Restricted Covariance Priors with Applications in Spatial Statistics

Theresa Smith, Jon Wakefield, Adrian Dobra

Research output: Contribution to journalArticle

5 Citations (Scopus)
34 Downloads (Pure)

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.
Original languageEnglish
Pages (from-to)965-990
Number of pages26
JournalBayesian Analysis
Volume10
Issue number4
Early online date4 Feb 2015
DOIs
Publication statusPublished - 1 Dec 2015

Keywords

  • G-Wishart distribution
  • Markov chain Monte Carlo (MCMC)
  • Spatial statistics
  • Disease Mapping

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