Talk:David Cox (statistician)

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Category of Bayesian statistician?[edit]

I added Cox as to the category "Bayesian statisticians".

Sir David R. Cox calls himself a (ardent?) "Bayesian" in his oral criticism of Lindsey's "Statistical Heresies" (JRSS D, The Statistician, c. 2000). (He also calls himself a "Neyman-Pearsonian", in his fine display of personal integrity and charity, which meets the very high traditions of academic and British fair play, I shall add as a personal observation.)

In his review of "Statistical Inference Theory" in the Biometrica 2000 (100th anniversary issue), Cox's student Anthony C. Davison notes that accountants identify Cox as a Bayesian statistician!

Being a member of the Bayesian category need not exclude Cox from being influenced by Neyman-Pearson or the later writings of Fisher, of course. Feel free to add Cox to other categories! Thanks, Kiefer.Wolfowitz (talk) 00:49, 29 October 2010 (UTC)

I'm not sure Sir David's philosophy fits easily into either camp. Maybe we need a new category "Coxian statisticians", or perhaps the somewhat broader "Neo-Fisherian synthesizers"... If I ran a cluster analysis I think i'd be worried if it didn't place him in the same cluster as John Nelder (there are approximately two kinds of statisticians: those who dichotomise everything, those who don't, and those who let the data decide). You may have just spurred me into starting rereading my copy of Principles of Statistical Inference over the weekend... Qwfp (talk) 09:19, 29 October 2010 (UTC)
Dear Qwfp, I was adding Cox when I was adding other Bayesian statisticians (BS) to the new category of BS. I wanted to draw other editors' notice to this addition, because Cox is generally regarded as neoFisherian, and unenthusiastic about some aspects of the Bayesian revival (or the "pop"-Bayesianism modeling that downgrades Bayesian/personal probability). I don't have objections to Cox being removed from the category (despite his affirmation and Davison's good-humored notice).
I would agree that Cox is more of a neo-Fisherian (model-based) --- while Oskar Kempthorne is more of a "paleoFisherian" (or rather a Peircian, as he acknowledged later in life; c.f. Hacking). Cox does discuss the randomization analysis of paleoFisherians in the last chapter of his principles, I believe. (Some discussion of randomization appears also in his book on asymptotic statistical theory with Barndorff Nielsen.)
His "principles" book does aim at breaking down barriers (and was written with concern about some of his followers' enthusiasms for pigeon-holing "schools" --- e.g. Lindsey's "heresies" --- and mindful of the harmful effects of partisan divisions e.g. between the followers of Newton & Leibniz)) I note
BTW, I only have the draft version of Cox's Principles (which was used in Wermuth & Sundberg's seminars in Sweden, as noted in the preface). I was unable to find Melcombe's reference (or referand) about a discussion of "confidence distribution" (sic.), which Melcombe referenced in the article on fiducial distribution (sic., imho).
Thanks again, Kiefer.Wolfowitz (talk) 16:32, 29 October 2010 (UTC)
If we wanted a directly applicable category for David Cox, it would be "pragmatic statistician", but we might have trouble finding anyone else to join that category. If we wanted "Bayesian statistician" to be someone who expounds Bayesianism to the exclusion of everything else, then David Cox wouldn't be included, but if we wanted it to mean someone who was prepared to use it when it provides a useful answer, then he would. This PDF might be of interest. Anf of course he did have (1978) "Foundations of Statistical Inference: the case for eclecticism", J. Australian Statist. Soc, 20, 43.
As for "confidence distribution", there is no difficulty with this, since it is even listed in the index of Cox's Principles of Statistical Inference (page 66, start of Section 5.3). A full version of the book is well worth the price.
And as for the accountancy application, I believe the exposition of it was set out in such a way that a frequentist interpretation was readily available, and possibly slightly dominant. But that may just have been my reading of it ... it was long ago.
Melcombe (talk) 10:16, 1 November 2010 (UTC)
I think the majority of the practising statisticians i know would describe themselves as "pragmatic" or "eclectic" if asked, though i guess it might be harder to find notable ones who have specifically exposed it as a philosophy in reliable sources (Chris Chatfield would be one exception [1] , though it seems we don't have an article on him... currently). Qwfp (talk) 13:13, 1 November 2010 (UTC)
I would suggest that "eclectic" or "pluralist" (or "ecumenical" or "post-Wald") would be good names.
I would agree that a corrupt use of "pragmatic" (following William James) is unfortunately commonly used improperly; Peirce invented "pragmaticism" to distinguish his viable pragmatism from James's confusing jumble. However, it would be improper to use "pragmatic" to describe Cox, because (imho) Cox's neo-Fisherian writings seem lacksadaisical about the precepts of Charles Sanders Peirce. Peirce insisted upon the Baconian precept that hypothesis-tests be carried out following a protocol, to prevent the most common & important "fallacy in inductive reasoning", stating the hypothesis after finding a pattern in a data set (and failing to test that data-generated hypothesis). (Bacon's arguments were based on social psychology while Peirce's were based on probability/statistics.) From my reading of Cox, following his collaboration with Barndorff-Nielsen and in his recent Principles, I cannot remember any discussion of the Baconian distinction --- that it matters whether the "statistical model" and "inference" follow a prescribed protocol or not (e.g. when a client gave us a data set which we tried to explore, perhaps with heuristic use of confidence intervals and hypothesis testing).
Additionally, Cox has much less emphasis on using design-based analysis (rather than assuming models for populations, following the post-Neyman Fisher) than would be consistent with orthodox pragmatism, following Peirce (who seems to have pioneered randomization particularly in randomized experiments).
(On the other hand, at times, Peirce was willing to use "likelihoods" as in the quotes in the likelihood function article.)
I shall put Cox's Principles on my Jultide list! Thanks! Sincerely, Kiefer.Wolfowitz (talk) 19:19, 1 November 2010 (UTC)

Following the above discussion, I removed Cox from the Bayesian category. I suggest that categories "Bayesian" or "neo-Fisherian" should be populated only when there are external sources calling the statistician Bayesian or neo-Fisherian, along with the subject calling himself Bayesian. Because almost every statistician uses Bayesian statistics sometimes or likelihood methods as well as sampling-theory methods, it doesn't seem useful to start an eclectic category. Thanks for the discussion. Kiefer.Wolfowitz (talk) 12:03, 2 November 2010 (UTC)

Ok. The Bayesian statistician category was started because someone thought it worthwhile placing the article about someone directly in the Bayesian statistics category, which is not appropriate for a topic category. If someone finds a need to add a person-article to some other topic category, some new category can be invented. But quite a few people-articles had "Bayesian statistician" in them. Melcombe (talk) 12:39, 2 November 2010 (UTC)