Abbreviated Table of Contents:
Here are some items for your Saturday-Sunday reading.
Link to complete discussion:
Mayo, Deborah G. On the Birnbaum Argument for the Strong Likelihood Principle (with discussion & rejoinder). Statistical Science 29 (2014), no. 2, 227-266.
Links to individual papers:
Mayo, Deborah G. On the Birnbaum Argument for the Strong Likelihood Principle. Statistical Science 29 (2014), no. 2, 227-239.
Dawid, A. P. Discussion of “On the Birnbaum Argument for the Strong Likelihood Principle”. Statistical Science 29 (2014), no. 2, 240-241.
Evans, Michael. Discussion of “On the Birnbaum Argument for the Strong Likelihood Principle”. Statistical Science 29 (2014), no. 2, 242-246.
Martin, Ryan; Liu, Chuanhai. Discussion: Foundations of Statistical Inference, Revisited. Statistical Science 29 (2014), no. 2, 247-251.
Fraser, D. A. S. Discussion: On Arguments Concerning Statistical Principles. Statistical Science 29 (2014), no. 2, 252-253.
Hannig, Jan. Discussion of “On the Birnbaum Argument for the Strong Likelihood Principle”. Statistical Science 29 (2014), no. 2, 254-258.
Bjørnstad, Jan F. Discussion of “On the Birnbaum Argument for the Strong Likelihood Principle”. Statistical Science 29 (2014), no. 2, 259-260.
Mayo, Deborah G. Rejoinder: “On the Birnbaum Argument for the Strong Likelihood Principle”. Statistical Science 29 (2014), no. 2, 261-266.
Abstract: An essential component of inference based on familiar frequentist notions, such as p-values, significance and confidence levels, is the relevant sampling distribution. This feature results in violations of a principle known as the strong likelihood principle (SLP), the focus of this paper. In particular, if outcomes x∗ and y∗ from experiments E1 and E2 (both with unknown parameter θ), have different probability models f1( . ), f2( . ), then even though f1(x∗; θ) = cf2(y∗; θ) for all θ, outcomes x∗ and y∗may have different implications for an inference about θ. Although such violations stem from considering outcomes other than the one observed, we argue, this does not require us to consider experiments other than the one performed to produce the data. David Cox [Ann. Math. Statist. 29 (1958) 357–372] proposes the Weak Conditionality Principle (WCP) to justify restricting the space of relevant repetitions. The WCP says that once it is known which Ei produced the measurement, the assessment should be in terms of the properties of Ei. The surprising upshot of Allan Birnbaum’s [J.Amer.Statist.Assoc.57(1962) 269–306] argument is that the SLP appears to follow from applying the WCP in the case of mixtures, and so uncontroversial a principle as sufficiency (SP). But this would preclude the use of sampling distributions. The goal of this article is to provide a new clarification and critique of Birnbaum’s argument. Although his argument purports that [(WCP and SP), entails SLP], we show how data may violate the SLP while holding both the WCP and SP. Such cases also refute [WCP entails SLP].
Key words: Birnbaumization, likelihood principle (weak and strong), sampling theory, sufficiency, weak conditionality
Regular readers of this blog know that the topic of the “Strong Likelihood Principle (SLP)” has come up quite frequently. Numerous informal discussions of earlier attempts to clarify where Birnbaum’s argument for the SLP goes wrong may be found on this blog. [SEE PARTIAL LIST BELOW.[i]] These mostly stem from my initial paper Mayo (2010) [ii]. I’m grateful for the feedback.
In the months since this paper has been accepted for publication, I’ve been asked, from time to time, to reflect informally on the overall journey: (1) Why was/is the Birnbaum argument so convincing for so long? (Are there points being overlooked, even now?) (2) What would Birnbaum have thought? (3) What is the likely upshot for the future of statistical foundations (if any)?
I’ll try to share some responses over the next week. (Naturally, additional questions are welcome.)
[i] A quick take on the argument may be found in the appendix to: “A Statistical Scientist Meets a Philosopher of Science: A conversation between David Cox and Deborah Mayo (as recorded, June 2011)”
- Midnight with Birnbaum (Happy New Year).
- New Version: On the Birnbaum argument for the SLP: Slides for my JSM talk.
- Don’t Birnbaumize that experiment my friend*–updated reblog.
- Allan Birnbaum, Philosophical Error Statistician: 27 May 1923 – 1 July 1976 .
- LSE seminar
- A. Birnbaum: Statistical Methods in Scientific Inference
- ReBlogging the Likelihood Principle #2: Solitary Fishing: SLP Violations
- Putting the brakes on the breakthrough: An informal look at the argument for the Likelihood Principle.
- Forthcoming paper on the strong likelihood principle.
UPhils and responses
- U-PHIL: Gandenberger & Hennig : Blogging Birnbaum’s Proof
- U-Phil: Mayo’s response to Hennig and Gandenberger
- Mark Chang (now) gets it right about circularity
- U-Phil: Ton o’ Bricks
- Blogging (flogging?) the SLP: Response to Reply- Xi’an Robert
- U-Phil: J. A. Miller: Blogging the SLP
- Mayo, D. G. (2010). “An Error in the Argument from Conditionality and Sufficiency to the Likelihood Principle” in Error and Inference: Recent Exchanges on Experimental Reasoning, Reliability and the Objectivity and Rationality of Science (D Mayo and A. Spanos eds.), Cambridge: Cambridge University Press: 305-14.
I love Martin and Liu’s first paragraph: “Birnbaum’s theorem (Birnbaum,1962) is arguably the most controversial result in statistics. The theorem’s conclusion is that a framework for statistical inference that satisfies two natural conditions, namely,the sufficiency principle (SP) and the conditionality principle (CP), must also satisfy an exclusive condition, the likelihood principle (LP). The controversy lies in the fact that LP excludes all those standard methods taught in Stat 101 courses. Professor Mayo successfully refutes Birnbaum’s claim, showing that violations of LP need not imply violations of SP or CP. The key to Mayo’s argument is a correct formulation of CP; see also Evans (2013). Her demonstration resolves the controversy around Birnbaum and LP, helping to put the statisticians’ house in order.”
Now all those standard methods taught in STAT 101 courses can be taught without feeling they’re actually “excluded” by Birnbaum’s result. Return from exile!
The story, of course, is more complicated than it at first appears.
Wonderful! I am very happy for you!
Very excited to see this finally come out, especially after seeing your seminar talk.