The fourth meeting of our New Phil Stat Forum*:
The Statistics Wars and Their Casualties
January 7, 16:00 – 17:30 (London time) 11 am-12:30 pm (New York, ET)** **note time modification and date change
Putting the Brakes on the Breakthrough,
or “How I used simple logic to uncover a flaw in a controversial 60-year old ‘theorem’ in statistical foundations”
Deborah G. Mayo
ABSTRACT: An essential component of inference based on familiar frequentist (error statistical) notions p-values, statistical significance and confidence levels, is the relevant sampling distribution (hence the term sampling theory). This results in violations of a principle known as the strong likelihood principle (SLP), or just the likelihood principle (LP), which says, in effect, that outcomes other than those observed are irrelevant for inferences within a statistical model. Now Allan Birnbaum was a frequentist (error statistician), but he found himself in a predicament: He seemed to have shown that the LP follows from uncontroversial frequentist principles! Bayesians, such as Savage, heralded his result as a “breakthrough in statistics”! But there’s a flaw in the “proof”, and that’s what I aim to show in my presentation by means of 3 simple examples:.
- Example 1: Trying and Trying Again
- Example 2: Two instruments with different precisions (you shouldn’t get credit/blame for something you didn’t do)
- The Breakthrough: Don’t Birnbaumize that data my friend
As in the last 9 years, I posted an imaginary dialogue (here) with Allan Birnbaum at the stroke of midnight, New Year’s Eve, and this will be relevant for the talk.
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One of the following 3 papers: My earliest treatment via counterexample:
- 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.
A deeper argument can be found in:
- Mayo 2014. “On the Birnbaum Argument for the Strong Likelihood Principle,” (with discussion & rejoinder) Statistical Science, 29(2), 227-239, 261-266.
For an intermediate Goldilocks version (based on a presentation given at the JSM 2013):
- Mayo 2013. “Presented Version: On the Birnbaum Argument for the Strong Likelihood Principle.” In JSM Proceedings, Section on Bayesian Statistical Science. Alexandria, VA: American Statistical Association, 440-453.
This post from the Error Statistics Philosophy blog will get you oriented. (It has links to other posts on the LP & Birnbaum, as well as background readings/discussions for those who want to dive deeper into the topic.)
Slides and Video Links:
D. Mayo’s slides: “Putting the Brakes on the Breakthrough, or ‘How I used simple logic to uncover a flaw in a controversial 60-year old ‘theorem’ in statistical foundations’” D. Mayo’s presentation:
- (Link to paste in browser): https://philstatwars.files.wordpress.com/2021/01/mayo_172021_presentation.mp4
- SHORT LINK (quick): https://wp.me/abBgTB-x4
Discussion on Mayo’s presentation:
- (Link to paste in browser): https://philstatwars.files.wordpress.com/2021/01/mayo-172021-discussion-1.mp4
- SHORT LINK (quick): https://wp.me/abBgTB-xc
Mayo’s Memos: Any info or events that arise that seem relevant to share with y’all before the meeting. You may wish to look at my rejoinder to a number of statisticians: Rejoinder “On the Birnbaum Argument for the Strong Likelihood Principle”. (It is also above in the link to the complete discussion in the 3rd reading option.) I often find it useful to look at other treatments. So I put together this short supplement to glance through to clarify a few select points. *Meeting 12 of our the general Phil Stat series which began with the LSE Seminar PH500 on May 21