Open Access
VOL. 3 | 2008 On predictive probability matching priors
Trevor J. Sweeting

Editor(s) Bertrand Clarke, Subhashis Ghosal

Inst. Math. Stat. (IMS) Collect., 2008: 46-59 (2008) DOI: 10.1214/074921708000000048


We revisit the question of priors that achieve approximate matching of Bayesian and frequentist predictive probabilities. Such priors may be thought of as providing frequentist calibration of Bayesian prediction or simply as devices for producing frequentist prediction regions. Here we analyse the O(n−1) term in the expansion of the coverage probability of a Bayesian prediction region, as derived in [Ann. Statist. 28 (2000) 1414–1426]. Unlike the situation for parametric matching, asymptotic predictive matching priors may depend on the level α. We investigate uniformly predictive matching priors (UPMPs); that is, priors for which this O(n−1) term is zero for all α. It was shown in [Ann. Statist. 28 (2000) 1414–1426] that, in the case of quantile matching and a scalar parameter, if such a prior exists then it must be Jeffreys’ prior. In the present article we investigate UPMPs in the multiparameter case and present some general results about the form, and uniqueness or otherwise, of UPMPs for both quantile and highest predictive density matching.


Published: 1 January 2008
First available in Project Euclid: 28 April 2008

MathSciNet: MR2459215

Digital Object Identifier: 10.1214/074921708000000048

Primary: 62F15
Secondary: 62E20

Keywords: Asymptotic theory , Bayesian inference , predictive inference , probability matching prior

Rights: Copyright © 2008, Institute of Mathematical Statistics

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