A Metropolized Adaptive Subspace Algorithm for High-Dimensional Bayesian Variable Selection

Bayesian Analysis, vol. 19

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.

Authors 3

1. Christian Staerk

   University Hospital Bonn

   Affiliation as printed

   Department of Medical Biometry, Informatics and Epidemiology, University Hospital Bonn, Venusberg Campus 1, 53127 Bonn, Germany

2. Maria Kateri Aachen Institute of Statistics

   RWTH Aachen University

   Affiliation as printed

   Institute of Statistics, RWTH Aachen University, Pontdriesch 14-16, 52062 Aachen, Germany

3. Ioannis Ntzoufras

   Athens University of Economics and Business

   Affiliation as printed

   Department of Statistics, Athens University of Economics and Business, Trias 2, Athina 113 62, Greece