The sufficiency of the evidence, the relevancy of the evidence, and quantifying both with a single number

David R. Bickel ()
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David R. Bickel: University of Ottawa

Statistical Methods & Applications, 2021, vol. 30, issue 4, No 3, 1157-1174

Abstract: Abstract Consider a data set as a body of evidence that might confirm or disconfirm a hypothesis about a parameter value. If the posterior probability of the hypothesis is high enough, then the truth of the hypothesis is accepted for some purpose such as reporting a new discovery. In that way, the posterior probability measures the sufficiency of the evidence for accepting the hypothesis. It would only follow that the evidence is relevant to the hypothesis if the prior probability were not already high enough for acceptance. A measure of the relevancy of the evidence is the Bayes factor since it is the ratio of the posterior odds to the prior odds. Measures of the sufficiency of the evidence and measures of the relevancy of the evidence are not mutually exclusive. An example falling in both classes is the likelihood ratio statistic, perhaps based on a pseudolikelihood function that eliminates nuisance parameters. There is a sense in which the likelihood ratio statistic measures both the sufficiency of the evidence and its relevancy. That result is established by representing the likelihood ratio statistic in terms of a conditional possibility measure that satisfies logical coherence rather than probabilistic coherence.

Keywords: Deductive closure; Deductive cogency; General law of likelihood; Likelihood paradigm; Possibility measure; Possibility theory; Pure likelihood methods; Restricted parameter space; Strength of statistical evidence (search for similar items in EconPapers)
Date: 2021
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Citations: View citations in EconPapers (1)

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DOI: 10.1007/s10260-020-00553-3

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