The Annals of Statistics

Bayesian prediction with approximate frequentist validity

Gauri Sankar Datta, Malay Ghosh, Rahul Mukerjee, and Trevor J. Sweeting

Full-text: Open access

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.

Article information

Source
Ann. Statist., Volume 28, Number 5 (2000), 1414-1426.

Dates
First available in Project Euclid: 12 March 2002

Permanent link to this document
https://projecteuclid.org/euclid.aos/1015957400

Digital Object Identifier
doi:10.1214/aos/1015957400

Mathematical Reviews number (MathSciNet)
MR1805790

Zentralblatt MATH identifier
1105.62312

Subjects
Primary: 62C10: Bayesian problems; characterization of Bayes procedures 62F15: Bayesian inference

Keywords
Highest predictive density region Jeffreys' prior noninformative prior posterior quantile prediction interval

Citation

Datta, Gauri Sankar; Mukerjee, Rahul; Ghosh, Malay; Sweeting, Trevor J. Bayesian prediction with approximate frequentist validity. Ann. Statist. 28 (2000), no. 5, 1414--1426. doi:10.1214/aos/1015957400. https://projecteuclid.org/euclid.aos/1015957400


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