update

2019.12.01_Metropolis_sampling/Metropolis_sampling_example_1.py

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+"""
+This code is supported by the website: https://www.guanjihuan.com
+The newest version of this code is on the web page: https://www.guanjihuan.com/archives/1247
+"""
+
+import random
+import math
+import numpy as np
+from scipy.stats import norm
+import matplotlib.pyplot as plt
+
+
+def function(x):  # 期望样品的分布，target distribution function
+    y = (norm.pdf(x, loc=2, scale=1)+norm.pdf(x, loc=-5, scale=1.5))/2   # loc代表了均值,scale代表标准差
+    return y
+
+
+T = 100000  # 取T个样品
+pi = [0 for i in range(T)]  # 任意选定一个马尔科夫链初始状态
+for t in np.arange(1, T):
+    pi_star = np.random.uniform(-10, 10)  # a proposed distribution， 例如是均匀分布的，或者是一个依赖pi[t - 1]的分布
+    alpha = min(1, (function(pi_star) / function(pi[t - 1])))  # 接收率
+    u = random.uniform(0, 1)
+    if u < alpha:
+        pi[t] = pi_star    # 以alpha的概率接收转移
+    else:
+        pi[t] = pi[t - 1]  # 不接收转移
+
+pi = np.array(pi)  # 转成numpy格式
+print(pi.shape)  # 查看抽样样品的维度
+plt.plot(pi, function(pi), '*')  # 画出抽样样品期望的分布   # 或用plt.scatter(pi, function(pi))
+plt.hist(pi, bins=100, density=1, facecolor='red', alpha=0.7)   # 画出抽样样品的分布   # bins是分布柱子的个数，density是归一化，后面两个参数是管颜色的
+plt.show()