  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.
