Author

Sing-chou Wu

Date of Award

1966

Degree Type

Report

Degree Name

Master of Science (MS)

Department

Mathematics and Statistics

First Advisor

David White

Abstract

Bayes' original paper "Essay Towards Solving a Problem in the Doctrine of Change" was published in Philosophical Transactions of the Royal Society, 1763. Over 200 years, Bayes' Concepts have survived numerous critical onslaughts. Even though Bayesian Inference is still regarded as being somewhat unorthodox, it is becoming more generally accepted each year by statisticians and other scientists.

It is the purpose of this paper to provide a bird's-eye view of Bayesian Inference with emphasis on the comparison of Bayesian approaches and conventional approaches. This paper is written for those who have had about one year's background in mathematical statistics.

Some conclusions from Bayesian Inferences and classic inferences are essentially the same. However, it is informative to know how a problem can be handled by two completely different procedures, even though the conclusions are the same. What is more, the Bayesian approach does have some advantages over the classic approach. Sometimes the Bayesian approach can handle a problem which has not been solved by the classic approach. For example. an exact test of the differences between two normal means with unequal variances can be developed by introducing Behrens' distribution; a solution has not been obtained by classical methods.

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