Dr. David Draper (UC Santa Cruz)

Title: Bayesian model specification: toward a Theory of Applied Statistics

Abstract: The Bayesian approach to statistical inference, prediction and decision-making has a simple structure, with one equation for each of these three fundamental activities, and it can be shown to be based on a straightforward logical progression from principles to axioms to a foundational theorem with corollaries. However, this approach requires the user to specify two ingredients (usually called the prior and sampling distributions) for inference and prediction and two more ingredients (an action space and a utility function) for decision-making, and as a profession we lack the same kind of logical progression from principles to axioms to theorems that would constitute optimal specification of these four ingredients (by "optimal" here I mean "coming as close as possible to the goal of {conditioning only on true/false propositions that are rendered true by the context of the problem and the design of the data-gathering activity}"). Successfully developing such a logical progression would yield a Theory of Applied Statistics, which we need and do not yet have. In this talk I'll explore the extent to which four principles (Calibration, Modeling-As-Decision, Prediction, and Decision-Versus-Inference) constitute progress toward this goal.