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Does anyone understand the difference between weak likelihood principle and strong likelihood principle?

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Yes, it's straightforward. The weak LP is within a given model and distribution (it's essentially just the sufficiency principle within a model), whereas the strong LP, SLP, makes the claim (of equivalent evidential import) for pairs of models. Easiest to refer to my paper here: http://errorstatistics.com/2014/09/06/statistical-science-the-likelihood-principle-issue-is-out

fortunately, it turns out the the SLP does not follow from sufficiency and conditionality, as had long been thought.

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    $\begingroup$ Could you please also give a complete reference? Links have a habit of dying. $\endgroup$
    – Glen_b
    Sep 10, 2014 at 2:42
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    $\begingroup$ You say that the SLP does not follow from sufficiency and conditionality, but in fact Mayo's disproof of Birnbaum's proof has been seriously challenged and may well be flawed. arxiv.org/abs/1711.08093 $\endgroup$ Mar 22, 2018 at 23:52

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