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

TL;DR

This paper develops a Bayesian framework for analyzing multiway tables in association studies, deriving Bayes factors for model comparison, and demonstrates its effectiveness in genomic applications like eQTL mapping.

Contribution

It introduces a Bayesian model comparison approach for multiway tables in association analysis, with explicit Bayes factor calculations and applications to genomics.

Findings

Derived analytic Bayes factors for model comparison.

Applied method successfully to genomic eQTL data.

Showed theoretical and computational advantages of the approach.

Abstract

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).