Model selection and parameter inference in phylogenetics using Nested Sampling

Bayesian inference methods rely on numerical algorithms for both model selection and parameter inference. In general, these algorithms require a high computational effort to yield reliable inferences. One of the major challenges in phylogenetics regards the estimation of the marginal likelihood. This quantity is commonly used for comparing different evolutionary models, but its calculation, even for simple models, incurs high computational cost. Another interesting challenge regards the estimation of the posterior distribution. Often, long Markov chains are required to get sufficient samples to carry out parameter inference, especially for tree distributions. In general, these problems are addressed separately by using different procedures. Nested sampling (NS) is a Bayesian algorithm which provides the means to estimate marginal likelihoods and to sample from the posterior distribution at no extra cost. In this paper, we introduce NS to phylogenetics. Its performance is analysed under different scenarios and compared to established methods. We conclude that NS is a very competitive and attractive algorithm for phylogenetic inference.