  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.
