The Annals of Statistics
- Ann. Statist.
- Volume 28, Number 5 (2000), 1414-1426.
Bayesian prediction with approximate frequentist validity
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.
Ann. Statist., Volume 28, Number 5 (2000), 1414-1426.
First available in Project Euclid: 12 March 2002
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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