyanCHQAAAABJRU5ErkJggg==","text/plain":["
"]},"metadata":{},"output_type":"display_data"}],"source":["import arviz as az\n","\n","az.plot_trace({\"mu\":mh_simulation[\"mu\"]})"]},{"cell_type":"markdown","metadata":{},"source":["### 调试(Tuning)Metropolis-Hastings 算法 \n","\n","在建议分布 $\\mu_{n+1} | \\mu_{n} \\; \\sim \\; \\text{Normal}(\\mu_{n}, \\sigma)$中，$\\sigma$反映了 建议选项的分布宽度，对$\\sigma$ 的选择也会影响马尔科夫链的表现 \n","\n","🧐思考：我们仍然使用MH算法，尝试三种不同的$\\sigma$ \n","* $\\sigma = 0.01$ \n","* $\\sigma = 1$ \n","* $\\sigma = 100$ \n"," \n","请你判断以下的轨迹图和密度图分别对应上述哪种情况 \n","\n","![Image Name](https://www.bayesrulesbook.com/bookdown_files/figure-html/ch7-bad-idea-1.png) \n","\n","\n","可以结合以下代码进行判断"]},{"cell_type":"code","execution_count":20,"metadata":{},"outputs":[],"source":["import numpy as np\n","import matplotlib.pyplot as plt\n","import arviz as az\n","import scipy.stats as st\n","import pandas as pd\n","\n","def one_mh_iteration(current, sigma = 1):\n","\n"," \"\"\"\n"," def后面为函数值，current为输入值，作为建议分布(正态分布)的均值\n"," \n"," 接下来的代码和之前一样\n","\n"," return 则是该函数返回的值，我们将建议值，接受概率，和下一个位置这三个值组成了一个数据框进行返回\n"," \"\"\"\n"," proposal = st.norm(current, sigma).rvs()\n","\n"," prior = st.norm(loc = 3, scale = 1)\n"," def likelihood(theta):\n"," # 假设数据 Y 为 6\n"," Y = 6\n"," return st.norm(loc = theta, scale = 0.75).pdf(Y)\n"," \n"," proposal_posterior = prior.pdf(proposal) * likelihood(proposal)\n"," current_posterior = prior.pdf(current) * likelihood(current)\n"," alpha = min(1,proposal_posterior/current_posterior)\n"," next_stop = np.random.choice([proposal, current], 1, p=[alpha,1-alpha])\n"," return pd.DataFrame({\"proposal\":[proposal],\n"," \"alpha\":[alpha], \n"," \"next_stop\":[next_stop[0]]})\n","\n","def mh_tour(N, sigma = 1):\n","\n"," \"\"\"\n"," N为迭代次数，w为均匀分布的一半宽度\n","\n"," 我们在单次采样函数的基础上叠加了一个循环\n"," 将每次的采样结果存在mu[i]中，\n"," 在每次采样结束后，将采样结果替换为当前位置\n","\n"," 返回值为迭代次数，和每次采样得到的结果\n"," \"\"\"\n"," current = 3\n"," mu = np.zeros(N)\n","\n"," for i in range(N):\n"," sim = one_mh_iteration(current,sigma)\n"," mu[i] = sim[\"next_stop\"][0]\n"," current = sim[\"next_stop\"][0]\n"," \n"," return pd.DataFrame({\"iteration\": range(1,N+1),\n"," 'mu': mu})"]},{"cell_type":"code","execution_count":null,"metadata":{},"outputs":[],"source":["#===========================================================================\n","# 请修改 ... 中的值。\n","#===========================================================================\n","np.random.seed(84735)\n","\n","mh_simulation = mh_tour(N=5000, sigma= ...)\n","az.plot_trace({\"mu\": mh_simulation[\"mu\"]})"]},{"cell_type":"code","execution_count":null,"metadata":{},"outputs":[],"source":["#===========================================================================\n","# 可以自行复制代码多试几次\n","#===========================================================================\n","mh_simulation = mh_tour(N=5000, sigma= ...)\n","az.plot_trace({\"mu\": mh_simulation[\"mu\"]})"]},{"cell_type":"markdown","metadata":{},"source":["**总结** \n","\n","* 当$w = 0.01$时： \n","\n"," 建议分布的范围很窄，比如$Normal(3, 0.001)$，这会导致下一个建议值和当前值非常接近，则$f(\\mu')L(\\mu'|y) \\approx f(\\mu)L(\\mu|y)$ \n"," $$ \n"," \\alpha = \\min\\left\\lbrace 1, \\; \\frac{f(\\mu')L(\\mu'|y)}{f(\\mu)L(\\mu|y)} \\right\\rbrace \\approx \\min\\left\\lbrace 1, \\; 1 \\right\\rbrace \\; = 1 . \n"," $$ \n"," 那么我们很容易接受下一个采样值，但尽管马尔科夫链一直在转移，但探索的范围太窄了，我们可以看到采样一直在3附近 \n","\n","* 当$w = 100$时： \n","\n"," 类似的，我们可以推知此时建议分布的范围太宽了，超出了$\\mu$可能的取值 \n","\n"," 下一个建议值和当前值间隔太远，这会导致我们经常拒绝下一个采样值，多次停在当前位置。"]},{"cell_type":"markdown","metadata":{},"source":["**补充介绍：细致平衡 (detail Balance)** \n","\n","我们已经感受到，从一个自定义的建议分布$q(x)$中采样，竟然可以得到关于参数的后验分布$p(x)$。 \n","\n","🤔这非常神奇，这到底是怎么做到的？ \n","\n","一切的关键在于，MCMC 的性质：细致平衡 (detail Balance)。 \n","- 正如之前关于心情的例子一样，只要我们每天都记录自己的开心程度。我们就可以得到关于自己心境的分布。 也对应了参数的**后验分布**。 \n","- 这个概率分布代表了心境的乐观水平，分布的均值越大，代表个体越乐观。 \n","- 而我们在最开始记录心情之前，并不知道这个后验分布是什么形态的。 \n","- 我们只是按照**转移矩阵**提供的概率转化心情。换句话说，心情受到影响后如何转化是我们确定的(建议分布)，但我们却不清楚自己的乐观程度(后验分布)。 \n","- 最后需要注意的是，后验分布也**与最开始的心情无关**。无论最开始是开心还是悲伤，都不影响个体总体上乐观的心态。"]},{"cell_type":"markdown","metadata":{},"source":["![Image Name](https://cdn.kesci.com/upload/image/rk6x7auvhk.png?imageView2/0/w/640/h/640) \n"]},{"cell_type":"markdown","metadata":{},"source":["它的数学基础在于，当心情无限演化下去，状态转移的概率达到平衡，也就是所谓的细致平衡： \n","\n","假设，状态转移矩阵为 P \n","\n","| 心情 | 开心$\\theta^{(n-1)}_{1}$ | 冷静$\\theta^{(n-1)}_{2}$ | 悲伤$\\theta^{(n-1)}_{3}$ | ... | \n","| :----: | :----: | :----: | :----: | :----: | \n","| 开心$\\theta^{(n)}_{1}$ | 0.5 | 0.25 | 0.25 | ... | \n","| 冷静$\\theta^{(n)}_{2}$ | 0.5 | 0 | 0.5 | ... | \n","| 悲伤$\\theta^{(n)}_{3}$ | 0.25 | 0.25 | 0.5 | ... | \n","| ... | ... | ... | ... | ... | \n","\n","假设每天记录 10000个个体的心情，我们可以用 $\\pi$ 来描述这个群体的心情分布。 \n","\n","- 可以想象，第二天这 10000个个体的心情可能发生变化，也就是 $\\pi * P$ (矩阵乘法)。 \n","- 由于这 10000个个体的乐观程度不太可能瞬间变化，所以在总体上，他们的分布不换变化，也就是 $\\pi * P = \\pi$。 \n","- 那么就会有 $\\pi(i)* P(i,j) = \\pi(j)* P(j,i)$。其中 i 代表上面矩阵的行，j代表矩阵的列。 \n","\n","其中，满足上述公式的 $\\pi$ 就是参数的后验分布。 \n","- 然而，我们一开始并不知道 $P$。 \n","- 但我们可以通过加入建议分布$q(x)$和拒绝率$\\alpha$来替代 $P$。 \n","- 得到： $\\pi(i)* q(i,j) * \\alpha(i,j) = \\pi(j)* q(j, i) * \\alpha(j, i)$ \n","\n","也就是，我们通过建议分布产生参数*拒绝率的方式来采样模拟了P。 \n","- 一个不恰当的比喻：状态转移矩阵 P 是你真实的乐观程度，但只有上帝知道你的本来面目 P。 \n","- 然而，你能认识到自己当下的情绪 Q，并且在漫长人生中，你可以识别那些不属于自己的情绪 $\\alpha$ 。 \n","- 最后，你对自己的认识越来越接近上帝.... \n"]},{"cell_type":"markdown","metadata":{},"source":["最后，推荐 MCMC 讲解最好的视频(没有之一)：【蒙特卡洛（Monte Carlo, MCMC）方法的原理和应用】 https://www.bilibili.com/video/BV17D4y1o7J2/?share_source=copy_web&vd_source=4b5b4646c3f53f1b80954c381226c913 \n","\n","如果还是不懂 MCMC 原理，那放弃也行..... \n","\n","不了解 MCMC 原理，并不影响对于它的使用。"]},{"cell_type":"markdown","metadata":{},"source":["### 小结\n","\n","无论是在这些相对简单的单参数模型设置中，还是在更复杂的模型设置中，Metropolis-Hastings 算法都是通过两步之间的迭代，从后验中产生近似样本： \n","- 设定建议分布 \n","- 根据建议分布的参数、未标准化后验计算接受率 \n","\n","本节课我们只考虑了一种 MCMC 算法，即 Metropolis-Hastings。这种算法虽然功能强大，但也有其局限性。 \n","- 在以后的章节中，我们的贝叶斯模型将增加大量参数。调整 Metropolis-Hastings 算法以充分探索每个参数会变得很笨重。 \n","- 然而，即使 Metropolis-Hastings 算法的实用性达到了极限，它仍然是一套更灵活的 MCMC 工具的基础，包括自适应 Metropolis-Hastings、Gibbs 和 Hamiltonian Monte Carlo (HMC) 算法。其中，HMC 是 pymc 默认使用的算法。"]},{"cell_type":"markdown","metadata":{},"source":["## PyMC实战\n","\n","## A Beta-Binomial example in pymc \n","\n","假设我们进行了一项随机点运动任务的实验，每个试验中参与者判断正确的概率用 $\\pi$ 表示。\n","\n","**模型假设**\n","\n","- 我们假设参与者判断正确的概率 $\\pi$ 是从 **Beta 分布**中抽样的：\n","\n","$$ \n","\\begin{equation} \n","\\pi \\sim \\text{Beta}(\\alpha, \\beta) \n","\\end{equation} \n","$$ \n","\n","- 在每次试验中，参与者的成功次数 $Y$ 服从一个 **Beta 分布**：\n","\n","$$ \n","\\begin{equation} \n","Y \\sim \\text{Binomial}(n, \\pi) \n","\\end{equation} \n","$$ \n","\n","其中，$n$是试验的总次数，$Y$是成功次数。\n","\n","**模型设定**\n","\n","在这个例子中，我们可以使用Beta-Binomial 模型来表示：\n","\n","> 先验分布为：$\\pi \\sim \\text{Beta}(2, 2)$ \n","> 似然函数为：$Y|\\pi \\sim \\text{Bin}(10, \\pi)$ \n","> 总试验数为10，成功次数为9 $(Y = 9)$ \n","\n","\n","接下来，我们将使用 Pymc 来表达和设定 Beta-Binomial 模型"]},{"cell_type":"code","execution_count":1,"metadata":{},"outputs":[],"source":["import pymc as pm\n","import arviz as az"]},{"cell_type":"code","execution_count":2,"metadata":{},"outputs":[],"source":["Y = 9\n","\n","bb_model = pm.Model()\n","\n","with bb_model:\n"," pi = pm.Beta('pi', alpha=2, beta=2)\n"," likelihood = pm.Binomial('likelihood', n=10, p=pi, observed=Y)"]},{"cell_type":"markdown","metadata":{},"source":["**代码解释** \n","\n","```python \n","Y = 9 \n","\n","bb_model = pm.Model() \n","\n","with bb_model: \n"," pi = pm.Beta('pi', alpha=2, beta=2) \n"," likelihood = pm.Binomial('likelihood', n=10, p=pi, observed=Y) \n","```\n","\n","在pymc中，一个模型的定义通常包含了先验和似然两部分(其复杂性视模型复杂程度而定)： \n","\n","1. 设立容器 \n"," * 在pymc中，你需要创建一个`pm.Model()`来容纳你模型中的变量 \n","\n"," * 接下来你需要定义模型里的各种参数，即`with bb_model:`，表明接下来你对模型中各参数的设定，都会被添加到该模型中 \n","\n"," * 或者也可以直接一步写成：`with pm.Model() as bb_model:` \n","\n","2. 定义先验 \n"," * 在这个例子中，我们需要对$\\pi$进行定义 \n","\n","3. 定义似然 \n"," * 我们通过observed = Y，将收集到的数据传入似然函数中 \n"]},{"cell_type":"markdown","metadata":{},"source":["### 模型可视化 \n","\n","可以通过PyMC3自带的可视化工具将模型关系可视化"]},{"cell_type":"code","execution_count":null,"metadata":{},"outputs":[{"data":{"text/html":[""],"text/plain":[""]},"metadata":{},"output_type":"display_data"}],"source":["pm.model_to_graphviz(bb_model)"]},{"cell_type":"markdown","metadata":{},"source":["### 使用mcmc进行采样 \n","\n","在以下例子中，将 MCMC 采样方法得到的参数样本赋值为 `trace`。 \n","- 使用 `sample` 方法进行 MCMC 采样模拟过程。 \n","- 设置参数 `draws` 来控制 MCMC 采样的次数。 \n","- `chains` 表示同时运行几条MCMC链。 \n","\n","我们可以使用 `arviz` 的方法 `plot_trace` 来可视化该结果 \n","- 左图为参数分布图 \n","- 右图为 trace 图，代表随着采样的进行(即x轴1-5000次采样)，每个参数值的大小(即y轴为每个采样参数的大小)。"]},{"cell_type":"code","execution_count":7,"metadata":{},"outputs":[{"name":"stderr","output_type":"stream","text":["Auto-assigning NUTS sampler...\n","Initializing NUTS using jitter+adapt_diag...\n","Sequential sampling (1 chains in 1 job)\n","NUTS: [pi]\n"]},{"data":{"application/vnd.jupyter.widget-view+json":{"model_id":"af34dc94f88146e5a40a2f49a01e94d6","version_major":2,"version_minor":0},"text/plain":["Output()"]},"metadata":{},"output_type":"display_data"},{"data":{"text/html":["
\n"],"text/plain":[]},"metadata":{},"output_type":"display_data"},{"name":"stderr","output_type":"stream","text":["Sampling 1 chain for 1_000 tune and 5_000 draw iterations (1_000 + 5_000 draws total) took 1 seconds.\n","Only one chain was sampled, this makes it impossible to run some convergence checks\n"]},{"data":{"text/plain":["array([[, ]],\n","      dtype=object)"]},"execution_count":7,"metadata":{},"output_type":"execute_result"},{"data":{"image/png":"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","text/plain":["
"]},"metadata":{},"output_type":"display_data"}],"source":["#采样过程仍在该容器中进行\n","with bb_model:\n","    trace = pm.sample(draws=5000,                   # 使用mcmc方法进行采样，draws为采样次数\n","                      chains=1,                     # 设置MCMC的链数\n","                      random_seed=84735)            # 设置随机状态，以获得与notebook相同的结果\n","\n","az.plot_trace(trace)"]},{"cell_type":"markdown","metadata":{},"source":["### 采样的时间进程  \n","\n","下图展示了第一条Makov链的前20个采样结果和前200个结果  \n"]},{"cell_type":"code","execution_count":8,"metadata":{},"outputs":[{"data":{"text/plain":["array([[, ]],\n","      dtype=object)"]},"execution_count":8,"metadata":{},"output_type":"execute_result"},{"data":{"image/png":"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","text/plain":["
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","text/plain":["
"]},"metadata":{},"output_type":"display_data"}],"source":["# 选取第一条Makov链的前20个采样结果和前200个结果\n","samples_20 = trace.posterior[\"pi\"].sel(chain=0).values[:20]\n","samples_200 = trace.posterior[\"pi\"].sel(chain=0).values[:200]\n","\n","# 绘图\n","az.plot_trace({\"pi\": samples_20})\n","az.plot_trace({\"pi\": samples_200})"]},{"cell_type":"code","execution_count":10,"metadata":{},"outputs":[{"data":{"text/html":["
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pi
00.741947
10.544469
20.858457
30.415141
40.739664
......
49950.730776
49960.938275
49970.821699
49980.821699
49990.821699
\n","
5000 rows × 1 columns
\n","
"],"text/plain":["            pi\n","0     0.741947\n","1     0.544469\n","2     0.858457\n","3     0.415141\n","4     0.739664\n","...        ...\n","4995  0.730776\n","4996  0.938275\n","4997  0.821699\n","4998  0.821699\n","4999  0.821699\n","\n","[5000 rows x 1 columns]"]},"execution_count":10,"metadata":{},"output_type":"execute_result"}],"source":["import pandas as pd\n","post_pi = pd.DataFrame({\"pi\": trace.posterior[\"pi\"].values.reshape(-1)})\n","post_pi"]},{"cell_type":"markdown","metadata":{},"source":["### 采样结果可视化  \n","\n","* 将采样结果(5000次采样)对比真实的后验分布(黑线)Beta(11, 3)  \n","\n","* 可以看到这个采样结果很好地近似了后验分布"]},{"cell_type":"code","execution_count":15,"metadata":{},"outputs":[{"data":{"image/png":"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"]},"metadata":{},"output_type":"display_data"}],"source":["import matplotlib.pyplot as plt\n","import seaborn as sns\n","import numpy as np\n","import scipy.stats as st \n","\n","fig, (axs1, axs2) = plt.subplots(1, 2, figsize=(15, 4))\n","\n","#绘制采样结果直方图\n","sns.histplot(data=post_pi, \n","             x=\"pi\", \n","             bins=30,\n","             ax=axs1,\n","             edgecolor='#20699d', \n","             color=\"#6497b1\",\n","             alpha = 1)\n","\n","#绘制采样结果密度分布图\n","sns.kdeplot(data=post_pi,\n","             x=\"pi\",\n","             color='#6497b1',\n","             fill=True,\n","             alpha = 1,\n","             ax=axs2)\n","\n","#绘制真实后验分布图\n","x = np.linspace(0.2, 1, 10000)\n","y = st.beta.pdf(x, 11, 3)\n","axs2.plot(x, y, color='black')\n","\n","\n","sns.despine()"]},{"cell_type":"markdown","metadata":{},"source":["## 练习  \n","> 📃以**Normal-Normal模型**为例来练习使用pymc进行MCMC模拟    \n","\n","在lec5中，我们利用基于**Normal-Normal模型**的例子练习了网格近似法莱估计参数。现在，我们将使用同样的模型，并通过 PyMC 实现 MCMC 采样 来近似后验分布。\n","\n","**模型设定：**  \n","- 假设 $\\mu$ 是参与者在随机点运动任务中的**平均反应时间**（单位：ms）。\n","- 假设 $\\sigma$ 是参与者在随机点运动任务中的**标准差**（单位：ms）。  \n","  \n","**先验分布**  \n","我们对参与者的反应时间有一个初步的假设：\n","- 先验分布设为正态分布，平均反应时间$\\mu$约为 300 ms，标准差 $\\sigma$ 为 50 ms。\n","- 因此， $\\mu$ 的先验分布可以表示为\n","$$\n","\\mu \\sim \\text{Normal}(300, 50)\n","$$  \n","\n","**观测数据**  \n","- 观测数据 $Y$ 表示参与者在实验中实际的反应时间。\n","- 假设我们收集了被试完成 5 次实验的反应时间：\n","$$\n","Y = [320, 310, 280, 340, 300] ms\n","$$\n","\n","- 反应时间 $Y$ 的标准差 $\\sigma$ 被认为是已知的，$\\sigma$ = 20 ms。\n","\n","**条件模型** \n","- 观测数据 $Y_i$服从一个均值为$\\mu$、标准差为 $\\sigma$ 的正态分布：\n","\n","$$\n","Y_i |\\mu \\stackrel{ind}{\\sim} \\text{Normal}(\\mu, \\sigma^2)\n","\\tag{1}\n","$$\n","\n","
\n","\n","\n","- 结合先验分布，完整的模型表示为：\n","\n","$$  \n","\\begin{equation}  \n","\\begin{split}  \n","Y_i|\\mu & \\stackrel{ind}{\\sim} \\text{Normal}(\\mu, \\sigma^2) \\\\  \n","\\mu & \\sim \\text{Normal}(\\mu_0, \\sigma_0^2) . \\\\  \n","\\end{split}  \n","\\tag{1}  \n","\\end{equation}  \n","$$  \n","\n","
"]},{"cell_type":"code","execution_count":41,"metadata":{"collapsed":false,"id":"D29892D9FCFB40EB970897403DB9B464","jupyter":{},"notebookId":"6536255793c31faf0a5a8dc8","scrolled":false,"slideshow":{"slide_type":"slide"},"tags":[],"trusted":true},"outputs":[],"source":["import pymc as pm\n","import arviz as az"]},{"cell_type":"code","execution_count":42,"metadata":{"collapsed":false,"id":"512B9E9C88FC4ABD8AD53894D80D291B","jupyter":{},"notebookId":"6536255793c31faf0a5a8dc8","scrolled":false,"slideshow":{"slide_type":"slide"},"tags":[],"trusted":true},"outputs":[],"source":["#===========================================================================\n","#                            请修改 ... 中的值。\n","#===========================================================================\n","\n","observed_data = [...]\n","\n","#1. 设立容器\n","\n","with pm.Model() as gp_model:\n","    #2. 定义先验\n","    mu_prior = pm.Normal('...', mu= ..., sigma= ...)\n","    #3. 定义似然\n","    Y_obs = pm.Normal('...', mu=..., sigma= ..., observed=...)"]},{"cell_type":"code","execution_count":43,"metadata":{"collapsed":false,"id":"5DF28BEE427F4F81B0C04D2ED2DF3676","jupyter":{},"notebookId":"6536255793c31faf0a5a8dc8","scrolled":false,"slideshow":{"slide_type":"slide"},"tags":[],"trusted":true},"outputs":[{"name":"stderr","output_type":"stream","text":["Auto-assigning NUTS sampler...\n","Initializing NUTS using jitter+adapt_diag...\n","Sequential sampling (1 chains in 1 job)\n","NUTS: [mu_prior]\n"]},{"data":{"application/vnd.jupyter.widget-view+json":{"model_id":"4be1233f079949e290e2a57bc3c3d936","version_major":2,"version_minor":0},"text/plain":["Output()"]},"metadata":{},"output_type":"display_data"},{"data":{"text/html":["
\n"],"text/plain":[]},"metadata":{},"output_type":"display_data"},{"name":"stderr","output_type":"stream","text":["Sampling 1 chain for 1_000 tune and 5_000 draw iterations (1_000 + 5_000 draws total) took 1 seconds.\n","Only one chain was sampled, this makes it impossible to run some convergence checks\n"]}],"source":["#===========================================================================\n","#                            请修改 ... 中的值。\n","#===========================================================================\n","with gp_model:\n","    trace = pm.sample(draws= ...,                    # 例如采样次数设为500-5000次\n","                      chains=1,                     # 链为1条\n","                      random_seed=84735)"]},{"cell_type":"code","execution_count":44,"metadata":{"collapsed":false,"id":"40B74FC26203418183EE59E85E43E10C","jupyter":{},"notebookId":"6536255793c31faf0a5a8dc8","scrolled":false,"slideshow":{"slide_type":"slide"},"tags":[],"trusted":true},"outputs":[{"data":{"text/html":["\n","            
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arviz.InferenceData
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      <xarray.Dataset>\n","Dimensions:   (chain: 1, draw: 5000)\n","Coordinates:\n","  * chain     (chain) int64 0\n","  * draw      (draw) int64 0 1 2 3 4 5 6 ... 4993 4994 4995 4996 4997 4998 4999\n","Data variables:\n","    mu_prior  (chain, draw) float64 326.3 308.7 308.7 ... 302.8 295.2 303.9\n","Attributes:\n","    created_at:                 2024-10-14T02:22:18.255920+00:00\n","    arviz_version:              0.19.0\n","    inference_library:          pymc\n","    inference_library_version:  5.17.0\n","    sampling_time:              0.9197731018066406\n","    tuning_steps:               1000

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      <xarray.Dataset>\n","Dimensions:                (chain: 1, draw: 5000)\n","Coordinates:\n","  * chain                  (chain) int64 0\n","  * draw                   (draw) int64 0 1 2 3 4 5 ... 4995 4996 4997 4998 4999\n","Data variables: (12/17)\n","    acceptance_rate        (chain, draw) float64 0.5652 1.0 ... 0.5689 1.0\n","    diverging              (chain, draw) bool False False False ... False False\n","    energy                 (chain, draw) float64 28.89 27.74 ... 28.47 27.81\n","    energy_error           (chain, draw) float64 0.8018 -0.9568 ... -0.6153\n","    index_in_trajectory    (chain, draw) int64 1 -1 0 -1 0 0 ... -1 1 -1 -1 1 -1\n","    largest_eigval         (chain, draw) float64 nan nan nan nan ... nan nan nan\n","    ...                     ...\n","    process_time_diff      (chain, draw) float64 0.000113 8.7e-05 ... 9.1e-05\n","    reached_max_treedepth  (chain, draw) bool False False False ... False False\n","    smallest_eigval        (chain, draw) float64 nan nan nan nan ... nan nan nan\n","    step_size              (chain, draw) float64 1.603 1.603 ... 1.603 1.603\n","    step_size_bar          (chain, draw) float64 1.338 1.338 ... 1.338 1.338\n","    tree_depth             (chain, draw) int64 2 1 1 1 1 1 2 2 ... 2 1 1 1 1 1 1\n","Attributes:\n","    created_at:                 2024-10-14T02:22:18.262637+00:00\n","    arviz_version:              0.19.0\n","    inference_library:          pymc\n","    inference_library_version:  5.17.0\n","    sampling_time:              0.9197731018066406\n","    tuning_steps:               1000

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      <xarray.Dataset>\n","Dimensions:      (Y_obs_dim_0: 5)\n","Coordinates:\n","  * Y_obs_dim_0  (Y_obs_dim_0) int64 0 1 2 3 4\n","Data variables:\n","    Y_obs        (Y_obs_dim_0) float64 320.0 310.0 280.0 340.0 300.0\n","Attributes:\n","    created_at:                 2024-10-14T02:22:18.264633+00:00\n","    arviz_version:              0.19.0\n","    inference_library:          pymc\n","    inference_library_version:  5.17.0

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dtype=object)"]},"execution_count":45,"metadata":{},"output_type":"execute_result"},{"data":{"image/png":"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","text/plain":["
"]},"metadata":{},"output_type":"display_data"}],"source":["az.plot_trace(trace)"]},{"cell_type":"code","execution_count":46,"metadata":{"collapsed":false,"id":"098AFCD3A3F942089AD001CFBA34F4E1","jupyter":{},"notebookId":"6536255793c31faf0a5a8dc8","scrolled":false,"slideshow":{"slide_type":"skip"},"tags":[],"trusted":true},"outputs":[],"source":["# 从 MCMC 采样结果中提取参数 mu 的后验分布样本\n","post_mu = pd.DataFrame({\"mu\": trace.posterior[\"mu_prior\"].values.reshape(-1)})"]},{"cell_type":"code","execution_count":63,"metadata":{},"outputs":[{"name":"stdout","output_type":"stream","text":["后验分布的均值: 309.68992248062017\n","后验分布的标准差: 8.804509063256237\n"]}],"source":["#===========================================================================\n","#                            为了和真实的后验分布进行比较，计算真实的后验分布。\n","#===========================================================================\n","\n","\n","# 先验分布的均值和标准差\n","mu_prior = 300  # 先验均值\n","sigma_prior = 50  # 先验标准差\n","\n","# 观测数据的标准差 (已知)\n","sigma_obs = 20\n","\n","# 计算观测数据的数量和均值\n","n = len(observed_data)  \n","y_mean = np.mean(observed_data)  \n","\n","# 计算后验分布的均值和方差\n","posterior_mean = (sigma_obs**2 * mu_prior + n * sigma_prior**2 * y_mean) / (n * sigma_prior**2 + sigma_obs**2)\n","posterior_variance = (sigma_prior**2 * sigma_obs**2) / (n * sigma_prior**2 + sigma_obs**2)\n","posterior_std = np.sqrt(posterior_variance)\n","\n","print(f\"后验分布的均值: {posterior_mean}\")\n","print(f\"后验分布的标准差: {posterior_std}\")"]},{"cell_type":"code","execution_count":64,"metadata":{"collapsed":false,"id":"FE166A2DE62142C4AFE9425EE8EF6354","jupyter":{},"notebookId":"6536255793c31faf0a5a8dc8","scrolled":false,"slideshow":{"slide_type":"slide"},"tags":[],"trusted":true},"outputs":[{"data":{"image/png":"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"]},"metadata":{},"output_type":"display_data"}],"source":["fig, (axs1, axs2) = plt.subplots(1, 2, figsize=(15, 4))\n","\n","sns.histplot(data=post_mu, \n","             x=\"mu\", \n","             bins=30,\n","             ax=axs1,\n","             edgecolor='#20699d', \n","             color=\"#6497b1\",\n","             alpha = 1)\n","\n","sns.kdeplot(data=post_mu,\n","             x=\"mu\",\n","             color='#6497b1',\n","             fill=True,\n","             alpha = 1,\n","             ax=axs2)\n","\n","\n","\n","# 计算真实的后验分布\n","x = np.linspace(200, 400, 10000)\n","y = st.norm.pdf(x, posterior_mean, posterior_std)\n","axs2.plot(x, y, color='black')\n","\n","sns.despine()\n"]},{"cell_type":"markdown","metadata":{"id":"7CE63A83CCDC48B694A365B9E85D3652","jupyter":{},"notebookId":"6536255793c31faf0a5a8dc8","runtime":{"execution_status":null,"is_visible":false,"status":"default"},"scrolled":false,"slideshow":{"slide_type":"slide"},"tags":[]},"source":["### 总结  \n","\n","在本节课中，我们深入探讨了 Metropolis-Hastings 算法 及其实际应用。通过 Normal-Normal 模型 的例子，我们演示了如何使用 MCMC 来近似后验分布。MCMC 是一种非常强大的工具，尤其在解析解无法直接求得时，提供了一种灵活且有效的计算方法。\n","\n","随着模型的复杂性增加，**后验分布可能变得难以解析，甚至无法获得。** 在这种情况下，近似方法是必要的。\n","\n","我们学习了两种用于逼近后验分布的技术：\n","1. **网格逼近法：** 通过离散化参数空间，计算每个点的后验分布，再通过这些点近似整个后验。\n","2. **马尔科夫链蒙特卡罗（MCMC）：** 通过随机采样，生成符合后验分布的样本，逼近目标分布。\n","\n"]}],"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":"3.12.4"}},"nbformat":4,"nbformat_minor":2}
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