Joseph Lang - Colloquium Speaker
“The Fiducialist attempts to make the Bayesian omelet [derive a post-data distribution] without breaking the Bayesian eggs [without specifying a prior].” — paraphrasing Savage (1961)
“...the fiducial argument has a very limited success and is now essentially dead.” — Pedersen (1978)
“Maybe Fisher’s biggest blunder [fiducial inference] will become a big hit in the 21st century!” — Efron (1998)
Of the three inference approaches, Bayesian, Frequentist, and Fiducial, the last is the most controversial and least understood. This presentation addresses this controversy and sets out to improve understanding with a new fiducial argument that does not rely on R.A. Fisher’s controversial “switching principle.” Unlike the conventional pivot-and-switch argument, the proposed slice-and-dice argument leads to straightforward interpretations of fiducial probabilities and distributions that are defensible using only fiducial slices and projections and an intuitive “unremarkable realization, dicing proposition.” Moreover, the proposed argument is directly applicable for a broad class of multi-parameter models. This presentation also gives a brief history of the fiducial approach, tracking its near demise in the mid 20th century through to its rebirth of sorts in the 21st century. The differences and similarities between the three (the BFF) inference approaches are highlighted using simple examples. Advantages and disadvantages of the fiducial approach vis-à-vis the frequentist and Bayesian approaches are discussed. Finally, the usefulness of the fiducial approach is supported by results of a small scale simulation study. In particular, these results corroborate reports that fiducial confidence intervals often have better frequentist coverage properties than commonly-used approximate frequentist intervals, especially for small sample sizes.