Report for 9-30-2016

[halasadi]

MCMC

I re-implemented the ladder MCMC approach. Looking at the runs in more detail, it seems like the colder temperature MCMC is accepting higher likelihood states from the hotter temperatures MCMC. However, the problem, is that both the hot and cold MCMC converge to areas of low likelihood.

For example, for 50 demes scenario with POPRES

5 chains with relatively high acceptance ratios (around 33%, 60% and rises to 80%)

One chains

You can see that the 5 chains have converged to an area of low log-likelihood.

Also, average contour plot is more blocky for the multiple chain run.

5 chains

one chain

Speculation to why

It seems like the hotter temperature MCMC is keeping the colder temperature MCMC in an area of low(er) likelihood. You can see that the cold temperature MCMC's log-likelihood increases over burn-in but in a muliple mcmc scenario, after a bit of increase, the MCMC is brought back to an area of lower log-likelihood. What about if we enforce that the likelihood strictly has to be greater?

Here, the acceptance ratio decreases to 10%

It helps.

[halasadi]

This shouldn't happen. Either an error with the code or the theory and the latter is interesting to know.