Joint variable selection of both fixed and random effects for Gaussian process-based spatially varying coefficient models

Spatially varying coefficient (SVC) models are a type of regression model for spatial data where covariate effects vary over space. If there several covariates, natural question is which covariates have spatially effect and not. We present new variable selection approach Gaussian process-based SVC models. It relies on penalized maximum likelihood estimation (PMLE) allows both with respect to fixed process random effects. validate our in simulation study as well real world set. Our novel shows good performance the study. In application, proposed PMLE yields sparser achieves smaller information criterion than classical MLE. cross-validation applied data, we show that PML estimated par ML predictive performance.