Evolutionary Stochastic Search for Bayesian model exploration

TL;DR

This paper introduces an Evolutionary Monte Carlo algorithm for Bayesian variable selection in high-dimensional linear regression, enabling analysis of datasets with thousands of covariates, particularly useful in genomics.

Contribution

The paper presents a novel evolutionary stochastic search algorithm tailored for large p, small n Bayesian model exploration, improving scalability and efficiency.

Findings

Successfully applied to genomics data with up to 10,000 covariates

Demonstrated superior performance over existing search algorithms in simulations

Enabled fully Bayesian multivariate analysis in high-dimensional settings

Abstract

Implementing Bayesian variable selection for linear Gaussian regression models for analysing high dimensional data sets is of current interest in many fields. In order to make such analysis operational, we propose a new sampling algorithm based upon Evolutionary Monte Carlo and designed to work under the "large p, small n" paradigm, thus making fully Bayesian multivariate analysis feasible, for example, in genetics/genomics experiments. Two real data examples in genomics are presented, demonstrating the performance of the algorithm in a space of up to 10,000 covariates. Finally the methodology is compared with a recently proposed search algorithms in an extensive simulation study.