Abstract
AbstractWe introduce an adapted form of the Markov random field (MRF) for Bayesian spatial smoothing with small‐area data. This new scheme allows the amount of smoothing to vary in different parts of a map by employing area‐specific smoothing parameters, related to the variance of the MRF. We take an empirical Bayes approach, using variance information from a standard MRF analysis to provide prior information for the smoothing parameters of the adapted MRF. The scheme is shown to produce proper posterior distributions for a broad class of models. We test our method on both simulated and real data sets, and for the simulated data sets, the new scheme is found to improve modelling of both slowly‐varying levels of smoothness and discontinuities in the response surface. Copyright © 2007 John Wiley & Sons, Ltd.
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