WinBUGS – A Bayesian modelling framework: Concepts, structure, and extensibility
Statistics and Computing
A stochastic neighborhood conditional autoregressive model for spatial data
Computational Statistics & Data Analysis
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In Bayesian disease mapping, one needs to specify a neighborhood structure to make inference about the underlying geographical relative risks. We propose a model in which the neighborhood structure is part of the parameter space. We retain the Markov property of the typical Bayesian spatial models: given the neighborhood graph, disease rates follow a conditional autoregressive model. However, the neighborhood graph itself is a parameter that also needs to be estimated. We investigate the theoretical properties of our model. In particular, we investigate carefully the prior and posterior covariance matrix induced by this random neighborhood structure, providing interpretation for each element of these matrices.