Bayesian prediction with approximate frequentist validity
Gauri Sankar Datta, Rahul Mukerjee, Malay Ghosh, and Trevor J. Sweeting
Source: Ann. Statist. Volume 28, Number 5 (2000), 1414-1426.
Abstract
We characterize priors which asymptotically match the posterior coverage probability of a Bayesian prediction region with the corresponding frequentist coverage probability. This is done considering both posterior quantiles and highest predictive density regions with reference to a future observation. The resulting priors are shown to be invariant under reparameterization. The role of Jeffreys’ prior in this regard is also investigated. It is further shown that, for any given prior, it may be possible to choose an interval whose Bayesian predictive and frequentist coverage probabilities are asymptotically matched.
Primary Subjects: 62C10, 62F15
Keywords: Highest predictive density region; Jeffreys' prior; noninformative prior; posterior quantile; prediction interval
Full-text: Open access
Links and Identifiers
Permanent link to this document: http://projecteuclid.org/euclid.aos/1015957400
Mathematical Reviews number (MathSciNet):
MR1805790
Digital Object Identifier: doi:10.1214/aos/1015957400
Zentralblatt MATH identifier:
01828989
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