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Activity Number: 343 - Contributed Poster Presentations: Section on Bayesian Statistical Science
Type: Contributed
Date/Time: Tuesday, August 9, 2022 : 2:00 PM to 3:50 PM
Sponsor: Section on Bayesian Statistical Science
Abstract #323294
Title: Bayesian Optimality and Intervals for Stein-Type Estimates
Author(s): Lingbo Ye* and Ken Rice
Companies: University of Washington, Seattle and University of Washington, Seattle
Keywords: Stein estimation; shrinkage; Bayesian estimates; Credible intervals; Decision theory

We provide a novel Bayesian decision-theoretic motivation for Stein-type estimates, producing them as an adaptive choice between standard point estimation and estimation that rewards proximity to the origin. Unlike conventional approaches our arguments provide shrunken estimates under any sampling model or prior. They also lead naturally to a form of credible interval, describing uncertainty about the underlying parameters yet focusing on the shrunken estimate. One specific method for constructing intervals provides a close Bayesian analog of Samworth (2005)'s approximate confidence intervals around Stein estimates. Several examples are given, showing how shrinkage's focus on regions remote to the high-support areas of the posterior can lead to substantially larger credible sets.

Authors who are presenting talks have a * after their name.

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