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Bayesian inference methods rely on numerical algorithms for both modelselection and parameter inference. In general, these algorithms require a highcomputational effort to yield reliable estimates. One of the major challengesin phylogenetics is the estimation of the marginal likelihood. This quantity iscommonly used for comparing different evolutionary models, but its calculation,even for simple models, incurs high computational cost. Another interestingchallenge relates to the estimation of the posterior distribution. Often, longMarkov chains are required to get sufficient samples to carry out parameterinference, especially for tree distributions. In general, these problems areaddressed separately by using different procedures. Nested sampling (NS) is aBayesian computation algorithm which provides the means to estimate marginallikelihoods together with their uncertainties, and to sample from the posteriordistribution at no extra cost. The methods currently used in phylogenetics formarginal likelihood estimation lack in practicality due to their dependence onmany tuning parameters and the inability of most implementations to provide adirect way to calculate the uncertainties associated with the estimates. Toaddress these issues, we introduce NS to phylogenetics. Its performance isassessed under different scenarios and compared to established methods. Weconclude that NS is a competitive and attractive algorithm for phylogeneticinference. An implementation is available as a package for BEAST 2 under theLGPL licence, accessible at https://github.com/BEAST2-Dev/nested-sampling.

Model selection and parameter inference in phylogenetics using Nested Sampling