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Objective priors for the bivariate normal model. (English) Zbl 1133.62014

Summary: Study of the bivariate normal distribution raises the full range of issues involving objective Bayesian inference, including the different types of objective priors (e.g., Jeffreys, invariant, reference, matching), the different modes of inference (e.g., Bayesian, frequentist, fiducial) and the criteria involved in deciding on optimal objective priors (e.g., ease of computation, frequentist performance, marginalization paradoxes). Summary recommendations as to optimal objective priors are made for a variety of inferences involving the bivariate normal distribution. In the course of the investigation, a variety of surprising results were found, including the availability of objective priors that yield exact frequentist inferences for many functions of the bivariate normal parameters, including the correlation coefficient.

MSC:

62F15 Bayesian inference
62F10 Point estimation
62A01 Foundations and philosophical topics in statistics
62F25 Parametric tolerance and confidence regions
62H12 Estimation in multivariate analysis
62H10 Multivariate distribution of statistics
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