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

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 based on an independent Metropolis-Hastings sampler, where individual proposal probabilities of explanatory variables are updated after each iteration using a form learning, way that they finally converge to respective covariates' inclusion probabilities. We prove ergodicity present parallel version with adaptation scheme combination information multiple chains. effectiveness demonstrated via various simulated real data examples, including problem more than 20,000 covariates.