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Intrinsic Gaussian Markov Random Fields (IGMRFs) can be used to induceconditional dependence in Bayesian hierarchical models. IGMRFs have both aprecision matrix, which defines the neighbourhood structure of the model, and aprecision, or scaling, parameter. Previous studies have shown the importance ofselecting this scaling parameter appropriately for different types of IGMRF, asit can have a substantial impact on posterior results. Here, we focus on thetwo-dimensional case, where tuning of the parameter is achieved by mapping itto the marginal standard deviation of a two-dimensional IGMRF. We compare theeffects of scaling various classes of IGMRF, including an application to bloodpressure data using MCMC methods.

Scaling priors in two dimensions for Intrinsic Gaussian MarkovRandom Fields