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On the Likelihood Principle and a Supposed Antinomy

Published online by Cambridge University Press:  28 February 2022

Barry Loewer ,
Robert Laddaga  and
Roger Rosenkrantz
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Extract

It is natural to regard a given datum, x, as favoring that one of two rival hypotheses, H or K, which affords x higher probability, so that H is favored iff the likelihood ratio; P(x|H):P(x|K) exceeds one. More generally, the relative support x accords the different members of a partition of hypotheses, H1,…,Hn, is assessed by comparing their likelihoods, P(x|Hi). Considered as a function of the Hi, L(Hi) = P(x|Hi) is called the likelihood function. If we view the likelihood function associated with an observed experimental outcome, x, as conveying the entire evidential import of the experiment, then it follows that the two outcomes, x and y, whether of the same or different experiments, are evidentially equivalent just in case they give rise to the same relative likelihoods, P(x|Hi):P(x|Hi) = P(y|Hi):P(y|Hj) for all i,j, or , in other words, iff P(x|Hi) α P(y|Hi) for all i.

Type
Part VIII. Applications of Statistical Ideas
Information
PSA: Proceedings of the Biennial Meeting of the Philosophy of Science Association , Volume 1978 , Issue 1: Volume One: Contributed Papers 1978 , 1978 , pp. 278 - 286
Copyright
Copyright © 1978 by the Philosophy of Science Association

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