The conditionality principle is a Fisherian principle of

statistical inference Statistical inference is the process of using data analysis to infer properties of an underlying probability distribution, distribution of probability.Upton, G., Cook, I. (2008) ''Oxford Dictionary of Statistics'', OUP. . Inferential statistical ...

that

Allan Birnbaum Allan Birnbaum (May 27, 1923 – July 1, 1976) was an American statistician who contributed to statistical inference, foundations of statistics, statistical genetics, statistical psychology, and history of statistics. Life and career Birnbaum w ...

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 In statistics, the likelihood principle is the proposition that, given a statistical model, all the evidence in a sample relevant to model parameters is contained in the likelihood function. A likelihood function arises from a probability density f ...

. 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 An ancillary statistic is a measure of a sample whose distribution (or whose pmf or pdf) does not depend on the parameters of the model. An ancillary statistic is a pivotal quantity that is also a statistic. Ancillary statistics can be used to ...

(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 Dice (singular die or dice) are small, throwable objects with marked sides that can rest in multiple positions. They are used for generating random values, commonly as part of tabletop games, including dice games, board games, role-playing g ...

(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: :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 actually conducted, ignoring the overall structure of the mixed experiment (see ). An illustration of the conditionality principle, in a

bioinformatics Bioinformatics () is an interdisciplinary field that develops methods and software tools for understanding biological data, in particular when the data sets are large and complex. As an interdisciplinary field of science, bioinformatics combi ...

context, is given by .

References

* * * ''(With discussion.)''

Formulation

References

Further reading