NOTE: This seminar is co-sponsored with the University of Washington Department of Biostatistics.

Confidence densities, uninformative priors, and the bootstrap

Seminar Speaker: Bradley Efron, PhD

Professor of Statistics and Biomedical Data Science
Stanford University

Abstract

There have been a series of conferences around the world under the label "BFF", standing for Bayesian, Frequentist, and Fiducial. I will give a version of the keynote talk at the most recent one. A general problem of BFF interest goes as follows: A family of densities with vector parameter "mu" has yielded data "X", from which the statistician wishes to infera real-valued parameter theta = t(mu). For example X might be multi-variate normal, X~N(m,V), and theta the trace of V. A statistical holy grail task is to find a convincing posterior density of theta given X, when there is no prior information on the distribution of mu. A suite of more or less related answers have been proposed: uninformative priors, matching priors, fiducial methods, and confidence densities (the last being derivatives of confidence distributions.) This talk reviews the various theories, connecting them to bootstrap methods for their implementation.

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