Bayesian Model Selection in Complex Linear Systems, as Illustrated in Genetic Association Studies

TL;DR

This paper develops a Bayesian framework for model selection in complex linear systems, motivated by genetic studies, using Bayes factors and MCMC methods for efficient comparison and application to eQTL mapping.

Contribution

It introduces a novel Bayesian approach with analytic Bayes factors and MCMC algorithms for model selection in complex linear models, tailored for genetic association data.

Findings

Bayes factors enable efficient model comparison in complex systems.

The approach is validated through simulations and real genetic data.

Results facilitate tissue-specific eQTL mapping.

Abstract

Motivated by examples from genetic association studies, this paper considers the model selection problem in a general complex linear model system and in a Bayesian framework. We discuss formulating model selection problems and incorporating context-dependent {\it a priori} information through different levels of prior specifications. We also derive analytic Bayes factors and their approximations to facilitate model selection and discuss their theoretical and computational properties. We demonstrate our Bayesian approach based on an implemented Markov Chain Monte Carlo (MCMC) algorithm in simulations and a real data application of mapping tissue-specific eQTLs. Our novel results on Bayes factors provide a general framework to perform efficient model comparisons in complex linear model systems.