Walkers in emcee not exploring parameter space?

Question

First of all: apologies for the lack of code and rather vague descriptions; the code I'm using is 1000+ lines long and I'm not sure what parts of it would be helpful to post.

I'm using emcee to do some Bayesian parameter estimation. My code uses 50 walkers each taking 600 iterations (with no thinning), but for whatever reason, the walker chains seem to converge rather quickly. While I initiate the 50 walkers with a random distribution between -1 and 1, they don't explore the entire parameter space, but seem to converge quickly (usually around the true parameter values). Pictures are below:

The real parameter values are .6 and .4

The real parameter values are -1. and 1.

Any suggestions are greatly appreciated!

Answer 1

That's what they are supposed to do - converge quickly to the regions of high posterior density. Another matter is that for bimodal densities emcee would generate suboptimal proposals and that would slow down the convergence. This is probably what happens in you case and is seen in the second graph in both examples.

Authors of emcee suggested (last time I read) working around this with parallel tempering (see the docs) which they have implemented. But their implementation (last time I checked) would not work when densities between modes differ by several orders of magnitude.

Anyway, multimodal posteriors are a bane of all MCMC and there are plenty of attempt to solve this, none being universally accepted (welcome to the cutting edge). You will have to explore several options, maybe beyond emcee, to find what works for you.