Subchain length problem

[MordorianGuy]

It is stated in the FAQ that sufficient subchain length can be defined as chain length of usual MCMC run divided by ESS. However, nested sampling & usual MCMC are guided by different distributions, prior & posterior (joint) respectively. We can set BEAST analysis prior only. If we are trying to enforce the independence of sampling, should we use guided only by prior run for determining the sufficient criterion?

The second question about FAQ recommendations is how to define the consistency of the number of parallel runs more than two? Comparing them all in pairs does not sound like an elegant way. Is there any appropriate method?

[rbouckaert]

As far as I am aware, both questions are research questions.

The suggested subchain length makes for a good starting value, but as you already pointed out in #13, actual performance depends on operator settings, so running multiple analyses is the only way to get some confidence that the subchain length is sufficiently large.

I suppose some formal statistical test can be applied to compare results of more than two such runs. However, if it is not immediately clear from pairwise comparison that results are consistent and a formal test is required to confirm consistence, the subchain length is probably too short, resulting in dependent samples and thus biased results.

[pmat747]

Just an idea: to avoid pairwise comparison, a principal component analysis could be used (PCA). A reduction to a one dimension would indicate consistency in the runs.