Conditionality principle

The conditionality principle is a Fisherian principle of statistical inference that Allan Birnbaum formally defined and studied in his 1962 JASA article. Informally, the conditionality principle can be taken as the claim that experiments which were not actually performed are statistically irrelevant.
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, for example, rolling a dice (whose value is "h" = 1 ... 6) to determine which of six experiments to conduct (experiment "E" ... "E").
The conditionality principle can be formally stated thus:
An illustration of the conditionality principle, in a bioinformatics context, is given by .