Gelman

Gelman at the PSA: “Confirmationist and Falsificationist Paradigms in Statistical Practice”: Comments & Queries

screen-shot-2016-10-26-at-10-23-07-pmTo resume sharing some notes I scribbled down on the contributions to our Philosophy of Science Association symposium on Philosophy of Statistics (Nov. 4, 2016), I’m up to Gelman. Comments on Gigerenzer and Glymour are here and here. Gelman didn’t use slides but gave a very thoughtful, extemporaneous presentation on his conception of “falsificationist Bayesianism”, its relation to current foundational issues, as well as to error statistical testing. My comments follow his abstract.

Confirmationist and Falsificationist Paradigms in Statistical Practice

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Andrew Gelman

There is a divide in statistics between classical frequentist and Bayesian methods. Classical hypothesis testing is generally taken to follow a falsificationist, Popperian philosophy in which research hypotheses are put to the test and rejected when data do not accord with predictions. Bayesian inference is generally taken to follow a confirmationist philosophy in which data are used to update the probabilities of different hypotheses. We disagree with this conventional Bayesian-frequentist contrast: We argue that classical null hypothesis significance testing is actually used in a confirmationist sense and in fact does not do what it purports to do; and we argue that Bayesian inference cannot in general supply reasonable probabilities of models being true. The standard research paradigm in social psychology (and elsewhere) seems to be that the researcher has a favorite hypothesis A. But, rather than trying to set up hypothesis A for falsification, the researcher picks a null hypothesis B to falsify, which is then taken as evidence in favor of A. Research projects are framed as quests for confirmation of a theory, and once confirmation is achieved, there is a tendency to declare victory and not think too hard about issues of reliability and validity of measurements. Continue reading

Categories: Bayesian/frequentist, Gelman, Shalizi, Statistics | 148 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

A new front in the statistics wars? Peaceful negotiation in the face of so-called ‘methodological terrorism’

images-30I haven’t been blogging that much lately, as I’m tethered to the task of finishing revisions on a book (on the philosophy of statistical inference!) But I noticed two interesting blogposts, one by Jeff Leek, another by Andrew Gelman, and even a related petition on Twitter, reflecting a newish front in the statistics wars: When it comes to improving scientific integrity, do we need more carrots or more sticks? 

Leek’s post, from yesterday, called “Statistical Vitriol” (29 Sep 2016), calls for de-escalation of the consequences of statistical mistakes:

Over the last few months there has been a lot of vitriol around statistical ideas. First there were data parasites and then there were methodological terrorists. These epithets came from established scientists who have relatively little statistical training. There was the predictable backlash to these folks from their counterparties, typically statisticians or statistically trained folks who care about open source.
Continue reading

Categories: Anil Potti, fraud, Gelman, pseudoscience, Statistics | 15 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

Can You change Your Bayesian prior? (ii)

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This is one of the questions high on the “To Do” list I’ve been keeping for this blog.  The question grew out of discussions of “updating and downdating” in relation to papers by Stephen Senn (2011) and Andrew Gelman (2011) in Rationality, Markets, and Morals.[i]

“As an exercise in mathematics [computing a posterior based on the client’s prior probabilities] is not superior to showing the client the data, eliciting a posterior distribution and then calculating the prior distribution; as an exercise in inference Bayesian updating does not appear to have greater claims than ‘downdating’.” (Senn, 2011, p. 59)

“If you could really express your uncertainty as a prior distribution, then you could just as well observe data and directly write your subjective posterior distribution, and there would be no need for statistical analysis at all.” (Gelman, 2011, p. 77)

But if uncertainty is not expressible as a prior, then a major lynchpin for Bayesian updating seems questionable. If you can go from the posterior to the prior, on the other hand, perhaps it can also lead you to come back and change it.

Is it legitimate to change one’s prior based on the data?

I don’t mean update it, but reject the one you had and replace it with another. My question may yield different answers depending on the particular Bayesian view. I am prepared to restrict the entire question of changing priors to Bayesian “probabilisms”, meaning the inference takes the form of updating priors to yield posteriors, or to report a comparative Bayes factor. Interpretations can vary. In many Bayesian accounts the prior probability distribution is a way of introducing prior beliefs into the analysis (as with subjective Bayesians) or, conversely, to avoid introducing prior beliefs (as with reference or conventional priors). Empirical Bayesians employ frequentist priors based on similar studies or well established theory. There are many other variants.

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S. SENN: According to Senn, one test of whether an approach is Bayesian is that while Continue reading

Categories: Bayesian/frequentist, Gelman, S. Senn, Statistics | 111 Comments

Gelman recognizes his error-statistical (Bayesian) foundations

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From Gelman’s blog:

“In one of life’s horrible ironies, I wrote a paper “Why we (usually) don’t have to worry about multiple comparisons” but now I spend lots of time worrying about multiple comparisons”

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Exhibit A: [2012] Why we (usually) don’t have to worry about multiple comparisons. Journal of Research on Educational Effectiveness 5, 189-211. (Andrew Gelman, Jennifer Hill, and Masanao Yajima)

Exhibit B: The garden of forking paths: Why multiple comparisons can be a problem, even when there is no “fishing expedition” or “p-hacking” and the research hypothesis was posited ahead of time, in press. (Andrew Gelman and Eric Loken) (Shortened version is here.)

 

The “forking paths” paper, in my reading,  basically argues that mere hypothetical possibilities about what you would or might have done had the data been different (in order to secure a desired interpretation) suffices to alter the characteristics of the analysis you actually did. That’s an error statistical argument–maybe even stronger than what some error statisticians would say. What’s really being condemned are overly flexible ways to move from statistical results to substantive claims. The p-values are illicit when taken to provide evidence for those claims because an actual p-value requires Prob(P < p;Ho) = p (and the actual p-value has become much greater by design). The criticism makes perfect sense if you’re scrutinizing inferences according to how well or severely tested they are. Actual error probabilities are accordingly altered or unable to be calculated. However, if one is going to scrutinize inferences according to severity then the same problematic flexibility would apply to Bayesian analyses, whether or not they have a way to pick up on it. (It’s problematic if they don’t.) I don’t see the magic by which a concern for multiple testing disappears in Bayesian analysis (e.g., in the first paper) except by assuming some prior takes care of it.

See my comment here.

Categories: Error Statistics, Gelman | 17 Comments

Deconstructing Andrew Gelman: “A Bayesian wants everybody else to be a non-Bayesian.”

At the start of our seminar, I said that “on weekends this spring (in connection with Phil 6334, but not limited to seminar participants) I will post some of my ‘deconstructions of articles”. I began with Andrew Gelman‘s note  “Ethics and the statistical use of prior information”[i], but never posted my deconstruction of it. So since it’s Saturday night, and the seminar is just ending, here it is, along with related links to Stat and ESP research (including me, Jack Good, Persi Diaconis and Pat Suppes). Please share comments especially in relation to current day ESP research. Continue reading

Categories: Background knowledge, Gelman, Phil6334, Statistics | 35 Comments

Objective/subjective, dirty hands and all that: Gelman/ Wasserman blogolog (ii)

Objectivity #2: The “Dirty Hands” Argument for Ethics in EvidenceAndrew Gelman says that as a philosopher, I should appreciate his blog today in which he records his frustration: “Against aggressive definitions: No, I don’t think it helps to describe Bayes as ‘the analysis of subjective beliefs’…”  Gelman writes:

I get frustrated with what might be called “aggressive definitions,” where people use a restrictive definition of something they don’t like. For example, Larry Wasserman writes (as reported by Deborah Mayo):

“I wish people were clearer about what Bayes is/is not and what 
frequentist inference is/is not. Bayes is the analysis of subjective
 beliefs but provides no frequency guarantees. Frequentist inference 
is about making procedures that have frequency guarantees but makes no 
pretense of representing anyone’s beliefs.”

I’ll accept Larry’s definition of frequentist inference. But as for his definition of Bayesian inference: No no no no no. The probabilities we use in our Bayesian inference are not subjective, or, they’re no more subjective than the logistic regressions and normal distributions and Poisson distributions and so forth that fill up all the textbooks on frequentist inference.

To quickly record some of my own frustrations:*: First, I would disagree with Wasserman’s characterization of frequentist inference, but as is clear from Larry’s comments to (my reaction to him), I think he concurs that he was just giving a broad contrast. Please see Note [1] for a remark from my post: Comments on Wasserman’s “what is Bayesian/frequentist inference?” Also relevant is a Gelman post on the Bayesian name: [2].

Second, Gelman’s “no more subjective than…” evokes  remarks I’ve made before. For example, in “What should philosophers of science do…” I wrote:

Arguments given for some very popular slogans (mostly by non-philosophers), are too readily taken on faith as canon by others, and are repeated as gospel. Examples are easily found: all models are false, no models are falsifiable, everything is subjective, or equally subjective and objective, and the only properly epistemological use of probability is to supply posterior probabilities for quantifying actual or rational degrees of belief. Then there is the cluster of “howlers” allegedly committed by frequentist error statistical methods repeated verbatim (discussed on this blog).

I’ve written a lot about objectivity on this blog, e.g., here, here and here (and in real life), but what’s the point if people just rehearse the “everything is a mixture…” line, without making deeply important distinctions? I really think that, next to the “all models are false” slogan, the most confusion has been engendered by the “no methods are objective” slogan. However much we may aim at objective constraints, it is often urged, we can never have “clean hands” free of the influence of beliefs and interests, and we invariably sully methods of inquiry by the entry of background beliefs and personal judgments in their specification and interpretation. Continue reading

Categories: Bayesian/frequentist, Error Statistics, Gelman, Objectivity, Statistics | 41 Comments

U-Phil: Deconstructions [of J. Berger]: Irony & Bad Faith 3

Memory Lane: 2 years ago:
My efficient Errorstat Blogpeople1 have put forward the following 3 reader-contributed interpretive efforts2 as a result of the “deconstruction” exercise from December 11, (mine, from the earlier blog, is at the end) of what I consider:

“….an especially intriguing remark by Jim Berger that I think bears upon the current mindset (Jim is aware of my efforts):

Too often I see people pretending to be subjectivists, and then using “weakly informative” priors that the objective Bayesian community knows are terrible and will give ridiculous answers; subjectivism is then being used as a shield to hide ignorance. . . . In my own more provocative moments, I claim that the only true subjectivists are the objective Bayesians, because they refuse to use subjectivism as a shield against criticism of sloppy pseudo-Bayesian practice. (Berger 2006, 463)” (From blogpost, Dec. 11, 2011)
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Andrew Gelman:

The statistics literature is big enough that I assume there really is some bad stuff out there that Berger is reacting to, but I think that when he’s talking about weakly informative priors, Berger is not referring to the work in this area that I like, as I think of weakly informative priors as specifically being designed to give answers that are _not_ “ridiculous.”

Keeping things unridiculous is what regularization’s all about, and one challenge of regularization (as compared to pure subjective priors) is that the answer to the question, What is a good regularizing prior?, will depend on the likelihood.  There’s a lot of interesting theory and practice relating to weakly informative priors for regularization, a lot out there that goes beyond the idea of noninformativity.

To put it another way:  We all know that there’s no such thing as a purely noninformative prior:  any model conveys some information.  But, more and more, I’m coming across applied problems where I wouldn’t want to be noninformative even if I could, problems where some weak prior information regularizes my inferences and keeps them sane and under control. Continue reading

Categories: Gelman, Irony and Bad Faith, J. Berger, Statistics, U-Phil | Tags: , , , | 3 Comments

Gelman est effectivement une erreur statistician

eiffel-tower-design-bill-cannonA reader calls my attention to Andrew Gelman’s blog announcing a talk that he’s giving today in French: “Philosophie et practique de la statistique bayésienne. He blogs:

I’ll try to update the slides a bit since a few years ago, to add some thoughts I’ve had recently about problems with noninformative priors, even in simple settings.

The location of the talk will not be convenient for most of you, but anyone who comes to the trouble of showing up will have the opportunity to laugh at my accent.

P.S. For those of you who are interested in the topic but can’t make it to the talk, I recommend these two papers on my non-inductive Bayesian philosophy:

[2013] Philosophy and the practice of Bayesian statistics (with discussion). British Journal of Mathematical and Statistical Psychology, 8–18. (Andrew Gelman and Cosma Shalizi)
[2013] Rejoinder to discussion. (Andrew Gelman and Cosma Shalizi)

[2011] Induction and deduction in Bayesian data analysis. Rationality, Markets and Morals}, special topic issue “Statistical Science and Philosophy of Science: Where Do (Should) They Meet In 2011 and Beyond?” (Andrew Gelman)

These papers, especially Gelman (2011), are discussed on this blog (in “U-Phils”). Comments by Senn, Wasserman, and Hennig may be found here, and here,with a response here (please use search for more).

As I say in my comments on Gelman and Shalizi, I think Gelman’s position is (or intends to be) inductive– in the sense of being ampliative (going beyond the data)– but simply not probabilist, i.e., not a matter of updating priors. (A blog post is here)[i]. Here’s a snippet from my comments: Continue reading

Categories: Error Statistics, Gelman | Tags: | 17 Comments

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