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A Distinguished Speaker Series Seminar by James Berger, Ph.D.

Part 1: The 250+ Year History of Objective Bayesian Analysis and the 100+ Year History of Classical Statistics

Statistics is perhaps unique among major scientific disciplines in that its history is not well known. Pierre-Simon Laplace created the first general statistical methodology – which came to be known as inverse probability – in 1776; today it is called objective Bayesian analysis. For 150 years, inverse probability was the dominant method of statistical analysis. In the 1920s, the Fisherian school and the frequentist school of statistics emerged, supposedly to correct difficulties with inverse probability that had been uncovered. The first hour will highlight this history and the conflict that ensued.

Part 2: The p-value Controversy

Nothing encapsulates the conflict between Objective Bayesian Analysis and Classical Statistics more than the p-value controversy. The history of this will be briefly reviewed, but the focus will be on examples that illustrate the stark differences that can occur and the impact of this on reproducibility of science. Simple suggestions that have been proposed to resolve the conflict will be discussed.

Part 3: Bayesian Multiplicity Adjustment and Subgroup Analysis

The Bayesian approach to controlling for multiple testing and other multiplicities will first be reviewed. The most interesting feature of this approach is that it occurs through the prior probabilities assigned to models/hypotheses and is, hence, independent of the error structure of the data, which is the main obstacle to adjustment for multiplicity in non-Bayesian statistics. Not all assignments of prior probabilities adjust for multiplicity, however, and assignments in huge model spaces typically require a mix of subjective assignment and appropriate hierarchical modeling. These issues will be reviewed through a variety of examples.

If time allows, discussion of the Bayesian approach to subgroup analysis will be given, including its relevance to personalized medicine.