Noninformative priors in Bayesian analysis

Keying Ye, Purdue University

Abstract

The reference priors, introduced by Bernardo (1979) and as further developed in Berger and Bernardo (1989a,b,c), are studied in several situations. These include nonlinear regression, sequential problems, and the unbalanced variance components problem. For nonlinear regression problems, there is a long history of the difficulties (such as impropriety of the posterior) resulting from common noninformative priors. The new "group-ordered" reference priors of Berger and Bernardo (1990b) are derived and shown to overcome the difficulties. Bayesian inferences under these priors are compared to each other and also compared to frequentist inference using the MLE. The results indicate considerable success for the preferred reference prior. In sequential experiments, where a stopping time is used, the Jeffreys noninformative prior for a multidimensional parameter is obtained as well as the reference prior. These noninformative priors depend on the expected stopping time. It is demonstrated that the Jeffreys prior depends on the stopping time in an inappropriate fashion for a multiparameter problem, while the reference prior does not. Some results on the admissibility of the resulting generalized Bayes rules are also developed. Finally, reference priors for the unbalanced variance components problem are derived and studied with respect to risk performance.

Degree

Ph.D.

Advisors

Berger, Purdue University.

Subject Area

Statistics

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