Multiple hypothesis screening using mixtures of non-local distributions with applications to genomic studies

TL;DR

This paper introduces a novel multiple hypothesis screening method using mixtures of non-local distributions, improving false discovery control in large-scale biomedical data analysis.

Contribution

It proposes weighted non-local density alternatives within the two-group model, enhancing hypothesis screening accuracy and providing efficient inference methods.

Findings

Improved Bayesian False Discovery Rate control.

Enhanced screening performance over existing methods.

Successful application to genomic differential expression analysis.

Abstract

The analysis of large-scale datasets, especially in biomedical contexts, frequently involves a principled screening of multiple hypotheses. The celebrated two-group model jointly models the distribution of the test statistics with mixtures of two competing densities, the null and the alternative distributions. We investigate the use of weighted densities and, in particular, non-local densities as working alternative distributions, to enforce separation from the null and thus refine the screening procedure. We show how these weighted alternatives improve various operating characteristics, such as the Bayesian False Discovery rate, of the resulting tests for a fixed mixture proportion with respect to a local, unweighted likelihood approach. Parametric and nonparametric model specifications are proposed, along with efficient samplers for posterior inference. By means of a simulation study, we exhibit how our model compares with both well-established and state-of-the-art alternatives in terms of various operating characteristics. Finally, to illustrate the versatility of our method, we conduct three differential expression analyses with publicly-available datasets from genomic studies of heterogeneous nature.