A simple general formula for tail probabilities for frequentist and Bayesian inference

D. A.S. Fraser; N. Reid; J. Wu

doi:10.1093/biomet/86.2.249

A simple general formula for tail probabilities for frequentist and Bayesian inference

D. A.S. Fraser, N. Reid, J. Wu

Internal Medicine

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98 Scopus citations

Abstract

We describe a simple general formula for approximating the p-value for testing a scalar parameter in the presence of nuisance parameters. The formula covers both frequentist and Bayesian contexts and does not require explicit nuisance parameterisation. Implementation is discussed in terms of computer algebra packages. Examples are given and the relationship to Barndorff-Nielsen's approximation is discussed.

Original language	English
Pages (from-to)	249-264
Number of pages	16
Journal	Biometrika
Volume	86
Issue number	2
DOIs	https://doi.org/10.1093/biomet/86.2.249
State	Published - 1999

Keywords

Asymptotic theory
Likelihood method
Pivotal quantity
Tail probability
Third-order inference

ASJC Scopus subject areas

Statistics and Probability
Mathematics (all)
Agricultural and Biological Sciences (miscellaneous)
Agricultural and Biological Sciences (all)
Statistics, Probability and Uncertainty
Applied Mathematics

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10.1093/biomet/86.2.249

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AB - We describe a simple general formula for approximating the p-value for testing a scalar parameter in the presence of nuisance parameters. The formula covers both frequentist and Bayesian contexts and does not require explicit nuisance parameterisation. Implementation is discussed in terms of computer algebra packages. Examples are given and the relationship to Barndorff-Nielsen's approximation is discussed.

KW - Asymptotic theory

KW - Likelihood method

KW - Pivotal quantity

KW - Tail probability

KW - Third-order inference

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JO - Biometrika

JF - Biometrika

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ER -

A simple general formula for tail probabilities for frequentist and Bayesian inference

Abstract

Keywords

ASJC Scopus subject areas

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