Editing Likelihood principle (section)

===The original Birnbaum argument===

According to Giere (1977),<ref>Giere, R. (1977) Allan Birnbaum's Conception of Statistical Evidence. ''Synthese'', 36, pp.5-13.</ref> Birnbaum rejected<ref name="Birnbaum1970" /> both his own conditionality principle and the likelihood principle because they were both incompatible with what he called the “confidence concept of statistical evidence”, which Birnbaum (1970) describes as taking “from the Neyman-Pearson approach techniques for systematically appraising and bounding the probabilities (under respective hypotheses) of seriously misleading interpretations of data” (<ref name="Birnbaum1970" /> p.&nbsp;1033). The confidence concept incorporates only limited aspects of the likelihood concept and only some applications of the conditionality concept. Birnbaum later notes that it was the unqualified equivalence formulation of his 1962 version of the conditionality principle that led “to the monster of the likelihood axiom” (<ref>Birnbaum, A., (1975) Discussion of J. D. Kalbfleisch's paper 'Sufficiency and Conditionality'. Biometrika, 62, pp. 262-264.</ref> p.&nbsp;263).

Birnbaum's original argument for the likelihood principle has also been disputed by other statisticians including [[Hirotugu Akaike|Akaike]],<ref>Akaike, H., 1982. On the fallacy of the likelihood principle. Statistics & probability letters, 1(2), pp.75-78]</ref> Evans<ref>
{{cite arXiv
 |author=Evans, Michael
 |year=2013
 |eprint=1302.5468
 |title=What does the proof of Birnbaum's theorem prove?
|class=math.ST
 }}
</ref> and philosophers of science, including [[Deborah Mayo]].<ref>
{{cite book
 |last=Mayo |first=D. |author-link=Deborah Mayo
 |year=2010
 |url=http://www.phil.vt.edu/dmayo/personal_website/ch%207%20mayo%20birnbaum%20proof.pdf
 |article=An error in the argument from Conditionality and Sufficiency to the Likelihood Principle
 |title=Error and Inference: Recent exchanges on experimental reasoning, reliability and the objectivity and rationality of science
 |editor1-first=D. |editor1-last=Mayo  |editor1-link=Deborah Mayo
 |editor2-first=A. |editor2-last=Spanos
 |place=Cambridge, GB
 |publisher=Cambridge University Press
 |pages=305–314
}}
</ref><ref>
{{cite journal
 |last=Mayo |first=D. |author-link=Deborah Mayo
 |year=2014
 |url=https://projecteuclid.org/euclid.ss/1408368565
 |title=On the Birnbaum argument for the Strong Likelihood Principle
 |journal=[[Statistical Science]]
 |volume=29 |pages=227–266 (with discussion)
}}
</ref> [[Philip Dawid|Dawid]] points out fundamental differences between Mayo's and Birnbaum's definitions of the conditionality principle, arguing Birnbaum's argument cannot be so readily dismissed.<ref>
{{cite journal
 |author=Dawid, A.P.
 |year=2014
 |url=https://projecteuclid.org/euclid.ss/1408368565
 |title=Discussion of "On the Birnbaum argument for the Strong Likelihood Principle"
 |journal=[[Statistical Science]]
 |volume=29 |issue=2
 |pages=240–241
|doi=10.1214/14-STS470
 |s2cid=55068072
 |doi-access=free
 |arxiv=1411.0807
 }}
</ref> A new proof of the likelihood principle has been provided by Gandenberger that addresses some of the counterarguments to the original proof.<ref>
{{cite journal
 |author=Gandenberger, Greg
 |year=2014
 |title=A new proof of the likelihood principle
 |journal=[[British Journal for the Philosophy of Science]]
 |volume=66 |issue=3
 |pages=475–503
 |doi=10.1093/bjps/axt039
}}
</ref>