Journal
AMERICAN STATISTICIAN
Volume 62, Issue 3, Pages 206-210Publisher
TAYLOR & FRANCIS INC
DOI: 10.1198/000313008X331530
Keywords
Bayesian inference; hierarchical models; prior distributions; selection paradox
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Funding
- EPSRC [EP/E018173/1] Funding Source: UKRI
- Engineering and Physical Sciences Research Council [EP/E018173/1] Funding Source: researchfish
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This article briefly reviews a selection paradox of Dawid's, whereby Bayesian inference appears to be unchanged whether or not treatments have been selected for inspection on the basis of extreme values. The problem is recast in terms of a hierarchical model. This offers an alternative explanation of the paradox but also reveals a disturbing dependence of inference on prior specification. The example may also be used to deepen students' understanding of the implications of using conjugate nonhierarchical priors in Bayesian analysis. To illustrate, some simulations are presented.
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