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Biometrika 1971 58(3):535-543; doi:10.1093/biomet/58.3.535
© 1971 by Biometrika Trust
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An empirical Bayes problem with a Markovian parameter

P. F. PRESTON

University of Melbourne

A study is made of an empirical Bayes estimation problem in which the set of parameter values is a realization of a stationary Markov chain. The Bayes rule is derived as a function of the transition probabilities of the Markov chain. The performance of empirical Bayes rules, which use estimates of these transition probabilities based on the observations, is investigated by simulation. Two other rules are shown to be competitors of the empirical Bayes rules in some particular cases. These are a two-step rule which uses only the (i–1)th, ith and (i+1)th observations when making the ith decision, and a rule based on the mode of the posterior distribution of the parameter sequence.

Key Words: Empirical Bayes procedures • Bayes decision rules • Markov chains • Industrial acceptance sampling


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