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Biometrika 2005 92(1):47-57; doi:10.1093/biomet/92.1.47
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© 2005 Biometrika Trust

On the implementation of local probability matching priors for interest parameters

Trevor J. Sweeting

Department of Statistical Science, University College London, London WC1E 6BT, U.K. trevor{at}stats.ucl.ac.uk

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).

Key Words: Coverage probability bias; Data-dependent prior; Higher-order asymptotics; Metropolis–Hastings algorithm; Nuisance parameter; Probability matching prior

Received July 2003. Revised April 2004.


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