Probability matching priors for some parameters of the bivariate normal distribution
Malay Ghosh, Upasana Santra, Dalho Kim
Abstract
This paper develops some objective priors for certain parameters of the bivariate normal distribution. The parameters considered are the regression coefficient, the generalized variance, and the ratio of the conditional variance of one variable given the other to the marginal variance of the other variable. The criterion used is the asymptotic matching of coverage probabilities of Bayesian credible intervals with the corresponding frequentist coverage probabilities. The paper uses various matching criteria, namely, quantile matching, matching of distribution functions, highest posterior density matching, and matching via inversion of test statistics. One particular prior is found which meets all the matching criteria individually for all the parameters of interest.
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Primary Subjects: 62F15, 62F25
Keywords: credible intervals; distribution functions; first order; generalized variance; highest posterior density; likelihood ratio; posteriors; propriety; quantiles; regression coefficient; second order
Full-text: Open access
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Permanent link to this document: http://projecteuclid.org/euclid.imsc/1209398461
Digital Object Identifier: doi:10.1214/074921708000000066
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