Confidence Distribution (CD) as a Unifying Framework for BFF Inference

• Activity Number: 339
• Type: Invited
• Date/Time: Tuesday, August 11, 2015 : 10:30 AM to 12:20 PM
• Sponsor: International Society for Bayesian Analysis (ISBA)
• Author(s): Regina Y. Liu* and Minge Xie
• Companies: Rutgers University and Rutgers University
• Keywords: confidence distribution ; fiducial inference ; Bayesian inference ; frequentist inference ; BFF

Abstract

A confidence distribution (CD) is a sample-dependent distribution function that can serve as a distribution estimate, contrasting with point or interval estimate, of a unknown parameter. It can represent confidence intervals of all levels for the parameter. It can provide "simple and interpretable summaries of what can reasonably be learned from data (and an assumed model)", as well as meaningful answers for all questions in statistical inference. An emerging theme from recent developments on CD is "Any statistical approach, regardless of being frequentist, fiducial or Bayesian (BFF), 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 serve as a unifying framework for all BFF inferences in all aspects, including estimation, testing and prediction. Moreover, we present several examples to show that these developments in CD actually lead to useful inference tools for statistical problems where methods with desirable properties have not been available or could not be easily obtained.