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On Inconsistent Bayes Estimates in the Discrete Case

David Freedman and Persi Diaconis
The Annals of Statistics
Vol. 11, No. 4 (Dec., 1983), pp. 1109-1118
Stable URL: http://www.jstor.org/stable/2241301
Page Count: 10
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On Inconsistent Bayes Estimates in the Discrete Case
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Abstract

Consider sampling from an unknown probability distribution on the integers. With a tail-free prior, the posterior distribution is consistent. With a mixture of a tail-free prior and a point mass, however, the posterior may be inconsistent. This is likewise true for a countable mixture of tail-free priors. Similar results are given for Dirichlet priors.

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