Bayesian Variable Selection via Hierarchical Gaussian Process Model in Computer Experiments

TL;DR

This paper introduces a Bayesian hierarchical Gaussian process model with embedded indicator variables for effective variable selection in complex computer experiments, utilizing MCMC for simultaneous estimation and selection.

Contribution

It develops a novel Bayesian hierarchical Gaussian process framework with latent indicators, enabling joint parameter estimation and variable selection in a unified approach.

Findings

Outperforms existing methods in simulated examples

Demonstrates effectiveness on real-world data

Provides efficient MCMC-based inference

Abstract

Identifying the active factors that have significant impacts on the output of the complex system is an important but challenging variable selection problem in computer experiments. In this paper, a Bayesian hierarchical Gaussian process model is developed and some latent indicator variables are embedded into this setting for the sake of labelling the important variables. The parameter estimation and variable selection can be processed simultaneously in a full Bayesian framework through an efficient Markov Chain Monte Carlo (MCMC) method -- Metropolis-within-Gibbs sampler. The much better performances of the proposed method compared with the related competitors are evaluated by the analysis of simulated examples and a practical application.