Conditionality principle

The conditionality principle is a Fisherian principle of statistical inference that Allan Birnbaum formally defined and studied in his 1962 JASA article. Together with the sufficiency principle, Birnbaum's version of the principle implies the famous likelihood principle. Although the relevance of the proof to data analysis remains controversial among statisticians, many Bayesians and likelihoodists consider the likelihood principle foundational for statistical inference.
Formulation
The conditionality principle makes an assertion about an experiment E that can be described as a mixture of several component experiments E_{h} where h is an ancillary statistic (i.e. a statistic whose probability distribution does not depend on unknown parameter values). This means that observing a specific outcome x of experiment E is equivalent to observing the value of h and taking an observation x_{h} from the component experiment E_{h}.
The conditionality principle can be formally stated thus:
Conditionality Principle: If E is any experiment having the form of a mixture of component experiments E_{h}, then for each outcome (E_{h},x_{h}) of E, [...] the evidential meaning of any outcome x of any mixture experiment E is the same as that of the corresponding outcome x_{h} of the corresponding component experiment E_{h}, ignoring the overall structure of the mixed experiment. (See Birnbaum 1962)
Informally, the conditionality principle can be taken as to claim the irrelevance of component experiments that were not actually performed.
References
 Berger, J.O.; and Wolpert, R.L. (1988). The Likelihood Principle (2nd ed.). Haywood, CA: The Institute of Mathematical Statistics. ISBN 0940600137.
 Birnbaum, Allan (1962). "On the foundations of statistical inference". Journal of the American Statistical Association 57 (298): 269–326. doi:10.2307/2281640. JSTOR 2281640. MR0138176. (With discussion.)
Further reading
Kalbfleisch, J. D. (1975). "Sufficiency and conditionality". Biometrika 62 (2): 251–259. doi:10.1093/biomet/62.2.251.
Categories: Statistical theory
 Statistical principles
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