Here are the slides from my discussion of Nancy Reid today at BFF4: The Fourth Bayesian, Fiducial, and Frequentist Workshop: May 1-3, 2017 (hosted by Harvard University)

# fiducial probability

## “Fusion-Confusion?” My Discussion of Nancy Reid: “BFF Four- Are we Converging?”

## R.A. Fisher: “Statistical methods and Scientific Induction”

I continue a week of Fisherian posts in honor of his birthday (Feb 17). This is his contribution to the “Triad”–an exchange between Fisher, Neyman and Pearson 20 years after the Fisher-Neyman break-up. They are each very short.

*“Statistical Methods and Scientific Induction”*

*by Sir Ronald Fisher (1955)
*

**SUMMARY**

The attempt to reinterpret the common tests of significance used in scientific research as though they constituted some kind of acceptance procedure and led to “decisions” in Wald’s sense, originated in several misapprehensions and has led, apparently, to several more.

The three phrases examined here, with a view to elucidating they fallacies they embody, are:

- “Repeated sampling from the same population”,
- Errors of the “second kind”,
- “Inductive behavior”.

Mathematicians without personal contact with the Natural Sciences have often been misled by such phrases. The errors to which they lead are not only numerical.

To continue reading Fisher’s paper.

The most noteworthy feature is Fisher’s position on Fiducial inference, typically downplayed. I’m placing a summary and link to Neyman’s response below–it’s that interesting. Continue reading

## Deconstructing the Fisher-Neyman conflict wearing fiducial glasses (continued)

This continues my previous post: “Can’t take the fiducial out of Fisher…” in recognition of Fisher’s birthday, February 17. I supply a few more intriguing articles you may find enlightening to read and/or reread on a Saturday night

Move up 20 years to the famous 1955/56 exchange between Fisher and Neyman. Fisher clearly connects Neyman’s adoption of a behavioristic-performance formulation to his denying the soundness of fiducial inference. When “Neyman denies the existence of inductive reasoning, he is merely expressing a verbal preference. For him ‘reasoning’ means what ‘deductive reasoning’ means to others.” (Fisher 1955, p. 74).

Fisher was right that Neyman’s calling the outputs of statistical inferences “actions” merely expressed Neyman’s preferred way of talking. Nothing earth-shaking turns on the choice to dub every inference “an act of making an inference”.[i] The “rationality” or “merit” goes into the rule. Neyman, much like Popper, had a good reason for drawing a bright red line between his use of probability (for corroboration or probativeness) and its use by ‘probabilists’ (who assign probability to hypotheses). Fisher’s Fiducial probability was in danger of blurring this very distinction. Popper said, and Neyman would have agreed, that he had no problem with our using the word induction so long it was kept clear it meant testing hypotheses severely. Continue reading

## Can’t Take the Fiducial Out of Fisher (if you want to understand the N-P performance philosophy) [i]

In recognition of R.A. Fisher’s birthday today, I’ve decided to share some thoughts on a topic that has so far has been absent from this blog: Fisher’s* fiducial probability*. **Happy Birthday Fisher.**

[Neyman and Pearson] “began an influential collaboration initially designed primarily, it would seem to clarify Fisher’s writing. This led to their theory of testing hypotheses and to Neyman’s development of confidence intervals, aiming to clarify Fisher’s idea of fiducial intervals (D.R.Cox, 2006, p. 195).

The entire episode of fiducial probability is fraught with minefields. Many say it was Fisher’s biggest blunder; others suggest it still hasn’t been understood. The majority of discussions omit the side trip to the Fiducial Forest altogether, finding the surrounding brambles too thorny to penetrate. Besides, a fascinating narrative about the Fisher-Neyman-Pearson divide has managed to bloom and grow while steering clear of fiducial probability–never mind that it remained a centerpiece of Fisher’s statistical philosophy. I now think that this is a mistake. It was thought, following Lehman (1993) and others, that we could take the fiducial out of Fisher and still understand the core of the Neyman-Pearson vs Fisher (or Neyman vs Fisher) disagreements. We can’t. Quite aside from the intrinsic interest in correcting the “he said/he said” of these statisticians, the issue is intimately bound up with the current (flawed) consensus view of frequentist error statistics.

So what’s *fiducial inference*? I follow Cox (2006), adapting for the case of the lower limit: Continue reading