Open Access
VOL. 3 | 2008 Probability matching priors for some parameters of the bivariate normal distribution
Malay Ghosh, Upasana Santra, Dalho Kim

Editor(s) Bertrand Clarke, Subhashis Ghosal

Inst. Math. Stat. (IMS) Collect., 2008: 71-81 (2008) DOI: 10.1214/074921708000000066


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.


Published: 1 January 2008
First available in Project Euclid: 28 April 2008

Digital Object Identifier: 10.1214/074921708000000066

Primary: 62F15 , 62F25

Keywords: credible intervals , distribution functions , first order , generalized variance , highest posterior density , likelihood ratio , posteriors , propriety , quantiles , regression coefficient , second order

Rights: Copyright © 2008, Institute of Mathematical Statistics

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