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Study of the bivariate normal distribution raises the full range of issuesinvolving objective Bayesian inference, including the different types ofobjective priors (e.g., Jeffreys, invariant, reference, matching), thedifferent modes of inference (e.g., Bayesian, frequentist, fiducial) and thecriteria involved in deciding on optimal objective priors (e.g., ease ofcomputation, frequentist performance, marginalization paradoxes). Summaryrecommendations as to optimal objective priors are made for a variety ofinferences involving the bivariate normal distribution. In the course of theinvestigation, a variety of surprising results were found, including theavailability of objective priors that yield exact frequentist inferences formany functions of the bivariate normal parameters, including the correlationcoefficient.

Objective priors for the bivariate normal model