A shrinkage-thresholding Metropolis adjusted Langevin algorithm for Bayesian variable selection

TL;DR

This paper proposes a novel MCMC algorithm combining Langevin dynamics and shrinkage-thresholding for efficient Bayesian variable selection in high-dimensional problems, with proven ergodicity and demonstrated superior performance.

Contribution

It introduces a new trans-dimensional MCMC method that integrates Langevin proposals with shrinkage-thresholding, enhancing Bayesian variable selection efficiency.

Findings

Proven geometric ergodicity of the proposed sampler.

Demonstrated improved performance over classical algorithms.

Effective in both simulated and real high-dimensional data.

Abstract

This paper introduces a new Markov Chain Monte Carlo method for Bayesian variable selection in high dimensional settings. The algorithm is a Hastings-Metropolis sampler with a proposal mechanism which combines a Metropolis Adjusted Langevin (MALA) step to propose local moves associated with a shrinkage-thresholding step allowing to propose new models. The geometric ergodicity of this new trans-dimensional Markov Chain Monte Carlo sampler is established. An extensive numerical experiment, on simulated and real data, is presented to illustrate the performance of the proposed algorithm in comparison with some more classical trans-dimensional algorithms.