Editing Likelihood principle (section)

== History ==

The likelihood principle was first identified by that name in print in 1962 (Barnard ''et al''., [[Allan Birnbaum|Birnbaum]], and Savage ''et al''.), but arguments for the same principle, unnamed, and the use of the principle in applications goes back to the works of [[Ronald A. Fisher|R.A. Fisher]] in the 1920s. The law of likelihood was identified by that name by [[Ian Hacking|I. Hacking]] (1965). More recently the likelihood principle as a general principle of inference has been championed by [[Anthony William Fairbank Edwards|A.W.F. Edwards]]. The likelihood principle has been applied to the [[philosophy of science]] by R. Royall.<ref>
{{cite book
 |last=Royall |first=Richard
 |year=1997
 |title=Statistical Evidence: A likelihood paradigm
 |publisher=Chapman and Hall
 |place=Boca Raton, FL
 |isbn=0-412-04411-0
}}
</ref>

[[Allan Birnbaum|Birnbaum]] (1962) initially argued that the likelihood principle follows from two more primitive and seemingly reasonable principles, the ''[[conditionality principle]]'' and the ''[[sufficiency principle]]'':
* The conditionality principle says that if an experiment is chosen by a random process independent of the states of nature <math>\ \theta\ ,</math> then only the experiment actually performed is relevant to inferences about <math>\ \theta ~.</math>
* The sufficiency principle says that if <math>\ T(X)\ </math> is a [[sufficient statistic]] for <math>\ \theta\ ,</math> and if in two experiments with data <math>\ x_1\ </math> and <math>\ x_2\ </math> we have <math>\ T(x_1) = T(x_2)\ ,</math> then the evidence about <math>\ \theta\ </math> given by the two experiments is the same.

However, upon further consideration  Birnbaum rejected both his conditionality principle and the likelihood principle.<ref name=Birnbaum1970>
{{cite journal
 |last = Birnbaum |first = A.  |author-link= Allan Birnbaum
 |date = 14 March 1970
 |title = Statistical methods in scientific inference
 |journal = [[Nature (journal)|Nature]]
 |volume = 225  |issue = 5237 |page = 1033
|doi = 10.1038/2251033a0 |bibcode = 1970Natur.225.1033B }}
</ref> The adequacy of Birnbaum's original argument has also been contested by others (''see below for details'').