258 Statistical Discussion Form/Journal of Statistical Planning and Inference 55 (1996) 255-264

a contradiction. For by assuming the applicability of the conditionality principle, he assumes that only the probability distribution in the component experiment actually performed say El, is relevant for estimating the parameter, and that in E2 is not relevant. But by applying the sufficiency principle to the mixture experiment he assumes that the probability distribution in E2 is relevant for estimating the parameter.

Note also - and this is the view of Fisher, Jeffreys, Birnbaum - that there are not two different Sufficiency Principles but only one which is universally applicable. But the principle applies to that distribution on which consistently with the other assump- tions in the theorem the estimate of the parameter is based.

References

Joshi, V.M. (1990). Fallacy in the proof of Birnbaum's Theorem. Statistical Discussion forum, F27, J. Statist. Plann. Inference 26, 111-112.

Berger, J.O. (1990). Reply to the above, F28, J. Statist. Plann. Inference 26, 112-113.

V.M. Joshi Department of Statistical and Actuarial Sciences

University of Western Ontario London, Ontario, Canada N6A 5B9

F44A. A question about F44

The sufficiency principle (Birnbaum, p. 270) states that a sufficient statistic contains all the evidence about some parameter, not that it is essential to use irrelevant parts of the evidence. So is F44 fair?

I.J. Good

F44B. A reply to F44A

A sufficient statistic must firstly be a statistic. A statistic is a measurable function defined on the sample space. The sample space is the set of all possible observations, namely all those observations which are possible under the pr. distribution which by the assumptions of the theorem is relevant for the estimation of the parameter. Thus the function considered by Berger and Wolpert is under the relevant distribution, not