On the Birnbaum Argument for the Strong Likelihood Principle

dc.contributor.authorMayo, Deborah G.en
dc.date.accessioned2017-11-20T16:26:14Zen
dc.date.available2017-11-20T16:26:14Zen
dc.date.issued2014en
dc.description.abstractAn essential component of inference based on familiar frequentist notions, such as p-values, significance and confidence levels, is the relevant sampling distribution. This feature results in violations of a principle known as the strong likelihood principle (SLP), the focus of this paper. In particular, if outcomes x∗ and y∗ from experiments E1 and E2 (both with unknown parameter θ) have different probability models f1(·), f2(·), then even though f1(x∗; θ) = cf2(y∗; θ) for all θ, outcomes x∗ and y∗ may have different implications for an inference about θ. Although such violations stem from considering outcomes other than the one observed, we argue this does not require us to consider experiments other than the one performed to produce the data. David Cox [Ann. Math. Statist. 29 (1958) 357–372] proposes the Weak Conditionality Principle (WCP) to justify restricting the space of relevant repetitions. The WCP says that once it is known which Ei produced the measurement, the assessment should be in terms of the properties of Ei . The surprising upshot of Allan Birnbaum’s [J. Amer. Statist. Assoc. 57 (1962) 269–306] argument is that the SLP appears to follow from applying the WCP in the case of mixtures, and so uncontroversial a principle as sufficiency (SP). But this would preclude the use of sampling distributions. The goal of this article is to provide a new clarification and critique of Birnbaum’s argument. Although his argument purports that [(WCP and SP) entails SLP], we show how data may violate the SLP while holding both the WCP and SP. Such cases also refute [WCP entails SLP].en
dc.description.notespp.227–239en
dc.identifier.doihttps://doi.org/10.1214/13-STS457en
dc.identifier.issue2en
dc.identifier.urihttp://hdl.handle.net/10919/80464en
dc.identifier.urlhttp://www.phil.vt.edu/dmayo/personal_website/bibliography%20complete.htmen
dc.identifier.volume29en
dc.language.isoen_USen
dc.publisherStatistical Scienceen
dc.rightsCreative Commons Attribution-NonCommercial-NoDerivs 3.0 United Statesen
dc.rights.urihttp://creativecommons.org/licenses/by-nc-nd/3.0/us/en
dc.subjectBirnbaumizationen
dc.subjectlikelihood principle (weak and strong)en
dc.subjectsampling theoryen
dc.subjectsufficiencyen
dc.subjectweak conditionalityen
dc.titleOn the Birnbaum Argument for the Strong Likelihood Principleen
dc.title.serialStatistical Scienceen
dc.typeArticle - Refereeden

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