Constructing Hierarchical Priors with Application to Bayesian Phylogenetic Analyses

Abstract

I present a model and computational algorithm for combining results from a number of complex Bayesian analyses from a number of exchangeable datasets. The individual analyses have already been fit independently using a standalone software that fits a complex Bayesian model using Markov Chain Monte Carlo (MCMC) simulation. Each individual analysis is computationally intensive and MCMC output from each of these complex Bayesian analyses is available. Instead of attempting to construct a single large complex model involving all the original datasets, which may be difficult if not impossible to implement, our strategy is to use the existing MCMC samples of the individual posteriors. We place a hierarchical model across the individual analyses for estimating parameters of interest within and across analyses. This allows us to improve on the inferences from the individual analyses. We are also interested in developing priors based on all of the data, and incorporating them into the standalone software for future analyses of individual data sets. Our hierarchical prior model has two key features. We use a mixture of Dirichlet process prior for the parameters of interest to relax parametric assumptions and to ensure the prior distribution for the parameters of interest is continuous. The conventional Gibbs sampling technique cannot be directly used to carry out our approach since we are using existing MCMC samples. Therefore we use an importance reweighting algorithm within Gibbs to sample values of the individual parameters. HIV-1 aligned sequences data were obtained from Los Alamos National Laboratory HIV databases. We use Bayesian phylogeny analyses generated from the MrBAYES phylogenetic software to demonstrate our approach. This is joint work with Dr. Robert Weiss.