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Activity Number: 409
Type: Invited
Date/Time: Tuesday, August 2, 2016 : 2:00 PM to 3:50 PM
Sponsor: Section on Bayesian Statistical Science
Abstract #318130 View Presentation
Title: Confidence Distribution for Bridging Posterior Probabilistic Inferences
Author(s): Minge Xie*
Companies: Rutgers University
Keywords: Confidence distribution ; Foundation of statistics ; Bridging BFF inferences ; Bootstrap ; Bayesian computing

A confidence distribution (CD) is a sample-dependent distribution function that can serve as a distribution estimate, contrasting with a point or interval estimate, of an unknown parameter. It can represent confidence intervals (regions) of all levels for the parameter. It can provide "simple and interpretable summaries of what can reasonably be learned from data," as well as meaningful answers for all questions in statistical inference. An emerging theme is "Any statistical approach, regardless of being frequentist, fiducial or Bayesian, can potentially be unified under the concept of confidence distributions, as long as it can be used to derive confidence intervals of all levels, exactly or asymptotically." We articulate the logic behind the developments, and show how CD can potentially bridge posterior probabilistic inferences in Bayesian, frequentist and fiducial (BFF) schools in all aspects, including estimation, testing and prediction. If times allows, we will also present examples to show that the developments in CD lead to useful inference tools for statistical problems where methods with desirable properties have not been available or could not be easily obtained.

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

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