fiducial probability

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

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Fisher/ Neyman

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). Continue reading

Categories: fiducial probability, Fisher, Neyman, Statistics | 4 Comments

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

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R.A. Fisher: February 17, 1890 – July 29, 1962

Continuing with posts in recognition of R.A. Fisher’s birthday, I post one from a couple of years ago on a topic that had previously not been discussed on this blog: Fisher’s fiducial probability

[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

Categories: fiducial probability, Fisher, Statistics | Leave a comment

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. The other two are below. They are each very short and bear rereading

17 February 1890 — 29 July 1962

“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:

  1. “Repeated sampling from the same population”,
  2. Errors of the “second kind”,
  3. “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.

 

Note on an Article by Sir Ronald Fisher

by Jerzy Neyman (1956)

Neyman

Neyman

Summary

(1) FISHER’S allegation that, contrary to some passages in the introduction and on the cover of the book by Wald, this book does not really deal with experimental design is unfounded. In actual fact, the book is permeated with problems of experimentation.  (2) Without consideration of hypotheses alternative to the one under test and without the study of probabilities of the two kinds, no purely probabilistic theory of tests is possible.  (3) The conceptual fallacy of the notion of fiducial distribution rests upon the lack of recognition that valid probability statements about random variables usually cease to be valid if the random variables are replaced by their particular values.  The notorious multitude of “paradoxes” of fiducial theory is a consequence of this oversight.  (4)  The idea of a “cost function for faulty judgments” appears to be due to Laplace, followed by Gauss.

 

E.S. Pearson

“Statistical Concepts in Their Relation to Reality”.

by E.S. Pearson (1955)

Controversies in the field of mathematical statistics seem largely to have arisen because statisticians have been unable to agree upon how theory is to provide, in terms of probability statements, the numerical measures most helpful to those who have to draw conclusions from observational data.  We are concerned here with the ways in which mathematical theory may be put, as it were, into gear with the common processes of rational thought, and there seems no reason to suppose that there is one best way in which this can be done.  If, therefore, Sir Ronald Fisher recapitulates and enlarges on his views upon statistical methods and scientific induction we can all only be grateful, but when he takes this opportunity to criticize the work of others through misapprehension of their views as he has done in his recent contribution to this Journal (Fisher 1955 “Scientific Methods and Scientific Induction” ), it is impossible to leave him altogether unanswered.

In the first place it seems unfortunate that much of Fisher’s criticism of Neyman and Pearson’s approach to the testing of statistical hypotheses should be built upon a “penetrating observation” ascribed to Professor G.A. Barnard, the assumption involved in which happens to be historically incorrect.  There was no question of a difference in point of view having “originated” when Neyman “reinterpreted” Fisher’s early work on tests of significance “in terms of that technological and commercial apparatus which is known as an acceptance procedure”. There was no sudden descent upon British soil of Russian ideas regarding the function of science in relation to technology and to five-year plans.  It was really much simpler–or worse.  The original heresy, as we shall see, was a Pearson one!…

To continue reading, “Statistical Concepts in Their Relation to Reality” click HERE

Categories: E.S. Pearson, fiducial probability, Fisher, Neyman, phil/history of stat | 3 Comments

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

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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)

Categories: Bayesian/frequentist, C.S. Peirce, confirmation theory, fiducial probability, Fisher, law of likelihood, Popper | Tags: | 1 Comment

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.

17 February 1890 — 29 July 1962

“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:

  1. “Repeated sampling from the same population”,
  2. Errors of the “second kind”,
  3. “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

Categories: fiducial probability, Fisher, Neyman, phil/history of stat | 6 Comments

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

imgres-4

Fisher/ Neyman

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

Categories: fiducial probability, Fisher, Neyman, Statistics | 55 Comments

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

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R.A. Fisher: February 17, 1890 – July 29, 1962

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

Categories: Error Statistics, fiducial probability, Fisher, Statistics | 18 Comments

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