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Post date: May 23, 2018 7:07:21 PM
The besag/bym model has been around for quite some time, and is extensively used. When applied to disconnected graphs, the current practice has varied, as the original formulation by BYM, implicitly assumed a connected graph. Anna.FS & Massimo.V have now defined this in general for a disconnected graph, including how to do proper scaling of the model so that priors make sense. This is how besag/bym/etc with scale.model=TRUE is implemented in R-INLA. The link to the paper is here, and is free before 12th July 2018. Otherwise, you'll find older versions on arxiv.
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