Posts Tagged With: Larry Wasserman

More on deconstructing Larry Wasserman (Aris Spanos)

This follows up on yesterday’s deconstruction:


 Aris Spanos (2012)[i] – Comments on: L. Wasserman “Low Assumptions, High Dimensions (2011)*

I’m happy to play devil’s advocate in commenting on Larry’s very interesting and provocative (in a good way) paper on ‘how recent developments in statistical modeling and inference have [a] changed the intended scope of data analysis, and [b] raised new foundational issues that rendered the ‘older’ foundational problems more or less irrelevant’.

The new intended scope, ‘low assumptions, high dimensions’, is delimited by three characteristics:

“1. The number of parameters is larger than the number of data points.

2. Data can be numbers, images, text, video, manifolds, geometric objects, etc.

3. The model is always wrong. We use models, and they lead to useful insights but the parameters in the model are not meaningful.” (p. 1)

In the discussion that follows I focus almost exclusively on the ‘low assumptions’ component of the new paradigm. The discussion by David F. Hendry (2011), “Empirical Economic Model Discovery and Theory Evaluation,” RMM, 2: 115-145,  is particularly relevant to some of the issues raised by the ‘high dimensions’ component in a way that complements the discussion that follows.

My immediate reaction to the demarcation based on 1-3 is that the new intended scope, although interesting in itself, excludes the overwhelming majority of scientific fields where restriction 3 seems unduly limiting. In my own field of economics the substantive information comes primarily in the form of substantively specified mechanisms (structural models), accompanied with theory-restricted and substantively meaningful parameters.

In addition, I consider the assertion “the model is always wrong” an unhelpful truism when ‘wrong’ is used in the sense that “the model is not an exact picture of the ‘reality’ it aims to capture”. Worse, if ‘wrong’ refers to ‘the data in question could not have been generated by the assumed model’, then any inference based on such a model will be dubious at best! Continue reading

Categories: Philosophy of Statistics, Spanos, Statistics, U-Phil, Wasserman | Tags: , , , , | 5 Comments

Deconstructing Larry Wasserman

 Greek dancing lady gold SavoyLarry Wasserman (“Normal Deviate”) has announced he will stop blogging (for now at least). That means we’re losing one of the wisest blog-voices on issues relevant to statistical foundations (among many other areas in statistics). Whether this lures him back or reaffirms his decision to stay away, I thought I’d reblog my (2012) “deconstruction” of him (in relation to a paper linked below)[i]

Deconstructing Larry Wasserman [i] by D. Mayo

The temptation is strong, but I shall refrain from using the whole post to deconstruct Al Franken’s 2003 quip about media bias (from Lies and Lying Liars Who Tell Them: A Fair and Balanced Look at the Right), with which Larry Wasserman begins his paper “Low Assumptions, High Dimensions” (2011) in his contribution to Rationality, Markets and Morals (RMM) Special Topic: Statistical Science and Philosophy of Science:

Wasserman: There is a joke about media bias from the comedian Al Franken:
‘To make the argument that the media has a left- or right-wing, or a liberal or a conservative bias, is like asking if the problem with Al-Qaeda is: do they use too much oil in their hummus?’

According to Wasserman, “a similar comment could be applied to the usual debates in the foundations of statistical inference.”

Although it’s not altogether clear what Wasserman means by his analogy with comedian (now senator) Franken, it’s clear enough what Franken meant if we follow up the quip with the next sentence in his text (which Wasserman omits): “The problem with al Qaeda is that they’re trying to kill us!” (p. 1). The rest of Franken’s opening chapter is not about al Qaeda but about bias in media. Conservatives, he says, decry what they claim is a liberal bias in mainstream media. Franken rejects their claim.

The mainstream media does not have a liberal bias. And for all their other biases . . . , the mainstream media . . . at least try to be fair. …There is, however, a right-wing media. . . . They are biased. And they have an agenda…The members of the right-wing media are not interested in conveying the truth… . They are an indispensable component of the right-wing machine that has taken over our country… .   We have to be vigilant.  And we have to be more than vigilant.  We have to fight back… . Let’s call them what they are: liars. Lying, lying, liars. (Franken, pp. 3-4)

When I read this in 2004 (when Bush was in office), I couldn’t have agreed more. How things change*. Now, of course, any argument that swerves from the politically correct is by definition unsound, irrelevant, and/ or biased. [ii](December 2016 update: This just shows how things get topsy-turvy every 5-8 years. Now we have extremes on both sides.)

But what does this have to do with Bayesian-frequentist foundations? What is Wasserman, deep down, really trying to tell us by way of this analogy (if only subliminally)? Such are my ponderings—and thus this deconstruction.  (I will invite your “U-Phils” at the end[a].) I will allude to passages from my contribution to  RMM (2011)  http://www.rmm-journal.de/htdocs/st01.html  (in red).

A.What Is the Foundational Issue?

Wasserman: To me, the most pressing foundational question is: how do we reconcile the two most powerful needs in modern statistics: the need to make methods assumption free and the need to make methods work in high dimensions… . The Bayes-Frequentist debate is not irrelevant but it is not as central as it once was. (p. 201)

One may wonder why he calls this a foundational issue, as opposed to, say, a technical one. I will assume he means what he says and attempt to extract his meaning by looking through a foundational lens. Continue reading

Categories: Philosophy of Statistics, Statistics, U-Phil | Tags: , , , | 10 Comments

U-PHIL: Gandenberger & Hennig: Blogging Birnbaum’s Proof

greg picDefending Birnbaum’s Proof

Greg Gandenberger
PhD student, History and Philosophy of Science
Master’s student, Statistics
University of Pittsburgh

In her 1996 Error and the Growth of Experimental Knowledge, Professor Mayo argued against the Likelihood Principle on the grounds that it does not allow one to control long-run error rates in the way that frequentist methods do.  This argument seems to me the kind of response a frequentist should give to Birnbaum’s proof.  It does not require arguing that Birnbaum’s proof is unsound: a frequentist can accommodate Birnbaum’s conclusion (two experimental outcomes are evidentially equivalent if they have the same likelihood function) by claiming that respecting evidential equivalence is less important than achieving certain goals for which frequentist methods are well suited.

More recently, Mayo has shown that Birnbaum’s premises cannot be reformulated as claims about what sampling distribution should be used for inference while retaining the soundness of his proof.  It does not follow that Birnbaum’s proof is unsound because Birnbaum’s original premises are not claims about what sampling distribution should be used for inference but instead as sufficient conditions for experimental outcomes to be evidentially equivalent.

Mayo acknowledges that the premises she uses in her argument against Birnbaum’s proof differ from Birnbaum’s original premises in a recent blog post in which she distinguishes between “the Sufficient Principle (general)” and “the Sufficiency Principle applied in sampling theory.“  One could make a similar distinction for the Weak Conditionality Principle.  There is indeed no way to formulate Sufficiency and Weak Conditionality Principles “applied in sampling theory” that are consistent and imply the Likelihood Principle.  This fact is not surprising: sampling theory is incompatible with the Likelihood Principle!

Birnbaum himself insisted that his premises were to be understood as “equivalence relations” rather than as “substitution rules” (i.e., rules about what sampling distribution should be used for inference) and recognized the fact that understanding them in this way was necessary for his proof.  As he put it in his 1975 rejoinder to Kalbfleisch’s response to his proof, “It was the adoption of an unqualified equivalence formulation of conditionality, and related concepts, which led, in my 1972 paper, to the monster of the likelihood axiom” (263).

Because Mayo’s argument against Birnbaum’s proof requires reformulating Birnbaum’s premises, it is best understood as an argument not for the claim that Birnbaum’s original proof is invalid, but rather for the claim that Birnbaum’s proof is valid only when formulated in a way that is irrelevant to a sampling theorist.  Reformulating Birnbaum’s premises as claims about what sampling distribution should be used for inference is the only way for a fully committed sampling theorist to understand them.  Any other formulation of those premises is either false or question-begging.

Mayo’s argument makes good sense when understood in this way, but it requires a strong prior commitment to sampling theory. Whether various arguments for sampling theory such as those Mayo gives in Error and the Growth of Experimental Knowledge are sufficient to warrant such a commitment is a topic for another day.  To those who lack such a commitment, Birnbaum’s original premises may seem quite compelling.  Mayo has not refuted the widespread view that those premises do in fact entail the Likelihood Principle.

Mayo has objected to this line of argument by claiming that her reformulations of Birnbaum’s principles are just instantiations of Birnbaum’s principles in the context of frequentist methods. But they cannot be instantiations in a literal sense because they are imperatives, whereas Birnabaum’s original premises are declaratives.  They are instead instructions that a frequentist would have to follow in order to avoid violating Birnbaum’s principles. The fact that one cannot follow them both is only an objection to Birnbaum’s principles on the question-begging assumption that evidential meaning depends on sampling distributions.

 ********

Birnbaum’s proof is not wrong but error statisticians don’t need to bother

Christian Hennig
Department of Statistical Science
University College London

I was impressed by Mayo’s arguments in “Error and Inference” when I came across them for the first time. To some extent, I still am. However, I have also seen versions of Birnbaum’s theorem and proof presented in a mathematically sound fashion with which I as a mathematician had no issue.

After having discussed this a bit with Phil Dawid, and having thought and read more on the issue, my conclusion is that
1) Birnbaum’s theorem and proof are correct (apart from small mathematical issues resolved later in the literature), and they are not vacuous (i.e., there are evidence functions that fulfill them without any contradiction in the premises),
2) however, Mayo’s arguments actually do raise an important problem with Birnbaum’s reasoning.

Here is why. Note that Mayo’s arguments are based on the implicit (error statistical) assumption that the sampling distribution of an inference method is relevant. In that case, application of the sufficiency principle to Birnbaum’s mixture distribution enforces the use of the sampling distribution under the mixture distribution as it is, whereas application of the conditionality principle enforces the use of the sampling distribution under the experiment that actually produced the data, which is different in the usual examples. So the problem is not that Birnbaum’s proof is wrong, but that enforcing both principles at the same time in the mixture experiment is in contradiction to the relevance of the sampling distribution (and therefore to error statistical inference). It is a case in which the sufficiency principle suppresses information that is clearly relevant under the conditionality principle. This means that the justification of the sufficiency principle (namely that all relevant information is in the sufficient statistic) breaks down in this case.

Frequentists/error statisticians therefore don’t need to worry about the likelihood principle because they shouldn’t accept the sufficiency principle in the generality that is required for Birnbaum’s proof.

Having understood this, I toyed around with the idea of writing this down as a publishable paper, but I now came across a paper in which this argument can already be found (although in a less straightforward and more mathematical manner), namely:
M. J. Evans, D. A. S. Fraser and G. Monette (1986) On Principles and Arguments to Likelihood. Canadian Journal of Statistics 14, 181-194, http://www.jstor.org/stable/3314794, particularly Section 7 (the rest is interesting, too).

NOTE: This is the last of this group of U-Phils. Mayo will issue a brief response tomorrow. Background to these U-Phils may be found here.

Categories: Philosophy of Statistics, Statistics, U-Phil | Tags: , , , , | 12 Comments

U-Phil: (concluding the deconstruction) Wasserman / Mayo

It is traditional to end the U-Phil deconstruction discussion with the author’s remarks on the deconstruction itself.  I take this from Wasserman’s initial comment on 7/28/12, and my brief reply. I especially want to highlight the question of goals that arises.

Wasserman:

I thank Deborah Mayo for deconstructing me and Al Franken. (And for the record, I couldn’t be further from Franken politically; I just liked his joke.)

I have never been deconstructed before. I feel a bit like Humpty Dumpty. Anyway, I think I agree with everything Deborah wrote. I’ll just clarify two points.

First, my main point was just that the cutting edge of statistics today is dealing with complex, high-dimensional data. My essay was an invitation to Philosophers to turn their analytical skills towards the problems that arise in these modern statistical problems.

Deborah wonders whether these are technical rather than foundational issues. I don’t know. When physicists went from studying medium sized, slow-moving objects to studying the very small, the very fast and the very massive, they found a plethora of interesting questions, both technical and foundational. Perhaps inference for high-dimensional, complex data can also serve as a venue for both both technical and foundational questions.

Second, I downplayed the Bayes-Frequentist perhaps more than I should have. Indeed, this debate still persists. But I also feel that only a small subset of statisticians care about the debate (because, they do what they were taught to do, without questioning it) and those that do care, will never be swayed by debate. The way I see it is that there are basically two goals:

  • Goal 1: Find ways to quantify your subjective degrees of belief.
  • Goal 2: Find procedures with good frequency properties. Continue reading
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U-PHIL: Wasserman Replies to Spanos and Hennig

Wasserman on Spanos and Hennig on  “Low Assumptions, High Dimensions” (2011)

(originating U-PHIL : “Deconstructing Larry Wasserman” by Mayo )

________

Thanks to Aris and others for comments .

Response to Aris Spanos:

1. You don’t prefer methods based on weak assumptions? Really? I suspect Aris is trying to be provocative. Yes such inferences can be less precise. Good. Accuracy is an illusion if it comes from assumptions, not from data.

2. I do not think I was promoting inferences based on “asymptotic grounds.” If I did, that was not my intent. I want finite sample, distribution free methods. As an example, consider the usual finite sample (order statistics based) confidence interval for the median. No regularity assumptions, no asymptotics, no approximations. What is there to object to?

3. Indeed, I do have to make some assumptions. For simplicity, and because it is often reasonable, I assumed iid in the paper (as I will here). Other than that, where am I making any untestable assumptions in the example of the median?

4. I gave a very terse and incomplete summary of Davies’ work. I urge readers to look at Davies’ papers; my summary does not do the work justice. He certainly did not advocate eyeballing the data. Continue reading

Categories: Philosophy of Statistics, Statistics, U-Phil | Tags: , , , , | 3 Comments

U-PHIL: Hennig and Gelman on Wasserman (2011)

Two further contributions in relation to

“Low Assumptions, High Dimensions” (2011)

Please also see : “Deconstructing Larry Wasserman” by Mayo, and Comments by Spanos

Christian Hennig:  Some comments on Larry Wasserman, “Low Assumptions, High Dimensions”

I enjoyed reading this stimulating paper. These are very important issues indeed. I’ll comment on both main concepts in the text.

1) Low Assumptions. I think that the term “assumption” is routinely misused and misunderstood in statistics. In Wasserman’s paper I can’t see such misuse explicitly, but I think that the “message” of the paper may be easily misunderstood because Wasserman doesn’t do much to stop people from this kind of misunderstanding.

Here is what I mean. The arithmetic mean can be derived as optimal estimator under an i.i.d. Gaussian model, which is often interpreted as “model assumption” behind it. However, we don’t really need the Gaussian distribution to be true for the mean to do a good job. Sometimes the mean will do a bad job in a non-Gaussian situation (for example in presence of gross outliers), but sometimes not. The median has nice robustness properties and is seen as admissible for ordinal data. It is therefore usually associated with “weaker assumptions”. However, the median may be worse than the mean in a situation where the Gaussian “assumption” of the mean is grossly violated. At UCL we ask students on a -2/-1/0/1/2 Likert scale for their general opinion about our courses. The distributions that we get here are strongly discrete and the scale is usually interpreted as of ordinal type. Still, for ranking courses, the median is fairly useless (pretty much all courses end up with a median of 0 or 1); whereas, the arithmetic mean can still detect statistically significant meaningful differences between courses.

Why? Because it’s not only the “official” model assumptions that matter but also whether a statistic uses all the data in an appropriate manner for the given application. Here it’s fatal that the median ignores all differences among observations north and south of it. Continue reading

Categories: Philosophy of Statistics, Statistics, U-Phil | Tags: , , , , | 3 Comments

U-PHIL: Aris Spanos on Larry Wasserman

Our first outgrowth of “Deconstructing Larry Wasserman”. 

Aris Spanos – Comments on:

“Low Assumptions, High Dimensions” (2011)

by Larry Wasserman*

I’m happy to play devil’s advocate in commenting on Larry’s very interesting and provocative (in a good way) paper on ‘how recent developments in statistical modeling and inference have [a] changed the intended scope of data analysis, and [b] raised new foundational issues that rendered the ‘older’ foundational problems more or less irrelevant’.

The new intended scope, ‘low assumptions, high dimensions’, is delimited by three characteristics:

“1. The number of parameters is larger than the number of data points.

2. Data can be numbers, images, text, video, manifolds, geometric objects, etc.

3. The model is always wrong. We use models, and they lead to useful insights but the parameters in the model are not meaningful.” (p. 1)

In the discussion that follows I focus almost exclusively on the ‘low assumptions’ component of the new paradigm. The discussion by David F. Hendry (2011), “Empirical Economic Model Discovery and Theory Evaluation,” RMM, 2: 115-145,  is particularly relevant to some of the issues raised by the ‘high dimensions’ component in a way that complements the discussion that follows.

My immediate reaction to the demarcation based on 1-3 is that the new intended scope, although interesting in itself, excludes the overwhelming majority of scientific fields where restriction 3 seems unduly limiting. In my own field of economics the substantive information comes primarily in the form of substantively specified mechanisms (structural models), accompanied with theory-restricted and substantively meaningful parameters.

In addition, I consider the assertion “the model is always wrong” an unhelpful truism when ‘wrong’ is used in the sense that “the model is not an exact picture of the ‘reality’ it aims to capture”. Worse, if ‘wrong’ refers to ‘the data in question could not have been generated by the assumed model’, then any inference based on such a model will be dubious at best! Continue reading

Categories: Philosophy of Statistics, Statistics, U-Phil | Tags: , , , , | 7 Comments

U-PHIL: Deconstructing Larry Wasserman

Deconstructing [i] Larry Wasserman

The temptation is strong, but I shall refrain from using the whole post to deconstruct Al Franken’s 2003 quip about media bias (from Lies and Lying Liars Who Tell Them: A Fair and Balanced Look at the Right), with which Larry Wasserman begins his paper “Low Assumptions, High Dimensions” (2011) in his contribution to Rationality, Markets and Morals (RMM) Special Topic: Statistical Science and Philosophy of Science:

Wasserman: There is a joke about media bias from the comedian Al Franken:
‘To make the argument that the media has a left- or right-wing, or a liberal or a conservative bias, is like asking if the problem with Al-Qaeda is: do they use too much oil in their hummus?’

According to Wasserman, “a similar comment could be applied to the usual debates in the foundations of statistical inference.”

Although it’s not altogether clear what Wasserman means by his analogy with comedian (now senator) Franken, it’s clear enough what Franken meant if we follow up the quip with the next sentence in his text (which Wasserman omits): “The problem with al Qaeda is that they’re trying to kill us!” (p. 1). The rest of Franken’s opening chapter is not about al Qaeda but about bias in media. Conservatives, he says, decry what they claim is a liberal bias in mainstream media. Franken rejects their claim.

The mainstream media does not have a liberal bias. And for all their other biases . . . , the mainstream media . . . at least try to be fair. …There is, however, a right-wing media. . . . They are biased. And they have an agenda…The members of the right-wing media are not interested in conveying the truth… . They are an indispensable component of the right-wing machine that has taken over our country… .   We have to be vigilant.  And we have to be more than vigilant.  We have to fight back… . Let’s call them what they are: liars. Lying, lying, liars. (Franken, pp. 3-4)

When I read this in 2004 (when Bush was in office), I couldn’t have agreed more. How things change*. Now, of course, any argument that swerves from the politically correct is by definition unsound, irrelevant, and/ or biased. [ii]

But what does this have to do with Bayesian-frequentist foundations? What is Wasserman, deep down, really trying to tell us by way of this analogy (if only subliminally)? Such are my ponderings—and thus this deconstruction.  (I will invite your “U-Phils” at the end.) I will allude to passages from my contribution to  RMM (2011)  http://www.rmm-journal.de/htdocs/st01.html  (in red).

A.What Is the Foundational Issue?

Wasserman: To me, the most pressing foundational question is: how do we reconcile the two most powerful needs in modern statistics: the need to make methods assumption free and the need to make methods work in high dimensions… . The Bayes-Frequentist debate is not irrelevant but it is not as central as it once was. (p. 201)

One may wonder why he calls this a foundational issue, as opposed to, say, a technical one. I will assume he means what he says and attempt to extract his meaning by looking through a foundational lens.

Let us examine the urgency of reconciling the need to make methods assumption-free and that of making them work in complex high dimensions. The problem of assumptions of course arises when they are made about unknowns that can introduce threats of error and/or misuse of methods. Continue reading

Categories: Philosophy of Statistics, Statistics, U-Phil | Tags: , , , | 21 Comments

Deconstructing Larry Wasserman–it starts like this…

In my July 8, 2012 post “Metablog: Up and Coming,” I wrote: “I will attempt a (daring) deconstruction of Professor Wasserman’s paper[i] and at that time will invite your “U-Phils” for posting around a week after (<1000 words).” These could reflect on Wasserman’s paper and/or my deconstruction of it. See an earlier post for the way we are using “deconstructing” here. For some guides, see “so you want to do a philosophical analysis“.

So my Wasserman deconstruction notes have been sitting in the “draft” version of this blog for several days as we focused on other things.  Here’s how it starts…

             Deconstructing Larry Wasserman–it starts like this…

1.Al Franken’s Joke

The temptation is strong, but I shall refrain from using the whole post to deconstruct Al Franken’s 2003 quip about media bias (from Lies and Lying Liars Who Tell Them: A Fair and Balanced Look at the Right), with which Larry Wasserman begins his paper “Low Assumptions, High Dimensions” (2011):

To make the argument that the media has a left- or right-wing, or a liberal or a conservative bias, is like asking if the problem with Al-Qaeda is: do they use too much oil in their hummus?

According to Wasserman, “a similar comment could be applied to the usual debates in the foundations of statistical inference.”

Although it’s not altogether clear what Wasserman means by his analogy with comedian (now senator) Franken, it’s clear enough what Franken means if we follow up the quip with the next sentence in his text (which Wasserman omits): “The problem with al Qaeda is that they’re trying to kill us!” (p. 1) The rest of Franken’s opening chapter is not about al Qaeda but about bias in media.

But what does this have to do with the usual debates in the foundations of statistical inference? What is Wasserman, deep down, perhaps unconsciously, really, really, possibly implicitly, trying to tell us by way of this analogy? Such are the ponderings in my deconstruction of him…

Yet the footnote to my July 8 blog also said that my post assumed ” I don’t chicken out”.  So I will put it aside until I get a chorus of encouragement to post it…

Categories: Philosophy of Statistics, Statistics, U-Phil | Tags: , , | 5 Comments

Metablog: Up and Coming

Dear Reader: Over the next week, in addition to a regularly scheduled post by Professor Stephen Senn, we will be taking up two papers[i] from the contributions to the special topic: “Statistical Science and Philosophy of Science: Where Do (Should) They Meet in 2011 and Beyond?” in Rationality, Markets and Morals: Studies at the Intersection of Philosophy and Economics.

I will attempt a (daring) deconstruction of Professor Wasserman’s paper[ii] and at that time will invite your “U-Phils” for posting around a week after (<1000 words).  I will be posting comments by Clark Glymour on Sir David Hendry’s paper later in the week. So you may want to study those papers in advance.

The first “deconstruction” (“Irony and Bad Faith, Deconstructing Bayesians 1”) may be found here / https://errorstatistics.com/2012/04/17/3466/; for a selection of both U-Phils and Deconstructions, see https://errorstatistics.com/2012/04/17/3466/

D. Mayo

P.S. Those who had laughed at me for using this old trusty typewriter were asking to borrow it last week when we lost power for 6 days and their computers were down.


[i] *L. Wasserman, “Low Assumptions, High Dimensions”. RMM Vol. 2, 2011, 201–209;

D. Hendry, “Empirical Economic Model Discovery and Theory Evaluation”. RMM Vol. 2, 2011, 115–145.

[ii] Assuming I don’t chicken out.

Categories: Metablog, Philosophy of Statistics, U-Phil | Tags: , | Leave a comment

Mayo, Senn, and Wasserman on Gelman’s RMM** Contribution

Picking up the pieces...

Continuing with our discussion of contributions to the special topic,  Statistical Science and Philosophy of Science in Rationality, Markets and Morals (RMM),* I am pleased to post some comments on Andrew **Gelman’s paper “Induction and Deduction in Bayesian Data Analysis”.  (More comments to follow—as always, feel free to comment.)

Note: March 9, 2012: Gelman has commented to some of our comments on his blog today: http://andrewgelman.com/2012/03/coming-to-agreement-on-philosophy-of-statistics/

D. Mayo

For now, I will limit my own comments to two: First, a fairly uncontroversial point, while Gelman writes that “Popper has argued (convincingly, in my opinion) that scientific inference is not inductive but deductive,” a main point of my series (Part 123) of “No-Pain” philosophy was that “deductive” falsification involves inductively inferring a “falsifying hypothesis”.

More importantly, and more challengingly, Gelman claims the view he recommends “corresponds closely to the error-statistics idea of Mayo (1996)”.  Now the idea that non-Bayesian ideas might afford a foundation for strands of Bayesianism is not as implausible as it may seem. On the face of it, any inference to a claim, whether to the adequacy of a model (for a given purpose), or even to a posterior probability, can be said to be warranted just to the extent that the claim has withstood a severe test (i.e, a test that would, at least with reasonable probability, have discerned a flaw with the claim, were it false).  The question is: How well do Gelman’s methods for inferring statistical models satisfy severity criteria?  (I’m not sufficiently familiar with his intended applications to say.)

Continue reading

Categories: Philosophy of Statistics, Statistics, U-Phil | Tags: , , , | 1 Comment

RMM-5: Special Volume on Stat Scie Meets Phil Sci

The article “Low Assumptions, High Dimensions” by Larry Wasserman has now been published in our special volume of the on-line journal, Rationality, Markets, and Morals (Special Topic: Statistical Science and Philosophy of Science: Where Do/Should They Meet?”)

www.frankfurt-school-verlag.de/rmm/downloads/Article_Wasserman.pdf

Abstract:
These days, statisticians often deal with complex, high dimensional datasets. Researchers in statistics and machine learning have responded by creating many new methods for analyzing high dimensional data. However, many of these new methods depend on strong assumptions. The challenge of bringing low assumption inference to high dimensional settings requires new ways to think about the foundations of statistics. Traditional foundational concerns, such as the Bayesian versus frequentist debate, have become less important.

Categories: Philosophy of Statistics, Statistics | Tags: | Leave a comment

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