Error Statistics

3 YEARS AGO (NOVEMBER 2013): MEMORY LANE

3 years ago...

3 years ago…

MONTHLY MEMORY LANE: 3 years ago: November 2013. I mark in red three posts from each month that seem most apt for general background on key issues in this blog, excluding those reblogged recently[1], and in green up to 3 others I’d recommend[2].  Posts that are part of a “unit” or a group count as one. Here I’m counting 11/9, 11/13, and 11/16 as one

November 2013

  • (11/2) Oxford Gaol: Statistical Bogeymen
  • (11/4) Forthcoming paper on the strong likelihood principle
  • (11/9) Null Effects and Replication (cartoon pic)
  • (11/9) Beware of questionable front page articles warning you to beware of questionable front page articles (iii)
  • (11/13) T. Kepler: “Trouble with ‘Trouble at the Lab’?” (guest post)
  • (11/16) PhilStock: No-pain bull
  • (11/16) S. Stanley Young: More Trouble with ‘Trouble in the Lab’ (Guest post)
  • (11/18) Lucien Le Cam: “The Bayesians hold the Magic”
  • (11/20) Erich Lehmann: Statistician and Poet
  • (11/23) Probability that it is a statistical fluke [i]
  • (11/27)The probability that it be a statistical fluke” [iia]
  • (11/30) Saturday night comedy at the “Bayesian Boy” diary (rejected post*)

[1] Monthly memory lanes began at the blog’s 3-year anniversary in Sept, 2014.

[2] New Rule, July 30, 2016-very convenient.

 

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Categories: 3-year memory lane, Error Statistics, Statistics | Leave a comment

3 YEARS AGO (OCTOBER 2013): MEMORY LANE

3 years ago...

3 years ago…

MONTHLY MEMORY LANE: 3 years ago: October 2013. I mark in red three posts from each month that seem most apt for general background on key issues in this blog, excluding those reblogged recently[1], and in green up to 3 others I’d recommend[2].  Posts that are part of a “unit” or a pair count as one.

October 2013

  • (10/3) Will the Real Junk Science Please Stand Up? (critical thinking)
     
  • (10/5) Was Janina Hosiasson pulling Harold Jeffreys’ leg?
  • (10/9) Bad statistics: crime or free speech (II)? Harkonen update: Phil Stat / Law /Stock
  • (10/12) Sir David Cox: a comment on the post, “Was Hosiasson pulling Jeffreys’ leg?”(10/5 and 10/12 are a pair)
     
  • (10/19) Blog Contents: September 2013
  • (10/19) Bayesian Confirmation Philosophy and the Tacking Paradox (iv)*
  • (10/25) Bayesian confirmation theory: example from last post…(10/19 and 10/25 are a pair)
  • (10/26) Comedy hour at the Bayesian (epistemology) retreat: highly probable vs highly probed (vs what ?)
  • (10/31) WHIPPING BOYS AND WITCH HUNTERS (interesting to see how things have changed and stayed the same over the past few years, share comments)

[1] Monthly memory lanes began at the blog’s 3-year anniversary in Sept, 2014.

[2] New Rule, July 30, 2016-very convenient.

 

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Categories: 3-year memory lane, Error Statistics, Statistics | 22 Comments

For Statistical Transparency: Reveal Multiplicity and/or Just Falsify the Test (Remark on Gelman and Colleagues)

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Gelman and Loken (2014) recognize that even without explicit cherry picking there is often enough leeway in the “forking paths” between data and inference so that by artful choices you may be led to one inference, even though it also could have gone another way. In good sciences, measurement procedures should interlink with well-corroborated theories and offer a triangulation of checks– often missing in the types of experiments Gelman and Loken are on about. Stating a hypothesis in advance, far from protecting from the verification biases, can be the engine that enables data to be “constructed”to reach the desired end [1].

[E]ven in settings where a single analysis has been carried out on the given data, the issue of multiple comparisons emerges because different choices about combining variables, inclusion and exclusion of cases…..and many other steps in the analysis could well have occurred with different data (Gelman and Loken 2014, p. 464).

An idea growing out of this recognition is to imagine the results of applying the same statistical procedure, but with different choices at key discretionary junctures–giving rise to a multiverse analysis, rather than a single data set (Steegen, Tuerlinckx, Gelman, and Vanpaemel 2016). One lists the different choices thought to be plausible at each stage of data processing. The multiverse displays “which constellation of choices corresponds to which statistical results” (p. 797). The result of this exercise can, at times, mimic the delineation of possibilities in multiple testing and multiple modeling strategies. Continue reading

Categories: Bayesian/frequentist, Error Statistics, Gelman, P-values, preregistration, reproducibility, Statistics | 9 Comments

Peircean Induction and the Error-Correcting Thesis (Part I)

C. S. Peirce: 10 Sept, 1839-19 April, 1914

C. S. Peirce: 10 Sept, 1839-19 April, 1914

Today is C.S. Peirce’s birthday. He’s one of my all time heroes. You should read him: he’s a treasure chest on essentially any topic, and he anticipated several major ideas in statistics (e.g., randomization, confidence intervals) as well as in logic. I’ll reblog the first portion of a (2005) paper of mine. Links to Parts 2 and 3 are at the end. It’s written for a very general philosophical audience; the statistical parts are pretty informal. Happy birthday Peirce.

Peircean Induction and the Error-Correcting Thesis
Deborah G. Mayo
Transactions of the Charles S. Peirce Society: A Quarterly Journal in American Philosophy, Volume 41, Number 2, 2005, pp. 299-319

Peirce’s philosophy of inductive inference in science is based on the idea that what permits us to make progress in science, what allows our knowledge to grow, is the fact that science uses methods that are self-correcting or error-correcting:

Induction is the experimental testing of a theory. The justification of it is that, although the conclusion at any stage of the investigation may be more or less erroneous, yet the further application of the same method must correct the error. (5.145)

Continue reading

Categories: Bayesian/frequentist, C.S. Peirce, Error Statistics, Statistics | 18 Comments

If you think it’s a scandal to be without statistical falsification, you will need statistical tests (ii)

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1. PhilSci and StatSci. I’m always glad to come across statistical practitioners who wax philosophical, particularly when Karl Popper is cited. Best of all is when they get the philosophy somewhere close to correct. So, I came across an article by Burnham and Anderson (2014) in Ecology:

While the exact definition of the so-called ‘scientific method’ might be controversial, nearly everyone agrees that the concept of ‘falsifiability’ is a central tenant [sic] of empirical science (Popper 1959). It is critical to understand that historical statistical approaches (i.e., P values) leave no way to ‘test’ the alternative hypothesis. The alternative hypothesis is never tested, hence cannot be rejected or falsified!… Surely this fact alone makes the use of significance tests and P values bogus. Lacking a valid methodology to reject/falsify the alternative science hypotheses seems almost a scandal.” (Burnham and Anderson p. 629)

Well I am (almost) scandalized by this easily falsifiable allegation! I can’t think of a single “alternative”, whether in a “pure” Fisherian or a Neyman-Pearson hypothesis test (whether explicit or implicit) that’s not falsifiable; nor do the authors provide any. I grant that understanding testability and falsifiability is far more complex than the kind of popularized accounts we hear about; granted as well, theirs is just a short paper.[1] But then why make bold declarations on the topic of the “scientific method and statistical science,” on falsifiability and testability? Continue reading

Categories: P-values, Severity, statistical tests, Statistics, StatSci meets PhilSci | 22 Comments

3 YEARS AGO (JULY 2013): MEMORY LANE

3 years ago...

3 years ago…

MONTHLY MEMORY LANE: 3 years ago: July 2013. I mark in red three posts that seem most apt for general background on key issues in this blog, excluding those reblogged recently [1], and in green up to 3 others I’d recommend[2].  Posts that are part of a “unit” or a group of “U-Phils”(you [readers] philosophize) count as one.

July 2013

  • (7/3) Phil/Stat/Law: 50 Shades of gray between error and fraud
  • (7/6) Bad news bears: ‘Bayesian bear’ rejoinder–reblog mashup
  • (7/10) PhilStatLaw: Reference Manual on Scientific Evidence (3d ed) on Statistical Significance (Schachtman)
  • (7/11) Is Particle Physics Bad Science? (memory lane)
  • (7/13) Professor of Philosophy Resigns over Sexual Misconduct (rejected post)
  • (7/14) Stephen Senn: Indefinite irrelevance
  • (7/17) Phil/Stat/Law: What Bayesian prior should a jury have? (Schachtman)
  • (7/19) Msc Kvetch: A question on the Martin-Zimmerman case we do not hear
  • (7/20) Guest Post: Larry Laudan. Why Presuming Innocence is Not a Bayesian Prior
  • (7/23) Background Knowledge: Not to Quantify, But To Avoid Being Misled By, Subjective Beliefs
  • (7/26) New Version: On the Birnbaum argument for the SLP: Slides for JSM talk

[1] Monthly memory lanes began at the blog’s 3-year anniversary in Sept, 2014.

[2] New Rule, July 30, 2016.

 

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Categories: 3-year memory lane, Error Statistics, Statistics | Leave a comment

3 YEARS AGO (JUNE 2013): MEMORY LANE

3 years ago...

3 years ago…

MONTHLY MEMORY LANE: 3 years ago: June 2013. I mark in red three posts that seem most apt for general background on key issues in this blog, excluding those reblogged recently [1].  Posts that are part of a “unit” or a group of “U-Phils”(you [readers] philosophize) count as one. Here I grouped 6/5 and 6/6.

June 2013

  • (6/1) Winner of May Palindrome Contest
  • (6/1) Some statistical dirty laundry*(recently reblogged)
  • (6/5) Do CIs Avoid Fallacies of Tests? Reforming the Reformers :(6/5 and6/6 are paired as one)
  • (6/6) PhilStock: Topsy-Turvy Game
  • (6/6) Anything Tests Can do, CIs do Better; CIs Do Anything Better than Tests?* (reforming the reformers cont.)
  • (6/8) Richard Gill: “Integrity or fraud… or just questionable research practices?*(recently reblogged)
  • (6/11) Mayo: comment on the repressed memory research [How a conceptual criticism, requiring no statistics, might go.]
  • (6/14) P-values can’t be trusted except when used to argue that p-values can’t be trusted!
  • (6/19) PhilStock: The Great Taper Caper
  • (6/19) Stanley Young: better p-values through randomization in microarrays
  • (6/22) What do these share in common: m&ms, limbo stick, ovulation, Dale Carnegie? Sat night potpourri*(recently reblogged)
  • (6/26) Why I am not a “dualist” in the sense of Sander Greenland
  • (6/29) Palindrome “contest” contest
  • (6/30) Blog Contents: mid-year

[1] Monthly memory lanes began at the blog’s 3-year anniversary in Sept, 2014.

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Allan Birnbaum: Foundations of Probability and Statistics (27 May 1923 – 1 July 1976)

27 May 1923-1 July 1976

27 May 1923-1 July 1976

Today is Allan Birnbaum’s birthday. In honor of his birthday this year, I’m posting the articles in the Synthese volume that was dedicated to his memory in 1977. The editors describe it as their way of  “paying homage to Professor Birnbaum’s penetrating and stimulating work on the foundations of statistics”. I paste a few snippets from the articles by Giere and Birnbaum. If you’re interested in statistical foundations, and are unfamiliar with Birnbaum, here’s a chance to catch up.(Even if you are,you may be unaware of some of these key papers.)

HAPPY BIRTHDAY ALLAN!

Synthese Volume 36, No. 1 Sept 1977: Foundations of Probability and Statistics, Part I

Editorial Introduction:

This special issue of Synthese on the foundations of probability and statistics is dedicated to the memory of Professor Allan Birnbaum. Professor Birnbaum’s essay ‘The Neyman-Pearson Theory as Decision Theory; and as Inference Theory; with a Criticism of the Lindley-Savage Argument for Bayesian Theory’ was received by the editors of Synthese in October, 1975, and a decision was made to publish a special symposium consisting of this paper together with several invited comments and related papers. The sad news about Professor Birnbaum’s death reached us in the summer of 1976, but the editorial project could nevertheless be completed according to the original plan. By publishing this special issue we wish to pay homage to Professor Birnbaum’s penetrating and stimulating work on the foundations of statistics. We are grateful to Professor Ronald Giere who wrote an introductory essay on Professor Birnbaum’s concept of statistical evidence and who compiled a list of Professor Birnbaum’s publications.

THE EDITORS

Continue reading

Categories: Birnbaum, Error Statistics, Likelihood Principle, Statistics, strong likelihood principle | 7 Comments

A. Spanos: Talking back to the critics using error statistics

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Given all the recent attention given to kvetching about significance tests, it’s an apt time to reblog Aris Spanos’ overview of the error statistician talking back to the critics [1]. A related paper for your Saturday night reading is Mayo and Spanos (2011).[2] It mixes the error statistical philosophy of science with its philosophy of statistics, introduces severity, and responds to 13 criticisms and howlers.

I’m going to comment on some of the ASA discussion contributions I hadn’t discussed earlier. Please share your thoughts in relation to any of this.

[1]It was first blogged here, as part of our seminar 2 years ago.

[2] For those seeking a bit more balance to the main menu offered in the ASA Statistical Significance Reference list.

 

See also on this blog:

A. Spanos, “Recurring controversies about p-values and confidence intervals revisited

A. Spanos, “Lecture on frequentist hypothesis testing

 

 

Categories: Error Statistics, frequentist/Bayesian, reforming the reformers, statistical tests, Statistics | 72 Comments

Your chance to continue the “due to chance” discussion in roomier quarters

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Comments get unwieldy after 100, so here’s a chance to continue the “due to chance” discussion in some roomier quarters. (There seems to be at least two distinct lanes being travelled.) Now one of the main reasons I run this blog is to discover potential clues to solving or making progress on thorny philosophical problems I’ve been wrangling with for a long time. I think I extracted some illuminating gems from the discussion here, but I don’t have time to write them up, and won’t for a bit, so I’ve parked a list of comments wherein the golden extracts lie (I think) over at my Rejected Posts blog[1]. (They’re all my comments, but as influenced by readers, so I thank you!) Over there, there’s no “return and resubmit”, but around a dozen posts have eventually made it over here, tidied up. Please continue the discussion on this blog (I don’t even recommend going over there). You can link to your earlier comments by clicking on the date.

[1] The Spiegelhalter (PVP)  link is here.

Categories: Error Statistics, P-values, Rejected Posts, Statistics | 36 Comments

Don’t throw out the error control baby with the bad statistics bathwater

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My invited comments on the ASA Document on P-values*

The American Statistical Association is to be credited with opening up a discussion into p-values; now an examination of the foundations of other key statistical concepts is needed.

Statistical significance tests are a small part of a rich set of “techniques for systematically appraising and bounding the probabilities (under respective hypotheses) of seriously misleading interpretations of data” (Birnbaum 1970, p. 1033). These may be called error statistical methods (or sampling theory). The error statistical methodology supplies what Birnbaum called the “one rock in a shifting scene” (ibid.) in statistical thinking and practice. Misinterpretations and abuses of tests, warned against by the very founders of the tools, shouldn’t be the basis for supplanting them with methods unable or less able to assess, control, and alert us to erroneous interpretations of data. Continue reading

Categories: Error Statistics, P-values, science communication, Statistics | 19 Comments

Statistical Challenges in Assessing and Fostering the Reproducibility of Scientific Results

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Statistical Challenges in Assessing and Fostering the Reproducibility of Scientific Results

I generally find National Academy of Science (NAS) manifestos highly informative. I only gave a quick reading to around 3/4 of this one. I thank Hilda Bastian for twittering the link. Before giving my impressions, I’m interested to hear what readers think, whenever you get around to having a look. Here’s from the intro*:

Questions about the reproducibility of scientific research have been raised in numerous settings and have gained visibility through several high-profile journal and popular press articles. Quantitative issues contributing to reproducibility challenges have been considered (including improper data management and analysis, inadequate statistical expertise, and incomplete data, among others), but there is no clear consensus on how best to approach or to minimize these problems…
Continue reading

Categories: Error Statistics, replication research, reproducibility, Statistics | 53 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

Gelman on ‘Gathering of philosophers and physicists unaware of modern reconciliation of Bayes and Popper’

 I’m reblogging Gelman’s post today: “Gathering of philosophers and physicists unaware of modern reconciliation of Bayes and Popper”. I concur with Gelman’s arguments against all Bayesian “inductive support” philosophies, and welcome the Gelman and Shalizi (2013) ‘meeting of the minds’ between an error statistical philosophy and Bayesian falsification (which I regard as a kind of error statistical Bayesianism). Just how radical a challenge these developments pose to other stripes of Bayesianism has yet to be explored. My comment on them is here.

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“Gathering of philosophers and physicists unaware of modern reconciliation of Bayes and Popper” by Andrew Gelman

Hiro Minato points us to a news article by physicist Natalie Wolchover entitled “A Fight for the Soul of Science.”

I have no problem with most of the article, which is a report about controversies within physics regarding the purported untestability of physics models such as string theory (as for example discussed by my Columbia colleague Peter Woit). Wolchover writes:

Whether the fault lies with theorists for getting carried away, or with nature, for burying its best secrets, the conclusion is the same: Theory has detached itself from experiment. The objects of theoretical speculation are now too far away, too small, too energetic or too far in the past to reach or rule out with our earthly instruments. . . .

Over three mild winter days, scholars grappled with the meaning of theory, confirmation and truth; how science works; and whether, in this day and age, philosophy should guide research in physics or the other way around. . . .

To social and behavioral scientists, this is all an old old story. Concepts such as personality, political ideology, and social roles are undeniably important but only indirectly related to any measurements. In social science we’ve forever been in the unavoidable position of theorizing without sharp confirmation or falsification, and, indeed, unfalsifiable theories such as Freudian psychology and rational choice theory have been central to our understanding of much of the social world.

But then somewhere along the way the discussion goes astray: Continue reading

Categories: Bayesian/frequentist, Error Statistics, Gelman, Shalizi, Statistics | 20 Comments

Statistical “reforms” without philosophy are blind (v update)

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Is it possible, today, to have a fair-minded engagement with debates over statistical foundations? I’m not sure, but I know it is becoming of pressing importance to try. Increasingly, people are getting serious about methodological reforms—some are quite welcome, others are quite radical. Too rarely do the reformers bring out the philosophical presuppositions of the criticisms and proposed improvements. Today’s (radical?) reform movements are typically launched from criticisms of statistical significance tests and P-values, so I focus on them. Regular readers know how often the P-value (that most unpopular girl in the class) has made her appearance on this blog. Here, I tried to quickly jot down some queries. (Look for later installments and links.) What are some key questions we need to ask to tell what’s true about today’s criticisms of P-values? 

I. To get at philosophical underpinnings, the single most import question is this:

(1) Do the debaters distinguish different views of the nature of statistical inference and the roles of probability in learning from data? Continue reading

Categories: Bayesian/frequentist, Error Statistics, P-values, significance tests, Statistics, strong likelihood principle | 193 Comments

Statistical rivulets: Who wrote this?

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[I]t seems to be useful for statisticians generally to engage in retrospection at this time, because there seems now to exist an opportunity for a convergence of view on the central core of our subject. Unless such an opportunity is taken there is a danger that the powerful central stream of development of our subject may break up into smaller and smaller rivulets which may run away and disappear into the sand.

I shall be concerned with the foundations of the subject. But in case it should be thought that this means I am not here strongly concerned with practical applications, let me say right away that confusion about the foundations of the subject is responsible, in my opinion, for much of the misuse of the statistics that one meets in fields of application such as medicine, psychology, sociology, economics, and so forth. It is also responsible for the lack of use of sound statistics in the more developed areas of science and engineering. While the foundations have an interest of their own, and can, in a limited way, serve as a basis for extending statistical methods to new problems, their study is primarily justified by the need to present a coherent view of the subject when teaching it to others. One of the points I shall try to make is, that we have created difficulties for ourselves by trying to oversimplify the subject for presentation to others. It would surely have been astonishing if all the complexities of such a subtle concept as probability in its application to scientific inference could be represented in terms of only three concepts––estimates, confidence intervals, and tests of hypotheses. Yet one would get the impression that this was possible from many textbooks purporting to expound the subject. We need more complexity; and this should win us greater recognition from scientists in developed areas, who already appreciate that inference is a complex business while at the same time it should deter those working in less developed areas from thinking that all they need is a suite of computer programs.

Who wrote this and when?

Categories: Error Statistics, Statistics | Leave a comment

Popper on pseudoscience: a comment on Pigliucci (i), (ii) 9/18, (iii) 9/20

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Jump to Part (ii) 9/18/15 and (iii) 9/20/15 updates

I heard a podcast the other day in which the philosopher of science, Massimo Pigliucci, claimed that Popper’s demarcation of science fails because it permits pseudosciences like astrology to count as scientific! Now Popper requires supplementing in many ways, but we can get far more mileage out of Popper’s demarcation than Pigliucci supposes.

Pigliucci has it that, according to Popper, mere logical falsifiability suffices for a theory to be scientific, and this prevents Popper from properly ousting astrology from the scientific pantheon. Not so. In fact, Popper’s central goal is to call our attention to theories that, despite being logically falsifiable, are rendered immune from falsification by means of ad hoc maneuvering, sneaky face-saving devices, “monster-barring” or “conventionalist stratagems”. Lacking space on Twitter (where the “Philosophy Bites” podcast was linked), I’m placing some quick comments here. (For other posts on Popper, please search this blog.) Excerpts from the classic two pages in Conjectures and Refutations (1962, pp. 36-7) will serve our purpose:

It is easy to obtain confirmations, or verifications, for nearly every theory–if we look for confirmations.

Popper

Popper

Confirmations should count only if they are the result of risky predictions; that is [if the theory or claim H is false] we should have expected an event which was incompatible with the theory [or claim]….

Every genuine test of a theory is an attempt to falsify it, or to refute it. Testability is falsifiability, but there are degrees of testability, some theories are more testable..

Confirming evidence should not count except when it is the result of a genuine test of the theory, and this means that it can be presented as a serious but unsuccessful attempt to falsify the theory. (I now speak of such cases as ‘corroborating evidence’).

Continue reading

Categories: Error Statistics, Popper, pseudoscience, Statistics | Tags: , | 5 Comments

(Part 3) Peircean Induction and the Error-Correcting Thesis

C. S. Peirce: 10 Sept, 1839-19 April, 1914

C. S. Peirce: 10 Sept, 1839-19 April, 1914

Last third of “Peircean Induction and the Error-Correcting Thesis”

Deborah G. Mayo
Transactions of the Charles S. Peirce Society 41(2) 2005: 299-319

Part 2 is here.

8. Random sampling and the uniformity of nature

We are now at the point to address the final move in warranting Peirce’s SCT. The severity or trustworthiness assessment, on which the error correcting capacity depends, requires an appropriate link (qualitative or quantitative) between the data and the data generating phenomenon, e.g., a reliable calibration of a scale in a qualitative case, or a probabilistic connection between the data and the population in a quantitative case. Establishing such a link, however, is regarded as assuming observed regularities will persist, or making some “uniformity of nature” assumption—the bugbear of attempts to justify induction.

But Peirce contrasts his position with those favored by followers of Mill, and “almost all logicians” of his day, who “commonly teach that the inductive conclusion approximates to the truth because of the uniformity of nature” (2.775). Inductive inference, as Peirce conceives it (i.e., severe testing) does not use the uniformity of nature as a premise. Rather, the justification is sought in the manner of obtaining data. Justifying induction is a matter of showing that there exist methods with good error probabilities. For this it suffices that randomness be met only approximately, that inductive methods check their own assumptions, and that they can often detect and correct departures from randomness.

… It has been objected that the sampling cannot be random in this sense. But this is an idea which flies far away from the plain facts. Thirty throws of a die constitute an approximately random sample of all the throws of that die; and that the randomness should be approximate is all that is required. (1.94)

Continue reading

Categories: C.S. Peirce, Error Statistics, phil/history of stat | Leave a comment

(Part 2) Peircean Induction and the Error-Correcting Thesis

C. S. Peirce 9/10/1839 – 4/19/1914

C. S. Peirce
9/10/1839 – 4/19/1914

Continuation of “Peircean Induction and the Error-Correcting Thesis”

Deborah G. Mayo
Transactions of the Charles S. Peirce Society: A Quarterly Journal in American Philosophy, Volume 41, Number 2, 2005, pp. 299-319

Part 1 is here.

There are two other points of confusion in critical discussions of the SCT, that we may note here:

I. The SCT and the Requirements of Randomization and Predesignation

The concern with “the trustworthiness of the proceeding” for Peirce like the concern with error probabilities (e.g., significance levels) for error statisticians generally, is directly tied to their view that inductive method should closely link inferences to the methods of data collection as well as to how the hypothesis came to be formulated or chosen for testing.

This account of the rationale of induction is distinguished from others in that it has as its consequences two rules of inductive inference which are very frequently violated (1.95) namely, that the sample be (approximately) random and that the property being tested not be determined by the particular sample x— i.e., predesignation.

The picture of Peircean induction that one finds in critics of the SCT disregards these crucial requirements for induction: Neither enumerative induction nor H-D testing, as ordinarily conceived, requires such rules. Statistical significance testing, however, clearly does. Continue reading

Categories: Bayesian/frequentist, C.S. Peirce, Error Statistics, Statistics | Leave a comment

Peircean Induction and the Error-Correcting Thesis (Part I)

C. S. Peirce: 10 Sept, 1839-19 April, 1914

C. S. Peirce: 10 Sept, 1839-19 April, 1914

Yesterday was C.S. Peirce’s birthday. He’s one of my all time heroes. You should read him: he’s a treasure chest on essentially any topic. I only recently discovered a passage where Popper calls Peirce one of the greatest philosophical thinkers ever (I don’t have it handy). If Popper had taken a few more pages from Peirce, he would have seen how to solve many of the problems in his work on scientific inference, probability, and severe testing. I’ll blog the main sections of a (2005) paper of mine over the next few days. It’s written for a very general philosophical audience; the statistical parts are pretty informal. I first posted it in 2013Happy (slightly belated) Birthday Peirce.

Peircean Induction and the Error-Correcting Thesis
Deborah G. Mayo
Transactions of the Charles S. Peirce Society: A Quarterly Journal in American Philosophy, Volume 41, Number 2, 2005, pp. 299-319

Peirce’s philosophy of inductive inference in science is based on the idea that what permits us to make progress in science, what allows our knowledge to grow, is the fact that science uses methods that are self-correcting or error-correcting:

Induction is the experimental testing of a theory. The justification of it is that, although the conclusion at any stage of the investigation may be more or less erroneous, yet the further application of the same method must correct the error. (5.145)

Inductive methods—understood as methods of experimental testing—are justified to the extent that they are error-correcting methods. We may call this Peirce’s error-correcting or self-correcting thesis (SCT):

Self-Correcting Thesis SCT: methods for inductive inference in science are error correcting; the justification for inductive methods of experimental testing in science is that they are self-correcting. Continue reading

Categories: Bayesian/frequentist, C.S. Peirce, Error Statistics, Statistics | Leave a comment

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