Bridging Bayesian, Frequentist And Fiducial Inferences Using Confidence Distributions

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Book Chapter

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Handbook Of Bayesian, Fiducial, And Frequentist Inference


Bayesian, frequentist, and fiducial (BFF) inferences are much more congruous than have been perceived historically in the scientific community (e.g., 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 chapter intends to bridge these different inferential methodologies by calling upon confidence distribution theory and Monte-Carlo simulation procedures, thereby increasing the range of possible techniques available to both statistical theorists and practitioners across all fields.

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