Bayesian/Fiducial/Frequentist Uncertainty Quantification by Artificial Samples

Professor Min-ge Xie, Rutgers University, mxie@stat.rutgers.edu

Bayesian, frequentist and fiducial (BFF) inferences are much more congruous than they have been perceived historically in the scientific community. Most practitioners are probably more familiar with the competing narratives of 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 talk intends to bridge these three different inferential methodologies through the lenses of confidence distribution theory and artificial sampling procedures. The talk attempts to understand how uncertainty quantifications in 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.

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