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Highest posterior density regions with approximate frequentist validity: The role of data-dependent priors

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  • Chang, In Hong
  • Mukerjee, Rahul

Abstract

For the general multiparameter case, we consider the problem of ensuring frequentist validity of highest posterior density regions with margin of error o(n-1), where n is the sample size. The role of data-dependent priors is investigated and it is seen that the resulting probability matching condition readily allows solutions, in contrast to what happens with data-free priors. Moreover, use of data-dependent priors is seen to be helpful even for models, such as mixture models, where closed form expressions for the expected information elements do not exist.

Suggested Citation

  • Chang, In Hong & Mukerjee, Rahul, 2010. "Highest posterior density regions with approximate frequentist validity: The role of data-dependent priors," Statistics & Probability Letters, Elsevier, vol. 80(23-24), pages 1791-1797, December.
    • Handle: RePEc:eee:stapro:v:80:y:2010:i:23-24:p:1791-1797
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    References listed on IDEAS

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    1. Kai-Tai Fang & Rahul Mukerjee, 2006. "Empirical-type likelihoods allowing posterior credible sets with frequentist validity: Higher-order asymptotics," Biometrika, Biometrika Trust, vol. 93(3), pages 723-733, September.
    2. J. Ghosh & Rahul Mukerjee, 1993. "Frequentist validity of highest posterior density regions in the multiparameter case," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 45(2), pages 293-302, June.
    3. Chang, In Hong & Mukerjee, Rahul, 2006. "Probability matching property of adjusted likelihoods," Statistics & Probability Letters, Elsevier, vol. 76(8), pages 838-842, April.
    4. Trevor J. Sweeting, 2005. "On the implementation of local probability matching priors for interest parameters," Biometrika, Biometrika Trust, vol. 92(1), pages 47-57, March.
    5. J. Ghosh & Rahul Mukerjee, 1993. "Corrections to “Frequentist validity of highest posterior density regions in the multiparameter case”," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 45(3), pages 602-602, September.
    6. 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.
    7. Ghosh Jayanta K. & Mukerjee Rahul, 1995. "Frequentist Validity Of Highest Posterior Density Regions In The Presence Of Nuisance Parameters," Statistics & Risk Modeling, De Gruyter, vol. 13(2), pages 131-140, February.
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