# Model selection and parameter inference in phylogenetics using Nested Sampling

## TL;DR

This paper introduces Nested Sampling as an efficient Bayesian method for model selection and parameter inference in phylogenetics, addressing computational challenges in marginal likelihood estimation and posterior sampling.

## Contribution

It adapts Nested Sampling to phylogenetics, providing a practical alternative to existing methods with uncertainty estimation and no extra computational cost.

## Key findings

- Nested Sampling performs competitively in various scenarios.
- It offers reliable marginal likelihood estimates with uncertainty quantification.
- The method reduces the need for long Markov chains in posterior sampling.

## Abstract

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 estimates. One of the major challenges in phylogenetics is 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 relates to 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 computation algorithm which provides the means to estimate marginal likelihoods together with their uncertainties, and to sample from the posterior distribution at no extra cost. The methods currently used in phylogenetics for marginal likelihood estimation lack in practicality due to their dependence on many tuning parameters and the inability of most implementations to provide a direct way to calculate the uncertainties associated with the estimates. To address these issues, we introduce NS to phylogenetics. Its performance is assessed under different scenarios and compared to established methods. We conclude that NS is a competitive and attractive algorithm for phylogenetic inference. An implementation is available as a package for BEAST 2 under the LGPL licence, accessible at https://github.com/BEAST2-Dev/nested-sampling.