In the past week, I’ve kvetched over at 3 of the blogs on my blog bagel (instead of using the time to work). Here are the main ones, you can follow up on their blogs if you wish:
I. I made a brief comment on a blatant error in Mark Chang’s treatment of my Birnbaum disproof on Xi’an’s Og. Chang is responding to Christian Robert’s critical review of his book, Paradoxes in Scientific Inference (2013)
I have only gotten to look at Mark Chang’s book a few days ago. I have many concerns regarding his treatment of points from Mayo and Spanos (2010), in particular the chapters by Cox and Mayo (2010) and Mayo (2010). Notably, having set out, nearly verbatim (but without quotes), my first variation of Birnbaum’s argument (Mayo 2010, 309), Chang takes, as evidence that “Mayo’s disproof is faulty”, assertions that I make only concerning the second variation of the Birnbaum argument (310-11). Chang has written (Chang, 138) the first version in detail, but obviously doesn’t understand it. The problem with the first version is that the two premises cannot both be true at the same time (the crucial term shifts its meaning in the two premises). The second formulation, by contrast, allows both premises to be true. I label the two premises of the second variation as (1) and (2)’. The problem in the second formulation is: “The antecedent of premise (1) is the denial of the antecedent of premise (2)’.”(Mayo 2010, 311). (Note the prime on (2)’. )These are both conditional claims, hence they have antecedents. Chang gives this quote, but has missed its reference. I might mention that I don’t see the relevance of Chang’s point about sufficiency to either variations of Birnbaum’s proof (bottom para, Chang 138).
A less informal and clearer treatment of my Birnbaum argument may be found in a recent paper: On the Birnbaum Argument for the Strong Likelihood Principle.
I am inviting comments for posting (some time in January) as explained at this link. I invite Chang to contribute, perhaps with a newly clarified attempt to reject my disproof of Birnbaum.
Mayo Posted December 24, 2012 at 9:22 pm
N.D.: I’m all for some well-needed name changes, but I would like to voice (a) some gripes/drawbacks with a few of these, and (b) some glaring omissions. I think in general it’s best not to hang a person’s name on these things, particularly if that name wasn’t already there (so I agree with another commentator). There are enough irrelevant attacks “against the man” slipping into the assessment of statistical tools. The p-value, or the “significance probability” or “significance level” will surely not benefit by being called the “Fisher statistic”, what with Fisher’s achievements being derogated, references to him as “The Wasp”, and as a man who wore rumpled clothes and smoked too much…It already appears as the main character in U-tube clips with titles like “what the p-value”, do we really need “what the #@$% Fisher statistic”?
Bayesian Inference—(N.D. suggests Laplacian Inference): why not just go back to inverse probability? I know many people who are irked that it was ever changed.
Bayesian Nets—(N.D. suggests Pearl graph): I do think a name change is very much needed. Pearl indicated to me long ago that he was intending just to refer to probability. So what’s wrong with a probabilistic net, or a DAG (as many already use), for a directed acyclic graph endowed with probability distribution?
Confidence Interval —(N.D. suggests Coverage set). I think the interval aspect, or even just the use of “bounds” or “limits” are essential. There are counterintuitive “sets” that can have reported coverage. Also, the fact that there is a “confidence concept” (Birnbaum, Fraser) and confidence distributions, might suggest retaining it. A sensible confidence interval should give corroboration bounds, in the sense of indicating well-corroborated values of a parameter. So it seems best to stick with CI bounds or corroboration bounds or the like.
Causal Inference. —(N.D. suggests formal inference): This would get confused with formal deductive inference which obviously needn’t be causal; if anything, causal inference is (strictly speaking) informal inference (in the sense often used in philosophy, i.e., inductive/qualitative).
The Central Limit Theorem and the Law of Large Numbers–N.D. thinks these are boring, but I think the LLN is extremely cool (so I agree with another commentator), and it already already has a BLLN version. The CLT is informative, where de Moivre is not.
Stigler’s law of eponymy. New Name: Stigler’s law of eponymy. I think there is something self-referentially wrong here, since Stigler did name it. That is, if Stigler is right, it should be named after non-Stigler.[i]
[i] additional note: Yes I know Stigler claims it was noted by Merton, but Merton didn’t coin Stigler’s law.
Neural nets. N.D. says, “Let’s call them what they are. (Not so) New name: Nonlinear regression”.
Now for (b): frequentist statistics, sampling theory, and “classical statistics”—must these remain as an equivocal mess? None of these work well. “Sampling theory” does make sense since the key is the use of the sampling distribution for inference, but it doesn’t capture it. Since sampling distributions are used for error probabilities (of methods), one might try error probability statistics, or error statistics for short. That’s the best I could come up with. (I know some people find “error probabilities” overly behavioristic, but I do not.)
You can find N.D.’s post and many other comments here.
[ii] How do you get comments to be numbered on WordPress?
Other trouble I’ve gotten into this week (just on blogs I mean):
III. I made some comments on a statistics chapter in Nate Silver’s book, discussed over at Gelman’s blog:
Here’s my last, in response to one of the comments.
Gelman and I have posted frank comments on each other’s blogs for a while now, and I had just read that chapter when I noticed Gelman was posting some reviews on his blog. I was not reviewing Silver’s book, just commenting on the chapter on frequentist statistics on a blog. Had I been reviewing it I would have read and discussed the other chapters. (I haven’t even discussed Silver on any of my blogs, though maybe now I will, having taken the time to write so much here.)[i]
I think one of the main reasons I was so disappointed with that Silver chapter is that I was expecting/hoping to like the book. Two months ago, an artist who was helping to paint a faux finish mural in my condo asked what I did. Philosophy of science is typically considered pretty esoteric, but when she heard I was interested in various statistical methods/knowledge, she asked, to my surprise, if I knew Nate Silver, and we discussed his 538 blog, and the day’s comments and dialogue. I thought it was great that he seemed to be bringing statistics into the popular culture, even if it was just polling and baseball.
So I was dismayed at his negative remarks on frequentist statistics and his kooky, gratuitious ridicule of R.A.Fisher. I am not alone in thinking this (see Kaiser below). I guess I’m just sorry Silver comes off looking so clownish here, because I had thought he’d be interesting and insightful. I’ll look at the other chapters at some point, I’ve loaned out my copy…
You are wrong to suppose that I am “angry because Nate wants to euthanize” methods that are widespread across the landscape of physical and social sciences, in experimental design, drug testing, model selection, law, etc., etc.
These methods won’t die so long as science and inquiry remain.
You see, science could never operate with a uniform algorithm (his “Bayes train”) where nothing brand new enters, and nothing old gets falsified and ousted. We’d never want to keep within such a bounded universe of possibilities: inquiry is open-ended. Getting beyond the Bayesian “catchall” hypothesis is an essential part of pushing the boundaries of current understanding and theorizing in science and in daily life.* Frequentist statistics, like science/learning in general, provides a cluster of tools, a storehouse by which the creative inquirer can invent, and construct, entirely new ways to ask questions, often circuitously and indirectly, while at the same time allowing (often ingenious) interconnected ways to control and distinguish patterns of error. As someone once said, statistics is “the study of the embryology of knowledge, of the processes by means of which truth is extracted from its native ore in which it is fused with much error.”**
They are methods for the critical scrutiny of the data and models entertained at a given time (not a hope for the indefinite long-run). The asymptotic convergence from a continual updating from more and more data (on the same query) that Silver happily touts, even in the cases where we imagine the special assumptions it requires are satisfied, is irrelevant to the day to day scrutiny/criticism of actual scientific results.
I agree that foundational discussions are good, but much more useful when coupled with published material or at least blogposts.
*An analogy made yesterday by Isaac Chatfield: frequentist statistical methods are a bit like surgical tools; they are designed to be used for a variety of robust probes which are open to being adaptively redesigned to solve new problems while in the midst of an operation/investigation.
**Fisher 1935, DOE, 39.
You can dig out as much of the back and forth as you care to, or can stand, here.
[i] As you can see, I did.