Bayesian Phylogenetics: Methods, Computational Algorithms, and Applications pages:59-94
In this chapter, we discuss recent advances in the field of Bayesian model testing and focus on methods that aim at either estimating (log) marginal likelihoods or at directly estimating (log) Bayes factors. We start by introducing several of the most popular (log) marginal likelihood estimators, which are attractive from a computational perspective. Because these estimators have recently been shown to perform poorly, we discuss computationally more demanding, but also more accurate path sampling approaches that can be used to either estimate (log) marginal likelihoods for di↵erent models, but also to directly estimate (log) Bayes factors between two competing models. For a specific class of evolutionary models, i.e., the relaxed molecular clock models, we also discuss how such methods compare to specific Bayesian model averaging approaches that allow constructing a classifier to approximate (log) Bayes factors between the models in the candidate model set. To demonstrate their practical use, we apply the presented techniques in a simulation study on relaxed molecular clocks and in a demographic model selection study that focuses on an HIV-1 data set.