M-H Python实现

import random
from scipy.stats import gamma,rayleigh
import matplotlib.pyplot as plt
def rayleigh_dist_prob(x,a): #提议分布
    y = rayleigh.pdf(x,a)
    return y
def gamma_dist_prob(x): #提议分布
    y = gamma.pdf(x,1,scale=1)
    return y
a=1.9
sigmaf=4
T = 10000#采样次数
pi = [0 for i in range(T)]              #每次采样的结果
sigma = 1                               #转移矩阵分布参数
t = 0
#采样次数初始化
pi[0] =gamma.rvs(a,1, scale=1)
jujue=0
while t < T-1:
    t = t + 1
    # rvs 产生服从指定分布的随机数
    pi[t]  =gamma.rvs(pi[t-1],1,scale=1)
#根据转移矩阵进行采样,从这个分布中抽一些样本
    alpha = min(1,(gamma_dist_prob(pi[t])*rayleigh_dist_prob(pi[t],sigmaf) )/ (rayleigh_dist_prob(pi[t - 1],sigmaf)*gamma_dist_prob(pi[t - 1])))
    u = random.uniform(0, 1)
    if u < alpha:
        pass            # 接受
    else:
        pi[t] = pi[t-1]               # 拒绝
        jujue+=1
#plt.scatter(pi, gamma.pdf(pi,1,scale=1))
num_bins = 50
#plt.hist(pi, num_bins, density=1, facecolor='red', alpha=0.7)
#alpha设置透明度,0为完全透明
#plt.show()
print(jujue)
"""
import random
from scipy.stats import gamma,rayleigh
import matplotlib.pyplot as plt
import numpy as np
x = np.arange(0, 10, 0.01)
y1 = gamma.pdf(x, 1, scale=1)
y2 = gamma.pdf(x, 1.5, scale=1)
y3 = gamma.pdf(x, 2, scale=1)
plt.plot(x, y1, lw=2, label='$r = 1$')
plt.plot(x, y2, lw=2, label='$r = 1.5$')
plt.plot(x, y3, lw=2, label='$r = 2$')
plt.xlabel('$x$')
plt.title('Gamma $(r, 1)$ Densities');
plt.legend()
plt.show()
"""