CARBayes: An R Package for Bayesian Spatial Modeling with Conditional Autoregressive Priors

Abstract

Conditional autoregressive models are commonly used to represent spatial autocorrelation in data relating to a set of non-overlapping areal units, which arise in a wide variety of applications including agriculture, education, epidemiology and image analysis. Such models are typically specified in a hierarchical Bayesian framework, with inference based on Markov chain Monte Carlo (MCMC) simulation. The most widely used software to fit such models is WinBUGS or OpenBUGS, but in this paper we introduce the R package CARBayes. The main advantage of CARBayes compared with the BUGS software is its ease of use, because: (1) the spatial adjacency information is easy to specify as a binary neighbourhood matrix; and (2) given the neighbourhood matrix the models can be implemented by a single function call in R. This paper outlines the general class of Bayesian hierarchical models that can be implemented in the CARBayes software, describes their implementation via MCMC simulation techniques, and illustrates their use with two worked examples in the fields of house price analysis and disease mapping.