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On the construction of Bayes-confidence regions

Sweeting, TJ; (1999) On the construction of Bayes-confidence regions. J ROY STAT SOC B , 61 849 - 861.

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Abstract

We obtain approximate Bayes-confidence intervals for a scalar parameter based on directed likelihood. The posterior probabilities of these intervals agree with their unconditional coverage probabilities to fourth order, and with their conditional coverage probabilities to third order. These intervals are constructed for arbitrary smooth prior distributions. A key feature of the construction is that log-likelihood derivatives beyond second order are not required, unlike the asymptotic expansions of Severini.

Type:Article
Title:On the construction of Bayes-confidence regions
Keywords:approximate Bayesian inference, approximate conditional inference, Bayesian Bartlett correction, directed likelihood, higher order asymptotics, unsmoothing, LOG LIKELIHOOD RATIO, MARGINAL TAIL PROBABILITIES, CONDITIONAL INFERENCE, APPROXIMATIONS, PARAMETERS, STATISTICS
UCL classification:UCL > School of BEAMS > Faculty of Maths and Physical Sciences > Statistical Science

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