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March 2024 A Metropolized Adaptive Subspace Algorithm for High-Dimensional Bayesian Variable Selection
Christian Staerk, Maria Kateri, Ioannis Ntzoufras
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Bayesian Anal. 19(1): 261-291 (March 2024). DOI: 10.1214/22-BA1351

Abstract

A simple and efficient adaptive Markov Chain Monte Carlo (MCMC) method, called the Metropolized Adaptive Subspace (MAdaSub) algorithm, is proposed for sampling from high-dimensional posterior model distributions in Bayesian variable selection. The MAdaSub algorithm is based on an independent Metropolis-Hastings sampler, where the individual proposal probabilities of the explanatory variables are updated after each iteration using a form of Bayesian adaptive learning, in a way that they finally converge to the respective covariates’ posterior inclusion probabilities. We prove the ergodicity of the algorithm and present a parallel version of MAdaSub with an adaptation scheme for the proposal probabilities based on the combination of information from multiple chains. The effectiveness of the algorithm is demonstrated via various simulated and real data examples, including a high-dimensional problem with more than 20,000 covariates.

Acknowledgments

We would like to thank the editor, the associate editor and two reviewers for their valuable comments and suggestions.

Citation

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Christian Staerk. Maria Kateri. Ioannis Ntzoufras. "A Metropolized Adaptive Subspace Algorithm for High-Dimensional Bayesian Variable Selection." Bayesian Anal. 19 (1) 261 - 291, March 2024. https://doi.org/10.1214/22-BA1351

Information

Published: March 2024
First available in Project Euclid: 22 January 2024

MathSciNet: MR4693264
Digital Object Identifier: 10.1214/22-BA1351

Keywords: adaptive MCMC , generalized linear models , High-dimensional data , Sparsity , Variable selection

Vol.19 • No. 1 • March 2024
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