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Biometrika 1996 83(1):111-125; doi:10.1093/biomet/83.1.111
© 1996 by Biometrika Trust
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A predictive approach to the Bayesian design problem with application to normal regression models

MORRIS L. EATON, ALESSANDRA GIOVAGNOLI and PAOLA SEBASTIANI

School of Statistics, University of Minnesota 270 Vincent Hall, 206 Church Street SE, Minneapolis, Minnesota 55455, U.S.A.
Dipartimento di Scienze Statistiche, Universitá di Bologna via Belle Arti 41, 40126 Bologna, Italy
Department of Actuarial Science and Statistics, The City University Northampton Square, London EC1V OHB, U.K.

A predictive decision-theoretic approach is developed for the Bayesian design problem. The loss functions used are fair Bayes, or proper scoring rules, and are quadratic measures of distance between probability measures. Optimal Bayesian designs are those which minimise the preposterior risk for the decision problem. Such designs typically depend on both the prior distribution and the loss function. The results are applied to certain normal regression models where explicit optimal designs are constructed.

Key Words: Bayesian optimal design • Decision theory • Fair Bayes loss function • Normal theory • Prediction • Regression


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