MCMC algorithms for Bayesian variable selection in the logistic regression model for large-scale genomic applications

TL;DR

This paper develops and compares MCMC algorithms that leverage dependence structures in Bayesian variable selection for large-scale genomic logistic regression, improving computational efficiency and convergence.

Contribution

It introduces dependence-aware MCMC samplers tailored for high-dimensional genomic data, enhancing scalability and performance over standard methods.

Findings

Dependence-aware samplers outperform standard Gibbs in mixing and convergence.

The proposed methods are effective in real gene expression data analysis.

Simulation studies confirm improved computational efficiency.

Abstract

In large-scale genomic applications vast numbers of molecular features are scanned in order to find a small number of candidates which are linked to a particular disease or phenotype. This is a variable selection problem in the "large p, small n" paradigm where many more variables than samples are available. Additionally, a complex dependence structure is often observed among the markers/genes due to their joint involvement in biological processes and pathways. Bayesian variable selection methods that introduce sparseness through additional priors on the model size are well suited to the problem. However, the model space is very large and standard Markov chain Monte Carlo (MCMC) algorithms such as a Gibbs sampler sweeping over all p variables in each iteration are often computationally infeasible. We propose to employ the dependence structure in the data to decide which variables should always be updated together and which are nearly conditionally independent and hence do not need to be considered together. Here, we focus on binary classification applications. We follow the implementation of the Bayesian probit regression model by Albert and Chib (1993) and the Bayesian logistic regression model by Holmes and Held (2006) which both lead to marginal Gaussian distributions. We in- vestigate several MCMC samplers using the dependence structure in different ways. The mixing and convergence performances of the resulting Markov chains are evaluated and compared to standard samplers in two simulation studies and in an application to a real gene expression data set.