A Bayesian Generalized CAR Model for Correlated Signal Detection

TL;DR

This paper introduces a flexible Bayesian generalized CAR model for correlated signal detection that accommodates independent points and various neighborhood structures, improving inference in large-scale multiple testing scenarios.

Contribution

It extends traditional CAR models to include isolated points and alternative neighborhood definitions, enhancing modeling of dependence in high-dimensional data.

Findings

Improved detection accuracy in simulated data.

Effective analysis of real microarray datasets.

Enhanced Bayesian inference with stronger posterior learning.

Abstract

Over the last decade, large-scale multiple testing has found itself at the forefront of modern data analysis. In many applications data are correlated, so that the observed test statistic used for detecting a non-null case, or signal, at each location in a dataset carries some information about the chances of a true signal at other locations. Brown, Lazar, Datta, Jang, and McDowell (2014) proposed in the neuroimaging context a Bayesian multiple testing model that accounts for the dependence of each volume element on the behavior of its neighbors through a conditional autoregressive (CAR) model. Here, we propose a generalized CAR model that allows for inclusion of points with no neighbors at all, something that is not possible under conventional CAR models. We consider also neighborhoods based on criteria other than physical location, such as genetic pathways in microarray determined from existing biological knowledge. This generalization provides a unified framework for the simultaneous modeling of dependent and independent cases, resulting in stronger Bayesian learning in the posterior and increased precision in the estimates of interesting signals. We justify the selected prior distribution and prove that the resulting posterior distribution is proper. We illustrate the effectiveness and applicability of our proposed model by using it to analyze both simulated and real microarray data in which the genes exhibit dependence that is determined by physical adjacency on a chromosome or predefined gene pathways.