The conditionality principle is a principle of statistical inference introduced by Allan Birnbaum in his 1962 JASA article which is foundational for Bayesian and likelihoodists statistical inference. Inferential statistics or statistical induction comprises the use of Statistics to make Inferences concerning some unknown aspect of a Population Allan Birnbaum ( May 27, 1923 &ndash July 1, 1976) was an American Statistician who contributed to Statistical inference Year 1962 ( MCMLXII) was a Common year starting on Monday (the link is to a full 1962 calendar of the Gregorian calendar. Jasa is a municipality located in the province of Huesca, Aragon, Spain. Together with the sufficiency principle, it implies the famous likelihood principle. In Statistics, sufficiency is the property possessed by a Statistic, with respect to a Parameter, "when no other statistic which can be calculated In Statistics,the likelihood principle is a controversial principle of Statistical inference which asserts that all of the Information in a sample
Formulation
The conditionality principle makes an assertion about an experiment E that can be described as a mixture of several component experiments Eh where h is an ancillary statistic (i. In Statistics, an ancillary statistic is a statistic whose Probability distribution does not depend on which of the probability distributions among those being considered 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 xh from the component experiment Eh.
The conditionality principle can be formally stated thus:
Conditionality Principle: If E is any experiment having the form of a mixture of component experiments Eh, then for each outcome (Eh,xh) of E, [. . . ] the evidential meaning of any outcome x of any mixture experiment E is the same as that of the corresponding outcome xh of the corresponding component experiment Eh, ignoring the over-all 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 edition, Haywood, CA: The Institute of Mathematical Statistics. ISBN 0-940600-13-7.
- Birnbaum, Allan (1962). Allan Birnbaum ( May 27, 1923 &ndash July 1, 1976) was an American Statistician who contributed to Statistical inference "On the foundations of statistical inference". J. Amer. Statist. Assoc. 57 (298): 269-326. ISSN 0162-1459. An International Standard Serial Number ( ISSN) is a unique eight-digit number used to identify a print or electronic Periodical publication. (With discussion. )
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