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Biometrika 1989 76(3):489-501; doi:10.1093/biomet/76.3.489
© 1989 by Biometrika Trust
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Approximate predictive pivots and densities

RONALD W. BUTLER

Department of Statistics, Colorado State University Fort Colins, Colorado 80523, U.S.A.

This paper suggests two predictive likelihoods that can be applied in almost any parametric model setting. The first can sometimes be interpreted as an approximate predictive pivot (Barnard, 1986) while the second is often an approximation to a Bayesian predictive density with a flat prior. The issue of calibrating various predictive likelihood in terms of long run predictive coverage is also discussed and a specific criterion by which these likelhoods can be compared is proposed.

Key Words: Ancillary statistic • Conditional predictive likelihood • Distribution-constant • Parameterization invariance • Predictive ancillary statistic • Predictive density • Predictive likelihood • Predictive pivot


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