A PREDICTION-ORIENTED BAYESIAN SITE SELECTION APPROACH FOR LARGE SPATIAL DATA

Abstract

The Gaussian geostatistical model has been widely used in spatial data modeling. In spite
of its popularity, this model suffers from a severe implementation problem for Bayesian
inference, for which a covariance matrix needs to be inverted at each iteration. This is
infeasible when the number of observations is large. In this paper, we propose a predictionoriented
Bayesian site selection (BSS) approach to tackle this difficulty. By dividing the
observations into two sets, response variables and explanatory variables, the BSS approach
forms a regression model which relates the observations through a conditional likelihood
derived from the original Gaussian geostatistical model, and then reduces the dimension
of the data using a stochastic variable selection procedure. Our numerical results indicate
that the BSS approach can produce very good parameter estimates and prediction for large
spatial data, while significantly reducing the computational time required by conventional
Bayesian approaches.