Bayesian posterior probabilities: revisited

Abstract

Huelsenbeck and Rannala (2004, Systematic Biology 53, 904-913) presented a series of simulations in order to assess the extent to which the bayesian posterior probabilities associated with phylogenetic trees represent the standard frequentist statistical interpretation. They concluded that when the analysis model matches the generating model then the bayesian posterior probabilities are correct, but that the probabilities are much too large when the model is under-specified and slightly too small when the model is over-specified. Here, I take issue with the first conclusion, and instead contend that their simulation data show that the posterior probabilities are still slightly too large even when the models match. Furthermore, I suggest that the data show that the degree of this over-estimation increases as the sequence length increases, and that it might increase as model complexity increases. I also provide some comments on the authors' conclusions concerning whether bootstrap proportions over- or under-estimate the true probabilities.