Monthly Archives: February 2014

Phil6334: Feb 24, 2014: Induction, Popper and pseudoscience (Day #4)

Phil 6334* Day #4: Mayo slides follow the comments below. (Make-up for Feb 13 snow day.) Popper reading is from Conjectures and Refutations.



As is typical in rereading any deep philosopher, I discover (or rediscover) different morsals of clues to understanding—whether fully intended by the philosopher or a byproduct of their other insights, and a more contemporary reading. So it is with Popper. A couple of key ideas to emerge from Monday’s (make-up) class and the seminar discussion (my slides are below):

  1. Unlike the “naïve” empiricists of the day, Popper recognized that observations are not just given unproblematically, but also require an interpretation, an interest, a point of view, a problem. What came first, a hypothesis or an observation? Another hypothesis, if only at a lower level, says Popper.  He draws the contrast with Wittgenstein’s “verificationism”. In typical positivist style, the verificationist sees observations as the given “atoms,” and other knowledge is built up out of truth functional operations on those atoms.[1] However, scientific generalizations beyond the given observations cannot be so deduced, hence the traditional philosophical problem of induction isn’t solvable. One is left trying to build a formal “inductive logic” (generally deductive affairs, ironically) that is thought to capture intuitions about scientific inference (a largely degenerating program). The formal probabilists, as well as philosophical Bayesianism, may be seen as descendants of the logical positivists–instrumentalists, verificationists, operationalists (and the corresponding “isms”). So understanding Popper throws a lot of light on current day philosophy of probability and statistics.
  2. The fact that observations must be interpreted opens the door to interpretations that prejudge the construal of data. With enough interpretive latitude, anything (or practically anything) that is observed can be interpreted as in sync with a general claim H. (Once you opened your eyes, you see confirmations everywhere, as with a gestalt conversion, as Popper put it.) For Popper, positive instances of a general claim H, i.e., observations that agree with or “fit” H, do not even count as evidence for H if virtually any result could be interpreted as according with H.
    Note a modification of Popper here: Instead of putting the “riskiness” on H itself, it is the method of assessment or testing that bears the burden of showing that something (ideally quite a lot) has been done in order to scrutinize the way the data were interpreted (to avoid “verification bias”). The scrutiny needs to ensure that it would be difficult (rather than easy) to get an accordance between data x and H (as strong as the one obtained) if H were false (or specifiably flawed). Continue reading
Categories: Phil 6334 class material, Popper, Statistics | 7 Comments

Winner of the Febrary 2014 palindrome contest (rejected post)

SamHeadWinner of February 2014 Palindrome Contest
Samuel Dickson

Rot, Cadet A, I’ve droned! Elba, revile deviant, naïve, deliverable den or deviated actor.

The requirement was: A palindrome with Elba plus deviate with an optional second word: deviant. A palindrome that uses both deviate and deviant tops an acceptable palindrome that only uses deviate.

Sam Dickson is a regulatory statistician at U.S. Army Medical Research Institute of Infectious Diseases (USAMRIID) with experience in statistical consulting, specializing in design and analysis of biological and genetics/genomics studies.

“It’s great to get a  chance to exercise the mind with something other than statistics, though putting words together to make a palindrome is a puzzle very similar to designing an experiment that answers the right question.  Thank you for hosting this contest!”

Choice of book:
Principles of Applied Statistics (D. R. Cox and C. A. Donnelly 2011, Cambridge: Cambridge University Press)

Congratulations, Sam! I hope that your opting to do two words (plus Elba) means we can go back to the tougher standard for palindromes, but I’d just as soon raise the level of competence for several months more (sticking to one word). 

Categories: Announcement, Palindrome, Rejected Posts, Statistics | Leave a comment

Phil 6334: February 20, 2014 (Spanos): Day #5

may-4-8-aris-spanos-e2809contology-methodology-in-statistical-modelinge2809dPHIL 6334 – “Probability/Statistics Lecture Notes 3 for 2/20/14: Estimation (Point and Interval)”:(Prof. Spanos)*

*This is Day #5 on the Syllabus, as Day #4 had to be made up (Feb 24, 2014) due to snow. Slides for Day #4 will go up Feb. 26, 2014. (See the revised Syllabus Second Installment.)

Categories: Phil6334, Philosophy of Statistics, Spanos | 5 Comments

Sir Harold Jeffreys’ (tail area) one-liner: Sat night comedy [draft ii]

Comedy hour icon

This headliner appeared last month, but to a sparse audience (likely because it was during winter break), so Management’s giving him another chance… 

You might not have thought there could be new material for 2014, but there is, and if you look a bit more closely, you’ll see that it’s actually not Jay Leno who is standing up there at the mike ….

IMG_1547It’s Sir Harold Jeffreys himself! And his (very famous) joke, I admit, is funny. So, since it’s Saturday night, let’s listen in on Sir Harold’s howler* in criticizing the use of p-values.

“Did you hear the one about significance testers rejecting H0 because of outcomes H0 didn’t predict?

‘What’s unusual about that?’ you ask?

What’s unusual, is that they do it when these unpredicted outcomes haven’t even occurred!”

Much laughter.

[The actual quote from Jeffreys: Using p-values implies that “An hypothesis that may be true is rejected because it has failed to predict observable results that have not occurred. This seems a remarkable procedure.” (Jeffreys 1939, 316)]

I say it’s funny, so to see why I’ll strive to give it a generous interpretation. Continue reading

Categories: Comedy, Fisher, Jeffreys, P-values, Stephen Senn | Leave a comment

STEPHEN SENN: Fisher’s alternative to the alternative

Reblogging 2 years ago:

By: Stephen Senn

This year [2012] marks the 50th anniversary of RA Fisher’s death. It is a good excuse, I think, to draw attention to an aspect of his philosophy of significance testing. In his extremely interesting essay on Fisher, Jimmie Savage drew attention to a problem in Fisher’s approach to testing. In describing Fisher’s aversion to power functions Savage writes, ‘Fisher says that some tests are more sensitive than others, and I cannot help suspecting that that comes to very much the same thing as thinking about the power function.’ (Savage 1976) (P473).

The modern statistician, however, has an advantage here denied to Savage. Savage’s essay was published posthumously in 1976 and the lecture on which it was based was given in Detroit on 29 December 1971 (P441). At that time Fisher’s scientific correspondence did not form part of his available oeuvre but in1990 Henry Bennett’s magnificent edition of Fisher’s statistical correspondence (Bennett 1990) was published and this throws light on many aspects of Fisher’s thought including on significance tests.

The key letter here is Fisher’s reply of 6 October 1938 to Chester Bliss’s letter of 13 September. Bliss himself had reported an issue that had been raised with him by Snedecor on 6 September. Snedecor had pointed out that an analysis using inverse sine transformations of some data that Bliss had worked on gave a different result to an analysis of the original values. Bliss had defended his (transformed) analysis on the grounds that a) if a transformation always gave the same result as an analysis of the original data there would be no point and b) an analysis on inverse sines was a sort of weighted analysis of percentages with the transformation more appropriately reflecting the weight of information in each sample. Bliss wanted to know what Fisher thought of his reply.

Fisher replies with a ‘shorter catechism’ on transformations which ends as follows: Continue reading

Categories: Fisher, Statistics, Stephen Senn | Tags: , , , | 31 Comments

R.A. Fisher: ‘Two New Properties of Mathematical Likelihood’

17 February 1890–29 July 1962

Exactly 1 year ago: I find this to be an intriguing discussion–before some of the conflicts with N and P erupted.  Fisher links his tests and sufficiency, to the Neyman and Pearson lemma in terms of power.  It’s as if we may see them as ending up in a similar place while starting from different origins. I quote just the most relevant portions…the full article is linked below.

by R.A. Fisher, F.R.S.

Proceedings of the Royal Society, Series A, 144: 285-307 (1934)

  The property that where a sufficient statistic exists, the likelihood, apart from a factor independent of the parameter to be estimated, is a function only of the parameter and the sufficient statistic, explains the principle result obtained by Neyman and Pearson in discussing the efficacy of tests of significance.  Neyman and Pearson introduce the notion that any chosen test of a hypothesis H0 is more powerful than any other equivalent test, with regard to an alternative hypothesis H1, when it rejects H0 in a set of samples having an assigned aggregate frequency ε when H0 is true, and the greatest possible aggregate frequency when H1 is true.

If any group of samples can be found within the region of rejection whose probability of occurrence on the hypothesis H1 is less than that of any other group of samples outside the region, but is not less on the hypothesis H0, then the test can evidently be made more powerful by substituting the one group for the other. Continue reading

Categories: Fisher, phil/history of stat, Statistics | Tags: , , , | 1 Comment

Aris Spanos: The Enduring Legacy of R. A. Fisher

spanos 2014

More Fisher insights from A. Spanos, this from 2 years ago:

One of R. A. Fisher’s (17 February 1890 — 29 July 1962) most re­markable, but least recognized, achievement was to initiate the recast­ing of statistical induction. Fisher (1922) pioneered modern frequentist statistics as a model-based approach to statistical induction anchored on the notion of a statistical model, formalized by:

Mθ(x)={f(x;θ); θ∈Θ}; x∈Rn ;Θ⊂Rm; m < n; (1)

where the distribution of the sample f(x;θ) ‘encapsulates’ the proba­bilistic information in the statistical model.

Before Fisher, the notion of a statistical model was vague and often implicit, and its role was primarily confined to the description of the distributional features of the data in hand using the histogram and the first few sample moments; implicitly imposing random (IID) samples. The problem was that statisticians at the time would use descriptive summaries of the data to claim generality beyond the data in hand x0:=(x1,x2,…,xn). As late as the 1920s, the problem of statistical induction was understood by Karl Pearson in terms of invoking (i) the ‘stability’ of empirical results for subsequent samples and (ii) a prior distribution for θ.

Fisher was able to recast statistical inference by turning Karl Pear­son’s approach, proceeding from data x0 in search of a frequency curve f(x;ϑ) to describe its histogram, on its head. He proposed to begin with a prespecified Mθ(x) (a ‘hypothetical infinite population’), and view x0 as a ‘typical’ realization thereof; see Spanos (1999).

In my mind, Fisher’s most enduring contribution is his devising a general way to ‘operationalize’ errors by embedding the material ex­periment into Mθ(x), and taming errors via probabilification, i.e. to define frequentist error probabilities in the context of a statistical model. These error probabilities are (a) deductively derived from the statistical model, and (b) provide a measure of the ‘effectiviness’ of the inference procedure: how often a certain method will give rise to correct in­ferences concerning the underlying ‘true’ Data Generating Mechanism (DGM). This cast aside the need for a prior. Both of these key elements, the statistical model and the error probabilities, have been refined and extended by Mayo’s error statistical approach (EGEK 1996). Learning from data is achieved when an inference is reached by an inductive procedure which, with high probability, will yield true conclusions from valid inductive premises (a statistical model); Mayo and Spanos (2011). Continue reading

Categories: Fisher, phil/history of stat, Statistics | Tags: , , , , , , | 2 Comments

R. A. Fisher: how an outsider revolutionized statistics

A SPANOSToday is R.A. Fisher’s birthday and I’m reblogging the post by Aris Spanos which, as it happens, received the highest number of views of 2013.

by Aris Spanos

Few statisticians will dispute that R. A. Fisher (February 17, 1890 – July 29, 1962) is the father of modern statistics; see Savage (1976), Rao (1992). Inspired by William Gosset’s (1908) paper on the Student’s t finite sampling distribution, he recast statistics into the modern model-based induction in a series of papers in the early 1920s. He put forward a theory of optimal estimation based on the method of maximum likelihood that has changed only marginally over the last century. His significance testing, spearheaded by the p-value, provided the basis for the Neyman-Pearson theory of optimal testing in the early 1930s. According to Hald (1998)

“Fisher was a genius who almost single-handedly created the foundations for modern statistical science, without detailed study of his predecessors. When young he was ignorant not only of the Continental contributions but even of contemporary publications in English.” (p. 738)

What is not so well known is that Fisher was the ultimate outsider when he brought about this change of paradigms in statistical science. As an undergraduate, he studied mathematics at Cambridge, and then did graduate work in statistical mechanics and quantum theory. His meager knowledge of statistics came from his study of astronomy; see Box (1978). That, however did not stop him from publishing his first paper in statistics in 1912 (still an undergraduate) on “curve fitting”, questioning Karl Pearson’s method of moments and proposing a new method that was eventually to become the likelihood method in his 1921 paper. Continue reading

Categories: Fisher, phil/history of stat, Spanos, Statistics | 6 Comments

Fisher and Neyman after anger management?

Photo on 2-15-13 at 11.47 PM

Monday is Fisher’s birthday, and to set the stage for some items to appear, I’m posing the anger management question from a year ago post (please also see the comments from then). Here it is:

Would you agree if your (senior) colleague urged you to use his/her book rather than your own –even if you thought doing so would change for the positive the entire history of your field? My guess is that the answer is no (but see “add on”). For that matter, would you ever try to insist that your (junior) colleague use your book in teaching a course rather than his/her own notes or book?  Again I guess no. But perhaps you’d be more tactful than were Fisher and Neyman.

It wasn’t just Fisher who seemed to need some anger management training, Erich Lehmann (in conversation and in 2011) points to a number of incidences wherein Neyman is the instigator of gratuitous ill-will. Their substantive statistical and philosophical disagreements, I now think, were minuscule in comparison to the huge animosity that developed over many years. Here’s how Neyman describes a vivid recollection he has of the 1935 book episode to Constance Reid (1998, 126). [i]

A couple of months “after Neyman criticized Fisher’s concept of the complex experiment” Neyman vividly recollects  Fisher stopping by his office at University College on his way to a meeting which was to decide on Neyman’s reappointment[ii]: Continue reading

Categories: phil/history of stat, Statistics | 9 Comments

January Blog Table of Contents


January, and the blogging was easy

BLOG Contents: January 2014
Compiled by Jean Miller and Nicole Jinn

(1/2) Winner of the December 2013 Palindrome Book Contest (Rejected Post)
(1/3) Error Statistics Philosophy: 2013
(1/4) Your 2014 wishing well. …
(1/7) “Philosophy of Statistical Inference and Modeling” New Course: Spring 2014: Mayo and Spanos: (Virginia Tech)
(1/11) Two Severities? (PhilSci and PhilStat)
(1/14) Statistical Science meets Philosophy of Science: blog beginnings
(1/16) Objective/subjective, dirty hands and all that: Gelman/Wasserman blogolog (ii)
(1/18) Sir Harold Jeffreys’ (tail area) one-liner: Sat night comedy [draft ii]
(1/22) Phil6334: “Philosophy of Statistical Inference and Modeling” New Course: Spring 2014: Mayo and Spanos (Virginia Tech) UPDATE: JAN 21
(1/24) Phil 6334: Slides from Day #1: Four Waves in Philosophy of Statistics
(1/25) U-Phil (Phil 6334) How should “prior information” enter in statistical inference?
(1/27) Winner of the January 2014 palindrome contest (rejected post)
(1/29) BOSTON COLLOQUIUM FOR PHILOSOPHY OF SCIENCE: Revisiting the Foundations of Statistics
(1/31) Phil 6334: Day #2 Slides

Categories: Metablog | Leave a comment

Phil6334 Statistical Snow Sculpture

Statistical Snow Sculpture

Statistical Snow Sculpture

No Seminar. Blizzard.

Categories: Announcement, Phil6334 | Leave a comment

Phil6334: Popper self-test

images-10Those reading Popper[i] with us might be interested in an (undergraduate) item I came across: Popper Self-Test Questions. It includes multiple choice questions, quotes to ponder, and thumbnail definitions at the end[ii].
[i]Popper reading (for Feb 13, 2014) from Conjectures and Refutations
[ii]I might note the “No-Pain philosophy” (3 part) Popper posts from this blog: parts 12, and 3.

Categories: Error Statistics | 1 Comment

Is it true that all epistemic principles can only be defended circularly? A Popperian puzzle

images-8Current day Popperians, the “critical rationalists”, espouse the following epistemic principle CR:[i]

(CR) it is reasonable to adopt or believe a claim or theory P which best survives serious criticism.

What justifies CR?  To merely declare it is a reasonable epistemic principle without giving evidence that following it advances any epistemic goals is entirely unsatisfactory, and decidedly un-Popperian in spirit.

Alan Musgrave (1999), leading critical rationalist, mounts a defence of CR that he openly concedes is circular, admitting, as he does, that such circular defences could likewise be used to argue for principles he himself regards as ‘crazy’.
However, he also gives a subtle and clever argument that it’s impossible to do better, that such a circular defense is the only kind possible. So since we’re reading Popper this week (some of us), and since an analogous argument arises in defending principles of statistical inference, try your hand at this conundrum. Continue reading

Categories: philosophy of science, Popper, Statistics | 2 Comments

Phil 6334: Day #3: Feb 6, 2014


Day #3: Spanos lecture notes 2, and reading/resources from Feb 6 seminar 

6334 Day 3 slides: Spanos-lecture-2


Crupi & Tentori (2010). Irrelevant Conjunction: Statement and Solution of a New Paradox, Phil Sci, 77, 1–13.

Hawthorne & Fitelson (2004). Re-Solving Irrelevant Conjunction with Probabilistic Independence, Phil Sci 71: 505–514.

Skryms (1975) Choice and Chance 2nd ed. Chapter V and Carnap (pp. 206-211), Dickerson Pub. Co.

Mayo posts on the tacking paradox: Oct. 25, 2013: “Bayesian Confirmation Philosophy and the Tacking Paradox (iv)*” &  Oct 25.

An update on this issue will appear shortly in a separate blogpost.


Selection (pp. 35-59) from: Popper (1962). Conjectures and RefutationsThe Growth of Scientific Knowledge. Basic Books. 

Categories: Bayes' Theorem, Phil 6334 class material, Statistics | Leave a comment

“Probabilism as an Obstacle to Statistical Fraud-Busting” (draft iii)

IMG_0244Update: Feb. 21, 2014 (slides at end)Ever find when you begin to “type” a paper to which you gave an off-the-cuff title months and months ago that you scarcely know just what you meant or feel up to writing a paper with that (provocative) title? But then, pecking away at the outline of a possible paper crafted to fit the title, you discover it’s just the paper you’re up to writing right now? That’s how I feel about “Is the Philosophy of Probabilism an Obstacle to Statistical Fraud Busting?” (the impromptu title I gave for my paper for the Boston Colloquium for the Philosophy of Science):

The conference is called: “Revisiting the Foundations of Statistics in the Era of Big Data: Scaling Up to Meet the Challenge.”  

 Here are some initial chicken-scratchings (draft (i)). Share comments, queries. (I still have 2 weeks to come up with something*.) Continue reading

Categories: P-values, significance tests, Statistical fraudbusting, Statistics | Leave a comment

PhilStock: Bad news is bad news on Wall St. (rejected post)

stock picture smaillI’ve been asked for a PhilStock tip. Well, remember when it could be said that “bad news is good news on wall street“?

No longer. Now bad is bad. I call these “blood days” on the stock market, and the only statistical advice that has held up over the past turbulent years is: Never try to catch a falling knife*.

*For more, you’ll have to seek my stock blog.

Categories: PhilStock, Rejected Posts | 8 Comments

Comedy hour at the Bayesian (epistemology) retreat: highly probable vs highly probed (vs B-boosts)

Since we’ll be discussing Bayesian confirmation measures in next week’s seminar—the relevant blogpost being here--let’s listen in to one of the comedy hours at the Bayesian retreat as reblogged from May 5, 2012.

Did you hear the one about the frequentist error statistical tester who inferred a hypothesis H passed a stringent test (with data x)?

The problem was, the epistemic probability in H was so low that H couldn’t be believed!  Instead we believe its denial H’!  So, she will infer hypotheses that are simply unbelievable!

So it appears the error statistical testing account fails to serve as an account of knowledge or evidence (i.e., an epistemic account). However severely I might wish to say that a hypothesis H has passed a test, this Bayesian critic assigns a sufficiently low prior probability to H so as to yield a low posterior probability in H[i].  But this is no argument about why this counts in favor of, rather than against, their particular Bayesian computation as an appropriate assessment of the warrant to be accorded to hypothesis H.

To begin with, in order to use techniques for assigning frequentist probabilities to events, their examples invariably involve “hypotheses” that consist of asserting that a sample possesses a characteristic, such as “having a disease” or “being college ready” or, for that matter, “being true.”  This would not necessarily be problematic if it were not for the fact that their criticism requires shifting the probability to the particular sample selected—for example, a student Isaac is college-ready, or this null hypothesis (selected from a pool of nulls) is true.  This was, recall, the fallacious probability assignment that we saw in Berger’s attempt, later (perhaps) disavowed. Also there are just two outcomes, say s and ~s, and no degrees of discrepancy from H. Continue reading

Categories: Comedy, confirmation theory | Tags: , , , , | 28 Comments

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