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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<sub>h</sub>'' 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<sub>h</sub>'' from the component experiment ''E<sub>h</sub>''.  
 
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<sub>h</sub>'', then for each outcome <math>(E_h, x_h)</math> of ''E'', [...] the evidential meaning of any outcome ''x'' of any mixture experiment ''E'' is the same as that of the corresponding outcome ''x<sub>h</sub>'' of the corresponding component experiment ''E<sub>h</sub>'', ignoring the over-all structure of the mixed experiment. (See Birnbaum 1962)
 
==References==
 
* {{cite book|last=Berger|first=J.O.|coauthors=and Wolpert, R.L.|title=The Likelihood Principle|edition=2nd|publisher=The Institute of Mathematical Statistics|location=Haywood, CA|year=1988|isbn=0-940600-13-7}}
* {{cite journal|last=Birnbaum|first=Allan|authorlink=Allan Birnbaum|year=1962|title=On the foundations of statistical inference|journal=[[Journal of the American Statistical Association]]|volume=57|issue=298|pages=269–326|doi= 10.2307/2281640|mr=0138176|jstor=2281640 }} ''(With discussion.)''
 
==Further reading==
{{Cite journal
| last1 = Kalbfleisch | first1 = J. D.  
| title = Sufficiency and conditionality
| doi = 10.1093/biomet/62.2.251
| journal = Biometrika
| volume = 62
| issue = 2
| pages = 251&ndash;259
| year = 1975
| pmid =  
| pmc =
}}
 
[[Category:Statistical theory]]
[[Category:Statistical principles]]

Revision as of 02:21, 20 June 2013

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 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)

References

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Further reading

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A vendor's stamp duty has been launched on industrial property for the primary time, at rates ranging from 5 per cent to 15 per cent. The Authorities might be trying to reassure the market that they aren't in opposition to foreigners and PRs investing in Singapore's property market. They imposed these measures because of extenuating components available in the market." The sale of new dual-key EC models will even be restricted to multi-generational households only. The models have two separate entrances, permitting grandparents, for example, to dwell separately. The vendor's stamp obligation takes effect right this moment and applies to industrial property and plots which might be offered inside three years of the date of buy. JLL named Best Performing Property Brand for second year running

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