Marginal likelihoods in phylogenetics: a review of methods and applications

Author(s): Oaks, JR; Cobb, KA; Minin, VN; Leache, AD | Abstract: By providing a framework of accounting for the shared ancestry inherent to all life, phylogenetics is becoming the statistical foundation of biology. The importance of model choice continues to grow as phylogenetic models continue to increase in complexity to better capture micro and macroevolutionary processes. In a Bayesian framework, the marginal likelihood is how data update our prior beliefs about models, which gives us an intuitive measure of comparing model fit that is grounded in probability theory. Given the rapid increase in the number and complexity of phylogenetic models, methods for approximating marginal likelihoods are increasingly important. Here we try to provide an intuitive description of marginal likelihoods and why they are important in Bayesian model testing. We also categorize and review methods for estimating marginal likelihoods of phylogenetic models. In doing so, we use simulations to evaluate the performance of one such method based on approximate-Bayesian computation (ABC) and find that it is biased as predicted by theory. Furthermore, we review some applications of marginal likelihoods to phylogenetics, highlighting how they can be used to learn about models of evolution from biological data. We conclude by discussing the challenges of Bayesian model choice and future directions that promise to improve the approximation of marginal likelihoods and Bayesian phylogenetics as a whole.