Monthly Archives: October 2018

severe testing or severe sabotage? Christian Robert and the book slasher.

severe testing or severe sabotage? [not a book review]

 

I came across this anomaly on Christian Robert’s blog

Last week, I received this new book of Deborah Mayo, which I was looking forward reading and annotating!, but thrice alas, the book had been sabotaged: except for the preface and acknowledgements, the entire book is printed upside down [a minor issue since the entire book is concerned] and with some part of the text cut on each side [a few letters each time but enough to make reading a chore!]. I am thus waiting for a tested copy of the book to start reading it in earnest!

How bizarre, my book has been slashed with a knife, cruelly stabbing the page,letting words bleed out helter skelter. Some part of the text cut on each side? It wasn’t words with “Bayesian” in them was it? The only anomalous volume I’ve seen has a slightly crooked cover. Do you think it is the Book Slasher out for Halloween, or something more sinister? It’s a bit like serving the Michelin restaurant reviewer by dropping his meal on the floor, or accidentally causing a knife wound. I hope they remedy this quickly. (Talk about Neyman and quality control).

Readers: Feel free to use the comments to share you particular tale of woe in acquiring the book.

Categories: Statistical Inference as Severe Testing | 4 Comments

Tour Guide Mementos (Excursion 1, Tour I of How to Get Beyond the Statistics Wars)

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Tour guides in your travels jot down Mementos and Keepsakes from each Tour[i] of my new book: Statistical Inference as Severe Testing: How to Get Beyond the Statistics Wars (CUP 2018). Their scribblings, which may at times include details, at other times just a word or two, may be modified through the Tour, and in response to questions from travelers (so please check back). Since these are just mementos, they should not be seen as replacements for the more careful notions given in the journey (i.e., book) itself. Still, you’re apt to flesh out your notes in greater detail, so please share yours (along with errors you’re bound to spot), and we’ll create Meta-Mementos.

Excursion 1. Tour I: Beyond Probabilism and Performance

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Notes from Section1.1 Severity Requirement: Bad Evidence, No Test (BENT)

1.1 Terms (quick looks, to be crystalized as we journey on)

  1. epistemology: The general area of philosophy that deals with knowledge, evidence, inference, and rationality.
  2. severity requirement. In its weakest form it supplies a minimal requirement for evidence:
    severity requirement (weak): One does not have evidence for a claim if little if anything has been done to rule out ways the claim may be false. If data x agree with a claim C but the method used is practically guaranteed to find such agreement, and had little or no capability of finding flaws with C even if they exist, then we have bad evidence, no test (BENT).
  3. error probabilities of a method: probabilities it leads or would lead  to erroneous interpretations of data. (We will formalize this as we proceed.)

error statistical account: one that revolves around the control and assessment of a method’s error probabilities. An inference is qualified by the error probability of the method that led to it.

(This replaces common uses of “frequentist” which actually has many other connotations.)
error statistician: one who uses error statistical methods.

severe testers: a proper subset of error statisticians: those who use error probabilities to assess and control severity. (They may use them for other purposes as well.)

The severe tester also requires reporting what has been poorly probed and inseverely tested,
Error probabilities can, but don’t necessarily, provide assessments of the capability of methods to reveal or avoid mistaken interpretations of data. When they do, they may be used to assess how severely a claim passes a test.

  1. methodology and meta-methodology: Methods we use to study statistical methods may be called our meta-methodology – it’s one level removed.

We can keep to testing language as part of the meta-language we use to talk about formal statistical methods, where the latter include estimation, exploration, prediction, and data analysis.

There’s a difference between finding H poorly tested by data x, and finding x renders H improbable – in any of the many senses the latter takes on.
H: Isaac knows calculus.
x: results of a coin flipping experiment

Even taking H to be true, data x has done nothing to probe the ways in which H might be false.

5. R.A. Fisher, against isolated statistically significant results (p.4).

[W]e need, not an isolated record, but a reliable method of procedure. In relation to the
test of significance, we may say that a phenomenon is experimentally demonstrable
when we know how to conduct an experiment which will rarely fail to give us
a statistically significant result. (Fisher 1935b/1947, p. 14)

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Notes from section 1.2 of SIST: How to get beyond the stat wars

6. statistical philosophy (associated with a statistical methodology): core ideas that direct its principles, methods, and interpretations.
two main philosophies about the roles of probability in statistical inference : performance (in the long run) and probabilism.
(i) performance: probability functions to control and assess the relative frequency of erroneous inferences in some long run of applications of the method
(ii) probabilism: probability functions to assign degrees of belief, support, or plausibility to hypotheses. They may be non-comparative (a posterior probability) or comparative (a likelihood ratio or Bayes Factor)

Severe testing introduces a third:
(iii) probativism: probability functions to assess and control a methods’ capability of detecting mistaken inferences, i.e., the severity associated with inferences.
• Performance is a necessary but not a sufficient condition for probativeness.
• Just because an account is touted as having a long-run rationale, it does not mean it lacks a short run rationale, or even one relevant for the particular case at hand.

7. Severity strong (argument from coincidence):
We have evidence for a claim C just to the extent it survives a stringent scrutiny. If C passes a test that was highly capable of finding flaws or discrepancies from C, and yet no or few are found, then the passing result, x, is evidence for C.
lift-off vs drag down
(i) lift-off : an overall inference can be more reliable and precise than its premises individually.
(ii) drag-down: An overall inference is only as reliable/precise as is its weakest premise.

• Lift-off is associated with convergent arguments, drag-down with linked arguments.
• statistics is the science par excellence for demonstrating lift-off!

8. arguing from error: there is evidence an error is absent to the extent that a procedure with a high capability of signaling the error, if and only if it is present, nevertheless detects no error.

Bernouilli (coin tossing) model: we record success or failure, assume a fixed probability of success θ on each trial, and that trials are independent. (P-value in the case of the Lady Tasting tea, pp. 16-17).

Error probabilities can be readily invalidated due to how the data (and hypotheses!) are generated or selected for testing.

9. computed (or nominal) vs actual error probabilities: You may claim it’s very difficult to get such an impressive result due to chance, when in fact it’s very easy to do so, with selective reporting (e.g., your computed P-value can be small, but the actual P-value is high.)

Examples: Peirce and Dr. Playfair (a law is inferred even though half of the cases required Playfair to modify the formula after the fact. ) Texas marksman (shooting prowess inferred from shooting bullets into the side of a barn, and painting a bull’s eye around clusters of bullet holes); Pickrite stock portfolio (Pickrite’s effectiveness at stock picking is inferred based on selecting those on which the “method” did best)
• We appeal to the same statistical reasoning to show the problematic cases as to show genuine arguments from coincidence.
• A key role for statistical inference is to identify ways to spot egregious deceptions and create strong arguments from coincidence.

10. Auditing a P-value (one part) checking if the results due to selective reporting, cherry picking, trying and trying again, or any number of other similar ruses.
• Replicability isn’t enough: Example. observational studies on Hormone Replacement therapy (HRT) reproducibly showed benefits, but had little capacity to unearth biases due to “the healthy women’s syndrome.”

Souvenir A.[ii] Postcard to Send: the 4 fallacies from the opening of 1.1.
• We should oust mechanical, recipe-like uses of statistical methods long lampooned,
• But simple significance tests have their uses, and shouldn’t be ousted simply because some people are liable to violate Fisher’s warnings.
• They have the means by which to register formally the fallacies in the postcard list. (Failed statistical assumptions, selection effects alter a test’s error probing capacities).
• Don’t throw out the error control baby with the bad statistics bathwater.

10. severity requirement (weak): If data x agree with a claim C but the method was practically incapable of finding flaws with C even if they exist, then x is poor evidence for C.
severity (strong): If C passes a test that was highly capable of finding flaws or discrepancies from C, and yet no or few are found, then the passing result, x, is an indication of, or evidence for, C.

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Notes from Section 1.3: The Current State of Play in Statistical Foundations: A View From a Hot-Air Balloon

The Bayesian versus frequentist dispute parallels disputes between probabilism and performance.

-Using Bayes’ Theorem doesn’t make you a Bayesian.

-subjective Bayesianism and non-subjective (default) Bayesians

11. Advocates of unifications are keen to show that (i) default Bayesian methods have good performance in a long series of repetitions – so probabilism may yield performance; or alternatively, (ii) frequentist quantities are similar to Bayesian ones (at least in certain cases) – so performance may yield probabilist numbers. Why is this not bliss? Why are so many from all sides dissatisfied?

It had long been assumed that only subjective or personalistic Bayesianism had a shot at providing genuine philosophical foundations, but some Bayesians have come to question whether the widespread use of methods under the Bayesian umbrella, however useful, indicates support for subjective Bayesianism as a foundation.

Marriages of Convenience? The current frequentist–Bayesian unifications are often marriages of convenience;

-some are concerned that methodological conflicts are bad for the profession.

-frequentist tribes have not disappeared; scientists still call for error control.

-Frequentists’ incentive to marry: Lacking a suitable epistemic interpretation of error probabilities – significance levels, power, and confidence levels – frequentists are constantly put on the defensive.

Eclecticism and Ecumenism. Current-day eclecticisms have a long history – the dabbling in tools from competing statistical tribes has not been thought to pose serious challenges.

Decoupling. On the horizon is the idea that statistical methods may be decoupled from the philosophies in which they are traditionally couched (e.g., Gelman and Cosma Shalizi 2013). The concept of severe testing is sufficiently general to apply to any of the methods now in use.

Why Our Journey? To disentangle the jumgle. Being hesitant to reopen wounds from old battles does not heal them. They show up in the current problems of scientific integrity, irreproducibility, questionable research practices, and in the swirl of methodological reforms and guidelines that spin their way down from journals and reports.

How it occurs: the new stat scrutiny (arising from failures of replication) collects from:

-the earlier social science “significance test controversy”

-the traditional frequentist and Bayesian accounts, and corresponding frequentist-Bayesian wars

-the newer Bayesian–frequentist unifications (non-subjective, default Bayesianism)

This jungle has never been disentangled.

Your Tour Guide invites your questions in the comments.

 

[i] As these are scribbled down in notebooks through ocean winds, wetlands and insects, do not expect neatness. Please share improvements nd corrections.

[ii] For a free copy of “Statistical Inference as Severe Testing”, send me your conception of Souvenir A, your real souvenir A, or a picture of your real Souvenir A (through Nov 16, 2018).

 

Categories: Error Statistics, Statistical Inference as Severe Testing | 7 Comments

Philosophy of Statistics & the Replication Crisis in Science: A philosophical intro to my book (slides)

a road through the jungle

In my talk yesterday at the Philosophy Department at Virginia Tech, I introduced my new book: Statistical Inference as Severe Testing: How to Get Beyond the Statistics Wars (Cambridge 2018). I began with my preface (explaining the meaning of my title), and turned to the Statistics Wars, largely from Excursion 1 of the book. After the sum-up at the end, I snuck in an example from the replication crisis in psychology. Here are the slides.

 

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Excursion 2 Tour II (3rd stop): Falsification, Pseudoscience, Induction (2.3)

StatSci/PhilSci Museum

Where you are in the Journey*  We’ll move from the philosophical ground floor to connecting themes from other levels, from Popperian falsification to significance tests, and from Popper’s demarcation to current-day problems of pseudoscience and irreplication. An excerpt from our Museum Guide gives a broad-brush sketch of the first few sections of Tour II:

Karl Popper had a brilliant way to “solve” the problem of induction: Hume was right that enumerative induction is unjustified, but science is a matter of deductive falsification. Science was to be demarcated from pseudoscience according to whether its theories were testable and falsifiable. A hypothesis is deemed severely tested if it survives a stringent attempt to falsify it. Popper’s critics denied he could sustain this and still be a deductivist …

Popperian falsification is often seen as akin to Fisher’s view that “every experiment may be said to exist only in order to give the facts a chance of disproving the null hypothesis” (1935a, p. 16). Though scientists often appeal to Popper, some critics of significance tests argue that they are used in decidedly non-Popperian ways. Tour II explores this controversy.

While Popper didn’t make good on his most winning slogans, he gives us many seminal launching-off points for improved accounts of falsification, corroboration, science versus pseudoscience, and the role of novel evidence and predesignation. These will let you revisit some thorny issues in today’s statistical crisis in science.

2.3 Popper, Severity, and Methodological Probability

Here’s Popper’s summary (drawing from Popper, Conjectures and Refutations, 1962, p. 53):

  • [Enumerative] induction … is a It is neither a psychological fact …nor one of scientific procedure.
  • The actual procedure of science is to operate with conjectures…
  • Repeated observation and experiments function in science as tests of our conjectures or hypotheses, i.e., as attempted refutations.
  • [It is wrongly believed that using the inductive method can] serve as a criterion of demarcation between science and pseudoscience. … None of this is altered in the least if we say that induction makes theories only probable.

There are four key, interrelated themes:

(1) Science and Pseudoscience. Redefining scientific method gave Popper a new basis for demarcating genuine science from questionable science or pseudoscience. Flexible theories that are easy to confirm – theories of Marx, Freud, and Adler were his exemplars – where you open your eyes and find confirmations everywhere, are low on the scientific totem pole (ibid., p. 35). For a theory to be scientific it must be testable and falsifiable. Continue reading

Categories: Statistical Inference as Severe Testing | 10 Comments

“It should never be true, though it is still often said, that the conclusions are no more accurate than the data on which they are based”

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My new book, Statistical Inference as Severe Testing: How to Get Beyond the Statistics Wars,” you might have discovered, includes Souvenirs throughout (A-Z). But there are some highlights within sections that might be missed in the excerpts I’m posting. One such “keepsake” is a quote from Fisher at the very end of Section 2.1

These are some of the first clues we’ll be collecting on a wide difference between statistical inference as a deductive logic of probability, and an inductive testing account sought by the error statistician. When it comes to inductive learning, we want our inferences to go beyond the data: we want lift-off. To my knowledge, Fisher is the only other writer on statistical inference, aside from Peirce, to emphasize this distinction.

In deductive reasoning all knowledge obtainable is already latent in the postulates. Rigour is needed to prevent the successive inferences growing less and less accurate as we proceed. The conclusions are never more accurate than the data. In inductive reasoning we are performing part of the process by which new knowledge is created. The conclusions normally grow more and more accurate as more data are included. It should never be true, though it is still often said, that the conclusions are no more accurate than the data on which they are based. (Fisher 1935b, p. 54)

How do you understand this remark of Fisher’s? (Please share your thoughts in the comments.) My interpretation, and its relation to the “lift-off” needed to warrant inductive inferences, is discussed in an earlier section, 1.2, posted here.   Here’s part of that. 

Continue reading

Categories: induction, keepsakes from Stat Wars, Statistical Inference as Severe Testing | 7 Comments

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