An alternative marginal likelihood estimator for phylogenetic models

TL;DR

This paper introduces a new generalized harmonic mean estimator for marginal likelihoods in Bayesian phylogenetics, addressing the variance issues of traditional methods and improving accuracy in model comparison.

Contribution

It presents a novel implementation of the generalized harmonic mean estimator that overcomes infinite variance problems, offering a more reliable and simple alternative for Bayesian model selection in phylogenetics.

Findings

Outperforms traditional harmonic mean estimator in accuracy.

Produces reliable marginal likelihood estimates from MCMC simulations.

Demonstrates effectiveness on simulated phylogenetic data.

Abstract

Bayesian phylogenetic methods are generating noticeable enthusiasm in the field of molecular systematics. Many phylogenetic models are often at stake and different approaches are used to compare them within a Bayesian framework. The Bayes factor, defined as the ratio of the marginal likelihoods of two competing models, plays a key role in Bayesian model selection. We focus on an alternative estimator of the marginal likelihood whose computation is still a challenging problem. Several computational solutions have been proposed none of which can be considered outperforming the others simultaneously in terms of simplicity of implementation, computational burden and precision of the estimates. Practitioners and researchers, often led by available software, have privileged so far the simplicity of the harmonic mean estimator (HM) and the arithmetic mean estimator (AM). However it is known that the resulting estimates of the Bayesian evidence in favor of one model are biased and often inaccurate up to having an infinite variance so that the reliability of the corresponding conclusions is doubtful. Our new implementation of the generalized harmonic mean (GHM) idea recycles MCMC simulations from the posterior, shares the computational simplicity of the original HM estimator, but, unlike it, overcomes the infinite variance issue. The alternative estimator is applied to simulated phylogenetic data and produces fully satisfactory results outperforming those simple estimators currently provided by most of the publicly available software.