Efficient Monte Carlo Fitting with Python Package Emcee and MCMC Analysis

[Silviu]

Hello I use a python package called emcee to fit a function to some data points. The fit looks great, but when I want to plot the value of each parameter at each step I get the plot.png below. In their example (with a different function and data points) they get the plot1.png image. Why is my function converging so fast, and why does it have that weird shape in the beginning. I apply MCMC using likelihood and posterior probability. And even if the fit looks very good, the error on parameters of function are very small (10^10 smaller than the actual value) and I think it is because of the random walks. Any idea how to fix it?

 

[Dale]

That looks like it is just the burn in period. Usually people just discard the first few thousand points in order to avoid that.

I have done all of my MCMC work in R, so I am not familiar with the Python package you mention, but it looks like it is either set with a burn in of 0 or it plots the burn in samples.

 

[MarneMath]

If you're using emcee something like this will help overcome the burn in:
sampler = EnsembleSampler(...)

pos, prob, state = sampler.run_mcmc(...)

sampler.reset()

sampler.run_mcmc(pos, 1000, rstate0=state)