Comparison of frequentist coverage probability and Bayesian posterior coverage probability, and applications

Chung-Bow Lee, Purdue University

Abstract

The work is to compare frequentist coverage probability and Bayesian posterior coverage probability from a large sample point of view. It extends that of Welch & Peers (1963) and Stein (1985), but the approach is different and simpler. The main technique is just the application of the approximate density of the sufficient statistic in Durbin (1980). A series expansion for frequentist coverage probability is obtained up to error order O(n$\sp{-3/2}$) for Bayesian credible sets with interesting shapes. Typically, the confidence sets we consider are either one-sided or symmetric in one-dimensional cases, and either elliptic regions for the parameters of interest in the presence of nuisance parameters, or half-spaces, in multiple dimensions. The technique of reparameterization will be applied to help in the search for reference priors. We also consider the case of two-dimensional parameters and the technique of parameter orthogonality. Finally, some computer results are given for comparing the credible sets based on three kinds of priors in some cases and some applications are also considered.

Degree

Ph.D.

Advisors

Sellke, Purdue University.

Subject Area

Statistics

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