Probability matching priors for some parameters of the bivariate normal distribution

TL;DR

This paper derives objective priors for key parameters of the bivariate normal distribution using asymptotic coverage probability matching, identifying a prior that satisfies multiple criteria for all parameters.

Contribution

It introduces a set of objective priors based on various matching criteria and identifies a specific prior that meets all criteria for the parameters considered.

Findings

A prior that achieves all matching criteria for the parameters.

The priors improve Bayesian credible interval coverage accuracy.

Methodology applicable to other multivariate distributions.

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.