Historical Remarks
The likelihood principle was first identified by that name in print in 1962 (Barnard et al., 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 R.A. Fisher in the 1920s. The law of likelihood was identified by that name by I. Hacking (1965). More recently the likelihood principle as a general principle of inference has been championed by A. W. F. Edwards. The likelihood principle has been applied to the philosophy of science by R. Royall.
Birnbaum proved 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, then only the experiment actually performed is relevant to inferences about . The sufficiency principle says that if is a sufficient statistic for, and if in two experiments with data and we have, then the evidence about given by the two experiments is the same.
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