Metropolis-Hastings采样算法的流程：
代码一：有助于理解算法流程
# -*- coding: utf-8 -*-'''Created on 5月15日@author: user'''import randomfrom scipy.stats import normimport matplotlib.pyplot as pltdef cauchy(theta):#从柯西分布p中采样数据y = 1.0 / (1.0 + theta ** 2)return yT = 5000sigma = 1thetamin = -30thetamax = 30theta = [0.0] * (T+1)theta[0] = random.uniform(thetamin, thetamax)t = 0while t < T:t = t + 1theta_star = norm.rvs(loc=theta[t - 1], scale=sigma, size=1, random_state=None)#从已知正态分布q中生成候选状态alpha = min(1, (cauchy(theta_star[0]) / cauchy(theta[t - 1])) )u = random.uniform(0, 1)if u <= alpha:#接受theta[t] = theta_star[0]else:theta[t] = theta[t - 1]#print (theta)ax1 = plt.subplot(211)ax2 = plt.subplot(212) plt.sca(ax1)plt.ylim(thetamin, thetamax)plt.plot(range(T+1), theta, 'g-')plt.sca(ax2)num_bins = 50plt.hist(theta, num_bins, normed=1, facecolor='red', alpha=0.5)plt.show()
结果：
代码2：有助于理解样本
# -*- coding: utf-8 -*-'''Created on 5月16日@author: userp:输入的概率分布，离散情况采用元素为概率值的数组表示N:认为迭代N次马尔可夫链收敛Nlmax:马尔可夫链收敛后又取的服从p分布的样本数isMH:是否采用MH算法，默认为True'''from __future__ import divisionimport matplotlib.pyplot as pltimport numpy as npfrom array import arraydef mcmc(p,N=10000,Nlmax=10000,isMH=True):A = np.array([p for y in range(len(p))], dtype=np.float64) X0 = np.random.randint(len(p))count = 0samplecount = 0L = array("d",[X0])l = array("d")while True:X = int(L[samplecount])cur = np.argmax(np.random.multinomial(1,A[X]))count += 1if isMH:a = (p[cur]*A[cur][X])/(p[X]*A[X][cur])alpha = min(a,1)else:alpha = p[cur]*A[cur][X]u = np.random.uniform(0,1) if u<alpha:samplecount += 1L.append(cur)if count>N:l.append(cur)if len(l)>=Nlmax:breakelse:continueLa = np.frombuffer(L)la = np.frombuffer(l)return La,ladef count(q,n):L = array("d")l1 = array("d")l2 = array("d")for e in q:L.append(e)for e in range(n):l1.append(L.count(e))for e in l1:l2.append(e/sum(l1))return l1,l2if __name__ == '__main__': p = np.array([0.6,0.3,0.1])a = mcmc(p)[1]l1 = ['state%d'% x for x in range(len(p))]plt.pie(count(a,len(p))[0],labels=l1,labeldistance=0.3,autopct='%1.2f%%')plt.title("sampling")plt.show()
结果：
