## A simple general formula for tail probabilities for frequentist and Bayesian inference.(English)Zbl 0932.62003

Summary: 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 O. E. Barndorff-Nielsen’s approximation [ibid. 78, 557-563 (1991)] is discussed.

### MSC:

 62A01 Foundations and philosophical topics in statistics 62F15 Bayesian inference
Full Text: