Posts Tagged With: Birnbaum

Midnight With Birnbaum-reblog

Posted on December 31, 2012 by Mayo

Reblogging Dec. 31, 2011:

You know how in that recent movie, “Midnight in Paris,” the main character (I forget who plays it, I saw it on a plane) is a writer finishing a novel, and he steps into a cab that mysteriously picks him up at midnight and transports him back in time where he gets to run his work by such famous authors as Hemingway and Virginia Wolf?  He is impressed when his work earns their approval and he comes back each night in the same mysterious cab…Well, imagine an error statistical philosopher is picked up in a mysterious taxi at midnight (New Year’s Eve 2011 2012) and is taken back fifty years and, lo and behold, finds herself in the company of Allan Birnbaum.[i]

ERROR STATISTICIAN: It’s wonderful to meet you Professor Birnbaum; I’ve always been extremely impressed with the important impact your work has had on philosophical foundations of statistics.  I happen to be writing on your famous argument about the likelihood principle (LP).  (whispers: I can’t believe this!)

BIRNBAUM: Ultimately you know I rejected the LP as failing to control the error probabilities needed for my Confidence concept.

ERROR STATISTICIAN: Yes, but I actually don’t think your argument shows that the LP follows from such frequentist concepts as sufficiency S and the weak conditionality principle WLP.[ii]  Sorry,…I know it’s famous… Read more »

Categories: Birnbaum Brakes, strong likelihood principle | Tags: , , , | Leave a comment

P-values as Frequentist Measures

Posted on July 27, 2012 by Mayo

Working on the last two chapters of my book on philosophy of statistical inference, I’m revisiting such topics as weak conditioning, Birnbaum, likelihood principle, etc., and was reading from the Proceedings of the Berkeley Conference in Honor of Jerzy Neyman and Jack Kiefer (1985)[i]. In a paper I had not seen (or had forgotten), Jim Berger “The Frequentist Viewpoint and Conditioning,” writes that the quoting of a P-value “may be felt to be a frequentist procedure by some, since it involves an averaging over the sample space. The reporting of P-values can be given no long-run frequency interpretation [in any of the set-ups generally considered].  A P-value actually lies closer to conditional (Bayesian) measures than to frequentist measures.” (Berger 1985, 23). These views are echoed in Berger’s more recent “Could Fisher,Jeffreys and Neyman Have Agreed on Testing?”(2003). This is at odds with what Fisher, N-P, Cox, Lehmann, etc. have held, and if true, would also seem to entail that a severity assessment had no frequentist interpretation!  The flaw lies in that all-too-common behavioristic, predesignated conception…

Among related posts:

http://errorstatistics.com/2012/04/28/3671/
http://errorstatistics.com/2012/05/10/excerpts-from-s-senns-letter-on-replication-p-values-and-evidence/

 

[i] Also because of Peter Gruenwald’s recent mention of Kiefer’s work, read long ago.

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

Don’t Birnbaumize that Experiment my Friend*

Posted on January 8, 2012 by Mayo

(A)  “It is not uncommon to see statistics texts argue that in frequentist theory one is faced with the following dilemma: either to deny the appropriateness of conditioning on the precision of the tool chosen by the toss of a coin[i], or else to embrace the strong likelihood principle which entails that frequentist sampling distributions are irrelevant to inference once the data are obtained.  This is a false dilemma … The ‘dilemma’ argument is therefore an illusion”. (Cox and Mayo 2010, p. 298)
Read more »

Categories: Statistics | Tags: , , , | 16 Comments

Midnight With Birnbaum

Posted on December 31, 2011 by Mayo

You know how in that recent movie, “Midnight in Paris,” the main character (I forget who plays it, I saw it on a plane) is a writer finishing a novel, and he steps into a cab that mysteriously picks him up at midnight and transports him back in time where he gets to run his work by such famous authors as Hemingway and Virginia Wolf?  He is impressed when his work earns their approval and he comes back each night in the same mysterious cab…Well, imagine an error statistical philosopher is picked up in a mysterious taxi at midnight (new Year’s Eve 2011) and is taken back fifty years and, lo and behold, finds herself in the company of Allan Birnbaum.[i] Read more »

Categories: Birnbaum Brakes | Tags: , , , | Leave a comment

The 3 stages of the acceptance of novel truths

Posted on December 22, 2011 by Mayo

There is an often-heard slogan about the stages of the acceptance of novel truths:

First people deny a thing.

Then they belittle it.

Then they say they knew it all along.

I don’t know who was first to state it in one form or another.  Here’s Schopenhauer with a slightly different variant:

“All truth passes through three stages: First, it is ridiculed; Second, it is violently opposed; and Third, it is accepted as self-evident.” – Arthur Schopenhauer

After recently presenting my paper criticizing the Birnbaum result on the likelihood principle (LP)[1] the reception of my analysis seems somewhere around stage two, in some cases, moving into stage three (see my blogposts of December 6 and 7, 2011). Read more »

Categories: Statistics | Tags: , , | 2 Comments

ReBlogging the Likelihood Principle #2: Solitary Fishing:SLP Violations

Posted on October 20, 2011 by Mayo

Reblogging from a year ago. The Appendix of the “Cox/Mayo Conversation” (linked below [i]) is an attempt to quickly sketch Birnbaum’s argument for the strong likelihood principle (SLP), and its sins.  Couple of notes: Firstly, I am a philosopher (of science and statistics) not a statistician.  That means, my treatment will show all of the typical (and perhaps annoying) signs of being a trained philosopher-logician.  I’ve no doubt statisticians would want to use different language, which is welcome.  Second, this is just a blog (although perhaps my published version is still too informal for some). Read more »

Categories: Likelihood Principle | Tags: , , | 9 Comments

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