A generalized measure of uncertainty in geostatistical model selection

Abstract

Model selection and model averaging are essential to regression analysis in environmental studies, but determining which of the two approaches is the more appropriate and under what circumstances remains an active research topic. In this paper, we focus on geostatistical regression models for spatially referenced environmental data. For a general information criterion, we develop a new perturbation-based criterion that measures the uncertainty (or, instability) of spatial model selection, as well as an empirical rule for choosing between model selection and model averaging. Statistical inference based on the proposed model selection instability measure is justified both in theory and via a s..