emcee MCMC采样未收敛到适当的参数值

emcee 在Python中用一个预定义的似然函数进行MCMC采样,以找到两个数据总体之间的最佳边界。

为了 http://dfm.io/emcee/current/user/line/

在给定一些线性边界线的情况下,似然函数计算真正分类和真负分类,并用于最小化两个值之间的差异,同时最大化它们的总和。

m b ,梯度和偏移(或偏差),对于边界线,我得到了一些非常大和/或非常小的值。

我在下面放了一个示例代码,它生成一些划分得很好的总体,然后围绕参数值的初始猜测生成mcmc。我不确定为什么MCMC链不能很好地收敛到适当的值,所以任何帮助都将不胜感激。

下面的代码应该是现成的。

import emcee
import numpy as np 
from sklearn.metrics import confusion_matrix
import matplotlib.pyplot as plt

#generate some test x and y data
folded_xy_train = np.random.uniform(0,1,10000) #test x data
folded_z_train = np.random.uniform(0,1,10000) #test y data
#define the true gradient and offset for the boundary line
m_true, b_true = 5,-2.5

#generate labels for the test data
rounded_labels_train = np.ones(len(folded_z_train))
model = (m_true*folded_xy_train) + b_true
difference = model - folded_z_train
rounded_labels_train[difference<0] = 0

#show the test data
plt.figure()
plt.scatter(folded_xy_train,folded_z_train,c=rounded_labels_train,s=1.0)

#define a likelihood function for the boundary line       
def lnlike(theta, x, y, labels):
        m, b = theta
        model = (m*x) + b
        difference = model - y
        classifications = np.ones(len(y))
        classifications[difference<0]=0
        cfm = confusion_matrix(labels,classifications)
        cm = cfm.astype('float') / cfm.sum(axis=1)[:, np.newaxis]
        tn, fp, fn, tp = cm.ravel()
        likelihood_val = (0.5*(tp+tn))/(1+np.abs(tp-tn))
        ln_like = -np.log(likelihood_val)
        return ln_like

#define a wide flat prior         
def lnprior(theta):
    m, b, = theta
    if 0 < m < 10 and -20 < b < 5:
        return 0.0
    return -np.inf 

#define the posterior         
def lnprob(p, x, y, labels):
    lp = lnprior(p)
    if not np.isfinite(lp):
        return 0
    return lp + lnlike(p, x, y, labels)

#setup the MCMC sampling  
nwalkers = 4
ndim = 2
p0 = np.array([4.2,-2]) + [np.random.rand(ndim) for i in range(nwalkers)]
sampler = emcee.EnsembleSampler(nwalkers, ndim, lnprob, args=(folded_xy_train, folded_z_train, rounded_labels_train))
sampler.run_mcmc(p0, 500)

#extract the MCMC paramater value chains       
samples = sampler.chain[:, 50:, :].reshape((-1, ndim))        

#view the parameter chains        
plt.figure()
plt.subplot(211)
plt.plot(samples[:,0])
plt.subplot(212)
plt.plot(samples[:,1])     

初始测试数据,显示给定x y数据的明显边界线(由二进制类标签着色):

样本移动,显示渐变参数(顶部)和偏移参数(底部)的奇怪采样。x轴表示MCMC行走步数,y轴表示给定步数下的MCMC参数值: