Bayesian Analysis of Multiway Tables in Association Studies: A Model Comparison Approach

We consider the problem of statistical inference on unknown quantities structured as a multiway table. We show that such multiway tables are naturally formed by arranging regression coefficients in complex systems of linear models for association analysis. In genetics and genomics, the resulting two-way and three-way tables cover many important applications. Within the Bayesian hierarchical model framework, we define the structure of a multiway table through prior specification. Focusing on model comparison and selection, we derive analytic expressions of Bayes factors and their approximations and discuss their theoretical and computational properties. Finally, we demonstrate the strength of our approach using a genomic application of mapping tissue-specific eQTLs (expression quantitative loci).