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Biometrika 1999 86(2):249-264; doi:10.1093/biomet/86.2.249
© 1999 by Biometrika Trust
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A simple general formula for tail probabilities for frequentist and Bayesian inference

DAS FraserA1, N ReidA and J WuA3

Department of Statistics, University of Toronto, Toronto, Canada M5S 3G3 E-mail: A1 dfraser@utstat.toronto.edu A reid@utstat.toronto.edu A3 jian@utstat.toronto.edu

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.

Key Words: Asymptotic theory; Likelihood method; Pivotal quantity; Tail probability; Third-order inference.


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