Inferindo a estrutura de vizinhança em modelos bayesianos espaciais

Abstract

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 Bayesianspatial 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 investigatecarefully the prior and posterior covariance matrix induced by this random neighborhood structure providing interpretation for each element of these matrices. We also illustrate the advantages of our model with simulated data and real disease mapping examples.