Conditionality Principle
Conditionality Principle is a rational rule of statistical inference proposed by Allan Birnbaum.
- AKA: Weak Conditionality Principle.
- It statets that: "the evidential meaning of any outcome of any mixture experiment is the same as that of the corresponding outcome of the corresponding component experiment, ignoring the over-all structure of the mixture experiment".
- See: Statistical Inference, Likelihood Principle, Ancillary Statistic, Sufficiency Principle, Birnbaum’s Theorem.
References
2015
- (Wikipedia, 2015) ⇒ http://en.wikipedia.org/wiki/Conditionality_principle Retrieved 2016-07-30
- 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 [math]\displaystyle{ (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 xh of the corresponding component experiment Eh, ignoring the over-all structure of the mixed experiment (See Birnbaum 1962). An illustration of the conditionality principle, in a bioinformatics context, is given by Barker (2014).
- 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.
2014
- (Dawid, 2014) ⇒ Dawid, A. P. (2014). Discussion of “On the Birnbaum Argument for the Strong Likelihood Principle”. Statistical Science, 29(2), 240-241. DOI: 10.1214/14-STS470 [1]
- Deborah Mayo claims to have refuted Birnbaum's argument that the Likelihood Principle is a logical consequence of the Sufficiency and Conditionality Principles. However, this claim fails because her interpretation of the Conditionality Principle is different from Birnbaum's. Birnbaum's proof cannot be so readily dismissed.
1996
- (Lavine, 1996) ⇒ Lavine, M. (1996). Conditionality is Alive and Well. Institute of Statistics & Decision Sciences, Duke University. DOI: 10.1.1.51.7743 [2]
- Helland (1995) argues through example that the Conditionality Principle does not always apply and that unconditional analyses are sometimes more informative than conditional ones. We try to counter his arguments (...) In Simple Counter-examples against the Conditionality Principle Helland purports to show that the Conditionality Principle does not have universal application. The argument is made through several ex- Supported by NSF Grant DMS-9300137 amples. Here we examine two of those examples in more detail and argue that the conclusion is not warranted. Example 1 Quoting from Helland: "As a small part of a larger medical experiment, two individuals (1 and 2) have been on a certain diet for some time, and by taking samples at the beginning of and at the end of that period some response like change in blood cholesterol levels is measured. For the individual h(h = 1; 2), the measured response i.