Hierarchical Models for Combining Phylogenetic Analyses Using an Iterative Re-weighting Algorithm

Molecular phylogeny is the art and science of inferring the family tree and underlying evolutionary parameters relating the molecular sequences from different genes, or viruses, or species and so on. Phylogenetic modeling is computationally challenging and most phylogenetic modeling estimates a single tree to a single set of molecular sequences. We develop a Bayesian hierarchical semi-parametric regression model to combine phylogenetic analyses of sets of HIV-1 nucleotide sequences. We describe several reweighting algorithms for combining completed Markov chain Monte Carlo (MCMC) analyses to shrink parameter estimates while adjusting for data set-specific covariates.

Individual phylogenetic analyses are performed independently using the publicly available software MrBayes (Huelsenbeck and Ronquist, 2001) that fits a computationally intensive Bayesian model using Markov chain Monte Carlo (MCMC) simulation. We place a hierarchical regression model across the individual analyses to estimate parameters of interest within and across analyses. We use a Mixture of Dirichlet processes (MDP) prior for the parameters of interest to relax inappropriate parametric assumptions and to insure the prior distribution for the parameters of interest is continuous. Constructing a large complex model involving all the original data is computationally challenging and would require rewriting the existing stand alone software. Instead we utilize existing MCMC samples from the individual analyses using an iteratively reweighted importance resampling algorithm within MCMC iterations.