Conditionality principle
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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. Together with the sufficiency principle, it implies the famous likelihood principle.
[edit] 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.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.
[edit] 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). "On the foundations of statistical inference". J. Amer. Statist. Assoc. 57 (298): 269-326. ISSN 0162-1459. (With discussion.)
