Objective Bayes Estimation and Hypothesis Testing: the reference-intrinsic approach
Abstract: Conventional frequentist solutions to point estimation and hypothesis testing typically need ad hoc modifications when dealing with non-regular models, and may prove to be misleading. The decision oriented objective Bayesian approach to point estimation using conventional loss functions produces noninvariant solutions, and conventional Bayes factors suffer from Jeffreys-Lindley-Bartlett paradox. In this paper we illustrate how the use of the intrinsic discrepancy combined with reference analysis produce solutions to both point estimation and precise hypothesis testing, which are shown to overcome these difficulties. Specifically, we illustrate the methodology with some non-regular examples. The solutions obtained are compared with some previous results.
Keywords: Bayesian reference criterion, intrinsic divergence, intrinsic estimator, logarithmic discrepancy, reference prior.