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On the implementation of local probability matching priors for interest parameters

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  • Trevor J. Sweeting

Abstract

Probability matching priors are priors for which the posterior probabilities of certain specified sets are exactly or approximately equal to their coverage probabilities. These priors arise as solutions of partial differential equations that may be difficult to solve, either analytically or numerically. Recently Levine & Casella (2003) presented an algorithm for the implementation of probability matching priors for an interest parameter in the presence of a single nuisance parameter. In this paper we develop a local implementation that is very much more easily computed. A local probability matching prior is a data-dependent approximation to a probability matching prior and is such that the asymptotic order of approximation of the frequentist coverage probability is not degraded. We illustrate the theory with a number of examples, including three discussed in Levine & Casella (2003). Copyright 2005, Oxford University Press.

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  • 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.
    • Handle: RePEc:oup:biomet:v:92:y:2005:i:1:p:47-57
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    File URL: http://hdl.handle.net/10.1093/biomet/92.1.47
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    Cited by:

    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. 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.
    3. Ventura, Laura & Cabras, Stefano & Racugno, Walter, 2009. "Prior Distributions From Pseudo-Likelihoods in the Presence of Nuisance Parameters," Journal of the American Statistical Association, American Statistical Association, vol. 104(486), pages 768-774.

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