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Evaluating improper priors and the recurrence of symmetric Markov chains: an overview. (English) Zbl 1268.62010
Dasgupta, Anirban (ed.), A Festschrift for Herman Rubin. Beachwood, OH: IMS, Institute of Mathematical Statistics (ISBN 0-940600-61-7/pbk). Institute of Mathematical Statistics Lecture Notes - Monograph Series 45, 5-20 (2004).
Summary: Given a parametric statistical model, an improper prior distribution can often be used to induce a proper posterior distribution (an inference). This inference can then be used to solve decision problems once an action space and loss have been specified. One way to evaluate the inference is to ask for which estimation problems does the above formal Bayes method produce admissible estimators. The relationship of this problem to the recurrence of an associated symmetric Markov chain is reviewed.
For the entire collection see [Zbl 1066.62002].

MSC:
62C10 Bayesian problems; characterization of Bayes procedures
62C15 Admissibility in statistical decision theory
62F10 Point estimation
62M05 Markov processes: estimation; hidden Markov models
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