Distributions for Parameters
N. Reid · 2024
This handbook is the outcome of a series of workshops, as described in the preface. In this introductory chapter, I attempt to give a high-level overview of different inferential approaches. I have addressed this through what I view as a common goal among Bayesian, fiducial and frequentist approaches — finding a distribution for a parameter or parameters of interest. Confidence distributions, generalized fiducial distributions, inferential models, and belief functions are some of the terms associated with these approaches. In this overview, I discuss both historical developments and modern versions. For a more detailed comparison of Bayesian and frequentist approaches, see Berger (2022 ). A more eclectic discussion of Bayes, Fiducial and Frequentist is given in Meng (2024 ) though a series of compelling examples. An exploration of frequentist properties of Bayesian methods in a quite different context, of testing fixed hypotheses, is presented in Berger et al. (2024 ).