The Effective Sample Size (ESS) of a parameter sampled from an MCMC (such as BEAST) is the number of effectively independent draws from the posterior distribution that the Markov chain is equivalent to.

How do I calculate an ESS?

The simplest way is to load your BEAST log files into Tracer.

Why do I need to increase it?

If the ESS of a parameter is small then the estimate of the posterior distribution of that parameter will be poor. In Tracer you can calculate the standard deviation of the estimated mean of a parameter. If the ESS is small then the standard deviation will be large. This is exactly the same as the sample size of an experiment consisting of measurements.

What size ESS is adequate?

The larger the better. Tracer flags up ESSs < 100 but this may be liberal and > 200 would be better. On the other hand chasing ESSs > 10000 may be a waste of computational resources.

Do I need adequate ESSs for all my parameters?

Possibly not. Really low ESSs may be indicative of poor mixing but if a couple of parameters that you are not interested in are a little low it probably doesn’t matter. The likelihoods (both of the tree and coalescent model) should have decent ESSs.

Is the ESS important if I am interested in the sample of trees?

Definitely. At the moment we don’t have anyway of directly examining the ESS of the tree or the clade frequencies. Therefore, it is important that the continuous parameters and likelihoods have adequate ESS to demonstrate good mixing of the MCMC.