Model Selection and Parameter Inference in Phylogenetics Using Nested 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 their inability of most implementations to provide a direct way to calculate the uncertainties associated with the estimates, unlike NS. 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 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.

Genomic and phylogenetic analysis ofSalmonellaTyphimurium and its monophasic variants responsible for invasive endemic infections in Colombia

“…Different molecular clock models were compared to find the one that best fitted the data. Using Nested Sampling package v1.0.0 of BEAST [41], relaxed exponential clock model was supported by the marginal likelihood value. The BEAST analysis was run for 80 million steps and was sampled every 200 steps using the GTR substitution model with γ correction for site specific variation.…”

BEAST 2.5: An Advanced Software Platform for Bayesian Evolutionary Analysis

“…The NS package implements nested sampling [47] for phylogenetics, which can also 592 be used for model selection. Nested sampling is a general purpose Bayesian 593 method [110] for estimating the marginal likelihood, which conveniently also provides an 594 estimate of the uncertainty of the marginal likelihood estimate.…”

“…Such uncertainty 595 estimates are not easily available for other methods. Furthermore, nested sampling can 596 be used to provide a posterior sample, and, for some cases where standard MCMC can 597 get stuck in a mode of a multi-modal posterior, nested sampling can produce consistent 598 posterior samples [47]. The marginal likelihood estimates produced by nested sampling 599 can be used to compare models, so provide a basis for model selection.…”

19 Dubious Ways to Compute the Marginal Likelihood of a Phylogenetic Tree Topology

“…The nested sampling algorithm uses a clever process of sampling from the prior (hence dX) and conditioning on the likelihood being above a given size (to achieve the likelihood condition of (1)) to approximate the input to such a quadrature technique [Skilling et al, 2006, Maturana Russel et al, 2018. The algorithm is initialized with N samples {θ 1 , .…”

“…Among single-chain methods, we include the well-known harmonic mean (HM) estimator [Newton and Raftery, 1994], a variation thereof known as the stabilized harmonic mean (SHM) [Newton and Raftery, 1994], bridge sampling (BS) [Overstall andForster, 2010, Gronau et al, 2017], conditional predictive ordinates (CPO) [Lewis et al, 2013], and the pointwise predictive density (PPD) [Vehtari et al, 2017]. Finally, the nested sampling (NS) method sits somewhere in between the single-and multiple-chain categories as it requires simulations from multiple short MCMC runs [Skilling, 2004, Skilling et al, 2006, Maturana Russel et al, 2018.…”