Date of Award

12-2012

Document Type

Thesis

Degree Name

Master of Science (MS)

Legacy Department

Mathematical Science

Advisor

Sun, Xiaoqian

Committee Member

Sun , Xiaoqian

Committee Member

Gallagher , Colin

Committee Member

Park , Chanseok

Abstract

One of the oldest problems in statistical area is to make inference on a common mean of several different normal populations with unknown and probably unequal variances. There are several different ways to make inference on the common mean. The most common methods are point estimation, hypothesis testing, and interval estimation. Point estimation uses sample data to calculate a single value serving as a best guess for the unknown population mean. Hypothesis testing assumes all populations have the same mean as the null hypothesis. Interval estimation is an interval of possible values of the unknown mean.
In this paper, we focus on point estimation and hypothesis testing and use Bayesian methods to make inference on the common mean of two different normal populations. Since the specification of a subjective prior is often difficult and polemical in scientific communication, information theory may be used to develop a prior, the reference prior, which only depends on the assumed model. We will introduce an invariant loss function -- intrinsic loss function to deal with the problem. The combination of the intrinsic discrepancy and appropriately defined reference prior provides an integrated objective Bayesian solution to both estimation and hypothesis testing problems.

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