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James O. BergerAn Overview of Objective Bayesian Analysis

James O. Berger

Visiting Professor
Duke University

Bayesian analysis is often thought of as a subjective approach to analysis of data. This is neither true historically, logically, nor in practice. The goal of this 5-lecture series is to introduce the elements of objective Bayesian analysis, in the context of a variety of applications. The lectures presume a significant grounding in statistics but, for the most part, do not presume extensive familiarity with Bayesian analysis.

 

LECTURE 1. Objective Bayesian Analysis: Introduction and a Casual History
Tuesday, April 5, 2011, 4:30-5:30, Eckhart 133, 5734 S. University Avenue.

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After an introductory example of medical diagnosis to set the notation and concepts, this lecture reviews the 250 year history of objective Bayesian analysis, through the work of Jeffreys and the beginnings of the 'upstart' subjective Bayesian approach.

 

LECTURE 2. Objective Bayesian Estimation
Tuesday, April 12, 2011, 4:30-5:30, Eckhart 133, 5734 S. University Avenue.

This lecture highlights a few of the modern approaches to objective Bayesian estimation, especially the 'reference prior,' 'matching prior,' and 'invariance prior' approaches. The unification of objective Bayes and frequentist estimation is also discussed. The concepts will be illustrated with the problem of determining the distance to Cepheid variable stars.

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LECTURE 3. Objective Bayesian Hypothesis Testing and Conditional Frequentist Testing
Tuesday, April 19, 2011, 4:30-5:30, Eckhart 133, 5734 S. University Avenue.

The lecture begins with examples to illustrate the severe inadequacy of p-values for testing, and goes on to introduce the basics of the objective Bayesian alternative to testing. The discussion is in the context of a pedagogical example of high-energy physics. The duality of the objective Bayesian approach with conditional frequentist testing is also discussed. (Thus both Bayesians and frequentists dislike the way p-values are misused.)

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LECTURE 4. Essentials of Objective Bayesian Model Uncertainty
Tuesday, May 3, 2011, 4:30-5:30, Eckhart 133, 5734 S. University Avenue.

The major essential is to recognize that it is crucial to account for model uncertainty in any use of statistics; the all-too-common approach of selecting a model, followed by making inferences and predictions based solely on that model, can lead to drastic overconfidence in inference and prediction. This is addressed within the Bayesian framework by techniques such as model averaging. There are surprises, however, such as the fact that the best predictive model is often not the highest probability model, but rather what is called the median probability model. More technical essentials, such as the need to recognize when proper priors must be utilized and the need to have priors for the parameters of models that are appropriately 'predictively matched' across models, will also be discussed.

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LECTURE 5. Methodology of Objective Bayesian Model Uncertainty
Tuesday, May 10, 2011, 4:30-5:30, Eckhart 133, 5734 S. University Avenue.

Conventional choices of priors for Bayesian analysis of model uncertainty will be discussed, as will computational issues and approximations. Illustrations will be given.

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