My samplers do not converge to maximum likelihood

[tga54]

General information:

• emcee version: 3.0.2
• platform: Ubuntu Linux
• installation method (pip/conda/source/other?): source

Problem description:

Expected behavior: The samplers converge to best-fit parameters that have the maximum likelihood

Actual behavior: corner plot shows that parameters converge to a group of parameters that do not have the maximum likelihood. Besides, best-fit parameters are not covered by [16%,84%] range of samples.

What have you tried so far?: I saved every group of parameters called by "log_likelihood" and the corresponding likelihood value returned by "log_likelihood" into a new file. I run MCMC sampling for 2000 steps with 12 chains and burned 0 steps. I found that "get_chain" returns 24000 samples while my file only saved less than 20000 samples. The samples returned by "get_chain" do not converge while samples saved by my file show that they are converged. When I was checking the likelihood value I found that samples do not converge to the best-fit parameters that gave the maximum likelihood. I guess the reason is that the best-fit parameters are too close to the boundary of parameter space defined in "log_prior". Therefore MCMC converged to a local minimum instead of the global minimum. To enlarge the parameter space would make it unphysical. What should I do?

Minimal example:

import emcee

## I paste my "log_likelihood" here.
import numpy as np
import os
def log_likelihood(par, y ,yerr):
    p1,p2,p3,p4,p5,p6 = par
    model = model(p1,p2,p3,p4,p5,p6)
    likelihood = -0.5*np.sum((y-model)**2/yerr**2)
# save parameters called by log_likelihood and likelihood to new files
    w = [p1,p2,p3,p4,p5,p6,likelihood]
    pid = os.getpid()
    f  =open(str(pid) + 'csv','a')
    csv_writer = csv.writer(f,dialect='excel')
    csv_writer.writerow(w)
    f.close()
    return likelihood

# sample code goes here...