In particular the 1965 paper with the innocent title " On the asymptotic behaviour of Bayes estimates in the discrete case II " finds the rather disappointing answer that when sampling from a countably infinite population the Bayesian procedure fails almost everywhere, i . e . one does not obtain the true distribution asymptotically.
22.
Note that the Bernstein-von Mises theorem asserts here the asymptotic convergence to the " true " distribution because the probability space corresponding to the discrete set of events \ { GD, G \ bar D, \ bar G D, \ bar G \ bar D \ } is finite ( see above section on asymptotic behaviour of the posterior ).
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