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On the construction of Bayes–confidence regions

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  • T. J. Sweeting

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.

Suggested Citation

  • T. J. Sweeting, 1999. "On the construction of Bayes–confidence regions," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 61(4), pages 849-861.
    • Handle: RePEc:bla:jorssb:v:61:y:1999:i:4:p:849-861
    DOI: 10.1111/1467-9868.00206
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    Cited by:

    1. Ventura, Laura & Ruli, Erlis & Racugno, Walter, 2013. "A note on approximate Bayesian credible sets based on modified loglikelihood ratios," Statistics & Probability Letters, Elsevier, vol. 83(11), pages 2467-2472.
    2. In Hong Chang & Rahul Mukerjee, 2008. "Bayesian and frequentist confidence intervals arising from empirical-type likelihoods," Biometrika, Biometrika Trust, vol. 95(1), pages 139-147.

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