Datta, GS; Mukerjee, R; Ghosh, M; Sweeting, TJ; (2000) Bayesian prediction with approximate frequentist validity. ANN STAT , 28 (5) 1414 - 1426.
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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.
|Title:||Bayesian prediction with approximate frequentist validity|
|Keywords:||highest predictive density region, Jeffreys' prior, noninformative prior, posterior quantile, prediction interval, NONINFORMATIVE PRIORS, POSTERIOR QUANTILES, BARTLETT CORRECTION, DISTRIBUTIONS, STATISTICS, INFERENCE, PARAMETER, INTERVALS, REGIONS|
|UCL classification:||UCL > School of BEAMS > Faculty of Maths and Physical Sciences > Statistical Science|
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