ABSTRACT
Spatially-referenced data pose challenges for Bayesian variable selection, including residual spatial correlation and cumbersome computing for large datasets. In this chapter, we discuss foundational approaches and recent advances in Bayesian variable selection for spatial regression models. We begin by introducing the canonical spatial regression model and discuss how Bayesian variable selection priors can be adapted to account for spatial correlation in the residuals. We then address the more challenging problem of allowing different regression relationships in different regions, including allowing the subset of covariates included in the model to vary across space. We introduce several models for this spatial variation, apply some of the models to a large spatial microbiome dataset
