Friday, May 2, 2014, I will attempt to present my critical analysis of the Birnbaum argument for the (strong) Likelihood Principle, so as to be accessible to a general philosophy audience (flyer below). Can it be done? I don’t know yet, this is a first. It will consist of:
- Example 1: Trying and Trying Again: Optional stopping
- Example 2: Two instruments with different precisions
[you shouldn’t get credit (or blame) for something you didn’t do]
- The Breakthough: Birnbaumization
- Imaginary dialogue with Allan Birnbaum
The full paper is here. My discussion takes several pieces a reader can explore further by searching this blog (e.g., under SLP, brakes e.g., here, Birnbaum, optional stopping). I will post slides afterwards.
I’d be interested in seeing more on relations between your results and other critiques of Birnbaum’s (non)theorem, especially since some expressed doubts about his nontheorem early on (as seen in the comments accompanying the original paper), and attempted formalizations have only reinforced such doubts, e.g., Evans at
In parallel, stepping away from theoretical treatises like Berger & Wolpert, Casella & Berger, or Royall, few applied Bayesian statistics books I see mention the nontheorem (although Birnbaum 1962 is sometimes cited for the likelihood principle), the offered motivations for Bayes instead being coherency and good field performance of the methods, e.g., see Box & Tiao, Carlin & Louis, Gelman et al., or Spiegelhalter et al. Leonard & Hsu’s book mentions the nontheorem, but skeptically in passing; elsewhere, Leonard refers to it as refuted:
Thus, fortunately, it seems the nontheorem has played an indiscernible role (if any) in applications of Bayesian statistics.