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Lindley's Paradox

1982
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Journal of the American Statistical Association
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A sharp null hypothesis may be strongly rejected by a standard sampling-theory test of significance and yet be awarded high odds by a Bayesian analysis based on a small prior probability for the null hypothesis and a diffuse distribution of one's remaining probability over the alternative hypothesis. This disagreement between sampling-theory and Bayesian methods was first studied by Harold Jeffreys (1939), and it was first called a paradox by Dennis Lindley (1957). The paradox can be exhibited

doi:10.1080/01621459.1982.10477809
fatcat:xdjxnhd7jjb7jcpo4to7nxhgjq