Modelling spatially varying coefficients via sparsity priors.

Sparsity inducing priors are widely used in Bayesian regression analysis, and seek dimensionality reduction to avoid unnecessarily complex models. An alternative to sparsity induction are discrete mixtures, such as spike and slab priors. These ideas extend to selection of random effects, either i ⁢ i ⁢ d or structured (e.g. spatially structured). In contrast to sparsity induction in mixed models with i ⁢ i ⁢ d random effects, in this paper we apply sparsity priors to spatial regression for area units (lattice data), and to spatial random effects in conditional autoregressive priors. In particular, we consider the use of global-local shrinkage to distinguish areas with average predictor effects from areas where the predictor effect is amplified or diminished because the response-predictor pattern is distinct from that of most areas. The operation and utility of this approach is demonstrated using simulated data, and in a real application to diabetes related deaths in New York counties. [ABSTRACT FROM AUTHOR]