Bridging Bayesian, frequentist and fiducial (BFF) inferences using confidence distribution

Abstract

Bayesian, frequentist and fiducial (BFF) inferences are much more congruous than they have been perceived historically in the scientific community (cf., Reid and Cox 2015; Kass 2011; Efron 1998). Most practitioners are probably more familiar with the two dominant statistical inferential paradigms, Bayesian inference and frequentist inference. The third, lesser known fiducial inference paradigm was pioneered by R.A. Fisher in an attempt to define an inversion procedure for inference as an alternative to Bayes' theorem. Although each paradigm has its own strengths and limitations subject to their different philosophical underpinnings, this article intends to bridge these different inferential methodologies through the lenses of confidence distribution theory and Monte-Carlo simulation procedures. This article attempts to understand how these three distinct paradigms, Bayesian, frequentist, and fiducial inference, can be unified and compared on a foundational level, thereby increasing the range of possible techniques available to both statistical theorists and practitioners across all fields.

arXiv comment30 pages, 5 figures, Handbook on Bayesian Fiducial and Frequentist (BFF) Inferences

References in corpus (6)

• Combining information from independent sources through confidence distributions
• Overall Objective Priors
• Statistical Inference: The Big Picture
• Confidence distribution (CD) -- distribution estimator of a parameter
• Incorporating external information in analyses of clinical trials with binary outcomes
• Individualized Group Learning

Cited by in corpus (1)

• Decision Making in Drug Development via Inference on Power