Bayesian spatial models with a mixture neighborhood structure

In Bayesian disease mapping, one needs to specify a neighborhood structure to make inference on 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 usual Bayesian spatial models: given the neighborhood graph, the 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. Palavras-chave: Disease mapping, Markov Random Field, Spatial Hierarchical Models.