title: Restricted Covariance Priors with Applications in Spatial Statistics.
abstract: We present a Bayesian model for area-level count data that uses Gaussian random effects with a novel type of G-Wishart prior on the inverse variance- covariance matrix. Specifically, we introduce a new distribution called the truncated G-Wishart distribution that has support over precision matrices that lead to positive associations between the random effects of neighboring regions while preserving conditional independence of non-neighboring regions. We describe Markov chain Monte Carlo sampling algorithms for the truncated G-Wishart prior in a disease mapping context and compare our results to Bayesian hierarchical models based on intrinsic autoregression priors. A simulation study illustrates that using the truncated G-Wishart prior improves over the intrinsic autoregressive priors when there are discontinuities in the disease risk surface. The new model is applied to an analysis of cancer incidence data in Washington State.
authors.affiliation: Department of Statistics, University of Washington, Seattle, WA 98195.
authors.forename: Theresa R
authors.initials: TR
authors.lastname: Smith
authors.affiliation: Departments of Statistics and Biostatistics, University of Washington, Seattle, WA 98195.
authors.forename: Jon
authors.initials: J
authors.lastname: Wakefield
authors.affiliation: Departments of Statistics, Biobehavioral Nursing, and Health Systems and the Center for Statistics and the Social Sciences, University of Washington, Seattle, WA 98195.
authors.forename: Adrian
authors.initials: A
authors.lastname: Dobra
keywords: G-Wishart distribution; Markov chain Monte Carlo (MCMC); disease mapping; spatial statistics