A note concerning a selection "paradox" of Dawid's

Stephen Senn

doi:10.1198/000313008X331530

A note concerning a selection "paradox" of Dawid's

Stephen Senn^*

^*Corresponding author for this work

Research output: Contribution to journal › Review article › peer-review

38 Citations (Scopus)

Abstract

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.

Original language	English
Pages (from-to)	206-210
Number of pages	5
Journal	American Statistician
Volume	62
Issue number	3
DOIs	https://doi.org/10.1198/000313008X331530
Publication status	Published - Aug 2008
Externally published	Yes

Keywords

Bayesian inference
Hierarchical models
Prior distributions
Selection paradox

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10.1198/000313008X331530

Cite this

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title = "A note concerning a selection {"}paradox{"} of Dawid's",

abstract = "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.",

keywords = "Bayesian inference, Hierarchical models, Prior distributions, Selection paradox",

author = "Stephen Senn",

note = "Funding Information: Stephen Senn is Professor of Statistics, Department of Statistics, University of Glasgow, Glasgow, G12 8QQ, UK (E-mail: [email protected]). I am grateful to the UK Engineering and Physical Research Council for funding through the Simplicity, Complexity and Modelling project and to Novartis for further funding. I thank the referees and editors for helpful comments.",

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N1 - Funding Information: Stephen Senn is Professor of Statistics, Department of Statistics, University of Glasgow, Glasgow, G12 8QQ, UK (E-mail: [email protected]). I am grateful to the UK Engineering and Physical Research Council for funding through the Simplicity, Complexity and Modelling project and to Novartis for further funding. I thank the referees and editors for helpful comments.

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N2 - 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.

AB - 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.

KW - Bayesian inference

KW - Hierarchical models

KW - Prior distributions

KW - Selection paradox

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DO - 10.1198/000313008X331530

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SP - 206

EP - 210

JO - American Statistician

JF - American Statistician

IS - 3

ER -

A note concerning a selection "paradox" of Dawid's

Abstract

Keywords

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