Bayesian multimodel inference by RJMCMC: A Gibbs sampling approach

img_5288Barker (from the lovely city of Dunedin) and Link published a paper in the American Statistician last September that I missed, as I missed their earlier email about the paper since it arrived The Day After… The paper is about a new specification of RJMCMC, almost twenty years after Peter Green’s (1995) introduction of the method. The authors use the notion of a palette, “from which all model specific parameters can be calculated” (in a deterministic way). One can see the palette ψ as an intermediary step in the move between two models. This reduces the number of bijections, if not the construction of the dreaded Jacobians!, but forces the construction of pseudo-priors on the unessential parts of ψ for every model. Because the dimension of ψ is fixed, a Gibbs sampling interleaving model index and palette value is then implementable. The conditional of the model index given the palette is available provided there are not too many models under competitions, with the probabilities recyclable towards a Rao-Blackwell approximation of the model probability. I wonder at whether or not another Rao-Blackwellisation is possible, namely to draw from all the simulated palettes a sample for the parameter of an arbitrarily chosen model.

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