Objective priors for the bivariate normal model

Details Objective priors for the bivariate normal model Objective priors for the bivariate normal model

2008-04-07

arxiv.org/abs/0804.0987v1

Annals of Statistics 2008, Vol. 36, No. 2, 963-982

Mathematics

Statistics Theory

Published in at http://dx.doi.org/10.1214/07-AOS501 the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of

Scientific paper

10.1214/07-AOS501

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.

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