ims.07

IMS

Session Slot: 10:30-12:20 Monday

Estimated Audience Size:

AudioVisual Request: Two Overheads

Session Title: First Wald Lecture

Theme Session: No

Applied Session: No

Session Organizer: Lindsay, Bruce The Pennsylvania State University

Address: 422 Thomas Building, Department of Statistics, University Park, PA16802

Phone: (814)865-1220

Fax: (814) 863-7114

Email: bgl@psu.edu

Session Timing: 110 minutes total (Sorry about format):

Opening Remarks by Chair - 5 First Speaker - 90 Floor Discussion - 10 minutes

Session Chair: Diaconis, Persi Cornell University

Address: Department of Mathematics, ORIE, Cornell University

Phone:

Fax:

Email: persi@orie.cornell.edu

1. Consistency of Bayes Estimators

Freedman, David,   University of California at Berkeley

Address: Department of Statistics University of California, Berkeley, CA 94720-4735

Phone: 510-642-2781

Fax:

Email: freedman@stat.berkeley.edu

Abstract: Consider a finite sequence of independent, identically distributed observations, with a distribution that depends smoothly on a parameter $\theta$. If $\theta$ is finite-dimensional, Bayes estimates are consistent in the frequentist sense: as the number of observations grows, the posterior distribution piles up near $\theta$--for almost all sample sequences governed by $\theta$. (Mild additional regularity conditions are needed.) As is often said, ``the data swamp the prior.'' On the other hand, if $\theta$ is infinite-dimensional, consistency is the exception not the rule: the prior often swamps the data. I will review some recent work in this area, including Bayesian non-parametric regression and the Bernstein-von Mises theorem for hierarchical linear models.

List of speakers who are nonmembers: None