19 May 2015 by Remco Bouckaert

Metropolis coupled MCMC (MCMCMC or MC3) allows running an MCMC analysis together with a number of ‘heated’ chains. These heated chains run over a distribution that is adjusted so that it is less peaked than the posterior we want to sample from, which means it is easier for these heated chains to move away from a local optimum. At regular intervals there is the option to switch states between chains (depending on a stochastic critereon), including the chain that samples from the posterior. This is supposed to help explore the sample space more efficient.

To set up an MCMCMC analysis in BEAST, you need to install the BEASTLabs package. The easiest way to set up the XML is by setting it up in BEAUti for a simple MCMC analysis, save the file and edit the XML by

- replacing the
`spec`attribute in the`run`element by`"beast.inference.MCMCMC"`. - add a
`chains`attribute with the number of chains you want to run.

After this, the XML should look something like this:

When running the analysis, you want to use at least as many chains as there are chains, so that each chain can run in its own thread. The current implementation is multi-threaded, but does not on multi-processors (yet).

## Does MCMCMC work?

The question remains whether it is better to run say 4 individual MCMC analyses and combine results instead of running a single MCMCMC analysis. From what I have seen so far, the BEAST proposals are typically very well tuned to explore tree space, and can handle correlations between various parameters quite well. If a BEAST analysis gets stuck — which shows up by running different chains that seem to converge, but all end up at a different posterior — anecdotal evidence with *BEAST analyses suggest that throwing MCMCMC at it does not solve the problem.

So, there are two criteria on how to judge whether MC3 works or not

- Can it get us out of local optima, where MCMC by itself has trouble?
- Can it produce better effective sample size (ESS) per computer cycle?

I can imagine that MC3 works in some cases, and it has been around for ages (notably in MrBayes), but perhaps this is due to the kind of MCMC proposals used, and maybe BEAST analyses do not benefit from MC3. I have not seen an example yet, so if you have a BEAST analysis where MC3 produces better results than MCMC alone, please let me know!