Particle Gibbs sampling for Bayesian phylogenetic inference

Online tree expansion could help solve the problem of scalability in Bayesian phylogenetics

Bayesian phylogenetics is now facing a critical point. Over the last 20 years, Bayesian methods have reshaped phylogenetic inference and gained widespread popularity due to their high accuracy, the ability to quantify the uncertainty of inferences and the possibility of accommodating multiple aspects of evolutionary processes in the models that are used. Unfortunately, Bayesian methods are computationally expensive, and typical applications involve at most a few hundred sequences. This is problematic in the age of rapidly expanding genomic data and increasing scope of evolutionary analyses, forcing researchers to resort to less accurate but faster methods, such as maximum parsimony and maximum likelihood. Does this spell doom for Bayesian methods? Not necessarily. Here, we discuss some recently proposed approaches that could help scale up Bayesian analyses of evolutionary problems considerably. We focus on two particular aspects: online phylogenetics, where new data sequences are added to existing analyses, and alternatives to Markov chain Monte Carlo (MCMC) for scalable Bayesian inference. We identify 5 specific challenges and discuss how they might be overcome. We believe that online phylogenetic approaches and Sequential Monte Carlo hold great promise and could potentially speed up tree inference by orders of magnitude. We call for collaborative efforts to speed up the development of methods for real-time tree expansion through online phylogenetics.

Genome-Wide Association with Uncertainty in the Genetic Similarity Matrix

Genome-wide association studies (GWASs) are often confounded by population stratification and structure. Linear mixed models (LMMs) are a powerful class of methods for uncovering genetic effects, while controlling for such confounding. LMMs include random effects for a genetic similarity matrix, and they assume that a true genetic similarity matrix is known. However, uncertainty about the phylogenetic structure of a study population may degrade the quality of LMM results. This may happen in bacterial studies in which the number of samples or loci is small, or in studies with low-quality genotyping. In this study, we develop methods for linear mixed models in which the genetic similarity matrix is unknown and is derived from Markov chain Monte Carlo estimates of the phylogeny. We apply our model to a GWAS of multidrug resistance in tuberculosis, and illustrate our methods on simulated data.

Scalable Bayesian phylogenetics

Recent advances in Bayesian phylogenetics offer substantial computational savings to accommodate increased genomic sampling that challenges traditional inference methods. In this review, we begin with a brief summary of the Bayesian phylogenetic framework, and then conceptualize a variety of methods to improve posterior approximations via Markov chain Monte Carlo (MCMC) sampling. Specifically, we discuss methods to improve the speed of likelihood calculations, reduce MCMC burn-in, and generate better MCMC proposals. We apply several of these techniques to study the evolution of HIV virulence along a 1536-tip phylogeny and estimate the internal node heights of a 1000-tip SARS-CoV-2 phylogenetic tree in order to illustrate the speed-up of such analyses using current state-of-the-art approaches. We conclude our review with a discussion of promising alternatives to MCMC that approximate the phylogenetic posterior. This article is part of a discussion meeting issue 'Genomic population structures of microbial pathogens'.

Estimating Distributions of Parameters in Nonlinear State Space Models with Replica Exchange Particle Marginal Metropolis–Hastings Method

Extracting latent nonlinear dynamics from observed time-series data is important for understanding a dynamic system against the background of the observed data. A state space model is a probabilistic graphical model for time-series data, which describes the probabilistic dependence between latent variables at subsequent times and between latent variables and observations. Since, in many situations, the values of the parameters in the state space model are unknown, estimating the parameters from observations is an important task. The particle marginal Metropolis–Hastings (PMMH) method is a method for estimating the marginal posterior distribution of parameters obtained by marginalization over the distribution of latent variables in the state space model. Although, in principle, we can estimate the marginal posterior distribution of parameters by iterating this method infinitely, the estimated result depends on the initial values for a finite number of times in practice. In this paper, we propose a replica exchange particle marginal Metropolis–Hastings (REPMMH) method as a method to improve this problem by combining the PMMH method with the replica exchange method. By using the proposed method, we simultaneously realize a global search at a high temperature and a local fine search at a low temperature. We evaluate the proposed method using simulated data obtained from the Izhikevich neuron model and Lévy-driven stochastic volatility model, and we show that the proposed REPMMH method improves the problem of the initial value dependence in the PMMH method, and realizes efficient sampling of parameters in the state space models compared with existing methods.