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Biometrika 1986 73(2):323-332; doi:10.1093/biomet/73.2.323
© 1986 by Biometrika Trust
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Approximate predictive likelihood

A. C. DAVISON

Center for Statistical Sciences, University of Texas Austin, Texas 78712, U.S.A.

A predictive likelihood is given which approximates both Bayes and maximum likelihood predictive inference by expansion of a posterior likelihood. This synthesizes and extends previous results and is widely applicable. The approximation usually differs from exact Bayes posterior predictive density by Op(n–2), and from exact predictive likelihood by Op(n–2) but does not depend on the availability of prior information and is applicable when exact predictive likelihood cannot be found. The results are applied to the prediction of extremes using the generalized extreme-value distribution.

Key Words: Generalized extreme-value distribution • Laplace's method for integrals • Maximum likeli hood estimation • Observed information • Posterior predictive density • Predictive likelihood


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