Parameter Expanded Algorithms for Bayesian Latent Variable Modeling of Genetic Pleiotropy Data

Bayesian latent variable models for hierarchical clustered count outcomes with repeated measures in microbiome studies

Motivated by the multivariate nature of microbiome data with hierarchical taxonomic clusters, counts that are often skewed and zero inflated, and repeated measures, we propose a Bayesian latent variable methodology to jointly model multiple operational taxonomic units within a single taxonomic cluster. This novel method can incorporate both negative binomial and zero-inflated negative binomial responses, and can account for serial and familial correlations. We develop a Markov chain Monte Carlo algorithm that is built on a data augmentation scheme using Pólya-Gamma random variables. Hierarchical centering and parameter expansion techniques are also used to improve the convergence of the Markov chain. We evaluate the performance of our proposed method through extensive simulations. We also apply our method to a human microbiome study.

Genetic Variant Selection: Learning Across Traits and Sites

We consider resequencing studies of associated loci and the problem of prioritizing sequence variants for functional follow-up. Working within the multivariate linear regression framework helps us to account for the joint effects of multiple genes; and adopting a Bayesian approach leads to posterior probabilities that coherently incorporate all information about the variants' function. We describe two novel prior distributions that facilitate learning the role of each variable site by borrowing evidence across phenotypes and across mutations in the same gene. We illustrate their potential advantages with simulations and reanalyzing a data set of sequencing variants.