Posts Tagged With: statistical foundations

Oxford Gaol: Statistical Bogeymen

Posted on October 31, 2014 by Mayo

Memory Lane: 3 years ago. Oxford Jail (also called Oxford Castle) is an entirely fitting place to be on (and around) Halloween! Moreover, rooting around this rather lavish set of jail cells (what used to be a single cell is now a dressing room) is every bit as conducive to philosophical reflection as is exile on Elba! (It is now a boutique hotel, though many of the rooms are still too jail-like for me.)  My goal (while in this gaol—as the English sometimes spell it) is to try and free us from the bogeymen and bogeywomen often associated with “classical” statistics. As a start, the very term “classical statistics” should, I think, be shelved, not that names should matter.

In appraising statistical accounts at the foundational level, we need to realize the extent to which accounts are viewed through the eyeholes of a mask or philosophical theory.  Moreover, the mask some wear while pursuing this task might well be at odds with their ordinary way of looking at evidence, inference, and learning. In any event, to avoid non-question-begging criticisms, the standpoint from which the appraisal is launched must itself be independently defended.   But for (most) Bayesian critics of error statistics the assumption that uncertain inference demands a posterior probability for claims inferred is thought to be so obvious as not to require support. Critics are implicitly making assumptions that are at odds with the frequentist statistical philosophy. In particular, they assume a certain philosophy about statistical inference (probabilism), often coupled with the allegation that error statistical methods can only achieve radical behavioristic goals, wherein all that matters are long-run error rates (of some sort)Unknown-2

Criticisms then follow readily: the form of one or both:

  • Error probabilities do not supply posterior probabilities in hypotheses, interpreted as if they do (and some say we just can’t help it), they lead to inconsistencies
  • Methods with good long-run error rates can give rise to counterintuitive inferences in particular cases.
  • I have proposed an alternative philosophy that replaces these tenets with different ones:
  • the role of probability in inference is to quantify how reliably or severely claims (or discrepancies from claims) have been tested
  • the severity goal directs us to the relevant error probabilities, avoiding the oft-repeated statistical fallacies due to tests that are overly sensitive, as well as those insufficiently sensitive to particular errors.
  • Control of long run error probabilities, while necessary is not sufficient for good tests or warranted inferences.

Continue reading →

Categories: 3-year memory lane, Bayesian/frequentist, Philosophy of Statistics, Statistics | Tags: ,

Deconstructing Larry Wasserman

Posted on December 27, 2013 by Mayo

 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) (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: , , ,

Oxford Gaol: Statistical Bogeymen

Posted on November 2, 2013 by Mayo

Memory Lane: 2 years ago. Oxford Jail (also called Oxford Castle) is an entirely fitting place to be on (and around) Halloween! Moreover, rooting around this rather lavish set of jail cells (what used to be a single cell is now a dressing room) is every bit as conducive to philosophical reflection as is exile on Elba! (I’m serious, it is now a boutique hotel.)  My goal (while in this gaol—as the English sometimes spell it) is to try and free us from the bogeymen and bogeywomen often associated with “classical” statistics. As a start, the very term “classical statistics” should I think be shelved, not that names should matter.

In appraising statistical accounts at the foundational level, we need to realize the extent to which accounts are viewed through the eyeholes of a mask or philosophical theory.  Moreover, the mask some wear while pursuing this task might well be at odds with their ordinary way of looking at evidence, inference, and learning. In any event, to avoid non-question-begging criticisms, the standpoint from which the appraisal is launched must itself be independently defended.   But for (most) Bayesian critics of error statistics the assumption that uncertain inference demands a posterior probability for claims inferred is thought to be so obvious as not to require support. Critics are implicitly making assumptions that are at odds with the frequentist statistical philosophy. In particular, they assume a certain philosophy about statistical inference (probabilism), often coupled with the allegation that error statistical methods can only achieve radical behavioristic goals, wherein all that matters are long-run error rates (of some sort)Unknown-2

Criticisms then follow readily: the form of one or both:

  • Error probabilities do not supply posterior probabilities in hypotheses, interpreted as if they do (and some say we just can’t help it), they lead to inconsistencies
  • Methods with good long-run error rates can give rise to counterintuitive inferences in particular cases.
  • I have proposed an alternative philosophy that replaces these tenets with different ones:
  • the role of probability in inference is to quantify how reliably or severely claims (or discrepancies from claims) have been tested
  • the severity goal directs us to the relevant error probabilities, avoiding the oft-repeated statistical fallacies due to tests that are overly sensitive, as well as those insufficiently sensitive to particular errors.
  • Control of long run error probabilities, while necessary is not sufficient for good tests or warranted inferences.

What is key on the statistics side of this alternative philosophy is that the probabilities refer to the distribution of a statistic d(x)—the so-called sampling distribution.  Hence such accounts are often called sampling theory accounts. Since the sampling distribution is the basis for error probabilities, another term might be error statistical. Continue reading →

Categories: Philosophy of Statistics | Tags: ,

Reblogging: Oxford Gaol: Statistical Bogeymen

Posted on October 29, 2012 by Mayo

Reblogging 1 year ago in Oxford: Oxford Jail is an entirely fitting place to be on Halloween!

Moreover, rooting around this rather lavish set of jail cells (what used to be a single cell is now a dressing room) is every bit as conducive to philosophical reflection as is exile on Elba!  My goal (while in this gaol—as the English sometimes spell it) is to try and free us from the bogeymen and bogeywomen often associated with “classical” statistics. As a start, the very term “classical statistics” should I think be shelved, not that names should matter.

In appraising statistical accounts at the foundational level, we need to realize the extent to which accounts are viewed through the eyeholes of a mask or philosophical theory.  Moreover, the mask some wear while pursuing this task might well be at odds with their ordinary way of looking at evidence, inference, and learning. In any event, to avoid non-question-begging criticisms, the standpoint from which the appraisal is launched must itself be independently defended.   But for Bayesian critics of error statistics the assumption that uncertain inference demands a posterior probability for claims inferred is thought to be so obvious as not to require support. Critics are implicitly making assumptions that are at odds with the frequentist statistical philosophy. In particular, they assume a certain philosophy about statistical inference (probabilism), often coupled with the allegation that error statistical methods can only achieve radical behavioristic goals, wherein all that matters are long-run error rates (of some sort) Continue reading →

Categories: Error Statistics, Philosophy of Statistics | Tags: ,

U-PHIL: Deconstructing Larry Wasserman

Posted on July 28, 2012 by Mayo

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) (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: , , ,

Oxford Gaol: Statistical Bogeymen

Posted on October 31, 2011 by Mayo

Oxford Jail is an entirely fitting place to be on Halloween!

Moreover, rooting around this rather lavish set of jail cells (what used to be a single cell is now a dressing room) is every bit as conducive to philosophical reflection as is exile on Elba!  My goal (while in this gaol—as the English sometimes spell it) is to try and free us from the bogeymen and bogeywomen often associated with “classical” statistics. As a start, the very term “classical statistics” should I think be shelved, not that names should matter.

In appraising statistical accounts at the foundational level, we need to realize the extent to which accounts are viewed through the eyeholes of a mask or philosophical theory.  Moreover, the mask some wear while pursuing this task might well be at odds with their ordinary way of looking at evidence, inference, and learning. In any event, to avoid non-question-begging criticisms, the standpoint from which the appraisal is launched must itself be independently defended.   But for Bayesian critics of error statistics the assumption that uncertain inference demands a posterior probability for claims inferred is thought to be so obvious as not to require support. Critics are implicitly making assumptions that are at odds with the frequentist statistical philosophy. In particular, they assume a certain philosophy about statistical inference (probabilism), often coupled with the allegation that error statistical methods can only achieve radical behavioristic goals, wherein all that matters are long-run error rates (of some sort)

Criticisms then follow readily: the form of one or both:

  • Error probabilities do not supply posterior probabilities in hypotheses, interpreted as if they do (and some say we just can’t help it), they lead to inconsistencies
  • Methods with good long-run error rates can give rise to counterintuitive inferences in particular cases.
  • I have proposed an alternative philosophy that replaces these tenets with different ones:
  • the role of probability in inference is to quantify how reliably or severely claims (or discrepancies from claims) have been tested
  • the severity goal directs us to the relevant error probabilities, avoiding the oft-repeated statistical fallacies due to tests that are overly sensitive, as well as those insufficiently sensitive to particular errors.
  • Control of long run error probabilities, while necessary is not sufficient for good tests or warranted inferences.

Continue reading →

Categories: Statistics | Tags: ,

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