I want to do a stepping stone analysis to test the monophyly of a particular clade. The clade appears to be monophyletic following the usual MCMC run, with PP=98. The problem is, the dataset is very difficult, I had to modify the topology proposals to get it going somewhere and nevertheless the analysis reached stationarity only after about 40 million generations (out of 70 total).
Unfortunately, there aren’t many tutorials on SS, and I feel I do not have enough understanding of how to design an efficient analysis. From my understanding, each step is equivalent to a standart MCMC chain sampling from a probability distribution, which in this case is a power posterior distribution in each step. That implies that in each step the chain will have to burn-in before it reaches stationarity with respect to this step’s power posterior distribution. If my burn-in leading to stationarity with respect to an actual posterior distribution was in fact 40 millions generations, does it mean that the SS chain will require the same amount to settle on a power posterior in each step?
My other questions are:
How many generations in total (all steps combined) should I run the chain for? And how many samples from each power posterior are sufficient for a reliable estimate of marginal likelihood?
Considering the SS chain starts to sample from the posterior (or rather the next closest power posterior) and moves to the prior during the course of a run, can I use the last parameters’ values sampled from the actual posterior by my chain during the standart MCMC run as a starting values for the SS chain?