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October 2015 Bayesian $T$-optimal discriminating designs
Holger Dette, Viatcheslav B. Melas, Roman Guchenko
Ann. Statist. 43(5): 1959-1985 (October 2015). DOI: 10.1214/15-AOS1333

Abstract

The problem of constructing Bayesian optimal discriminating designs for a class of regression models with respect to the $T$-optimality criterion introduced by Atkinson and Fedorov [Biometrika 62 (1975a) 57–70] is considered. It is demonstrated that the discretization of the integral with respect to the prior distribution leads to locally $T$-optimal discriminating design problems with a large number of model comparisons. Current methodology for the numerical construction of discrimination designs can only deal with a few comparisons, but the discretization of the Bayesian prior easily yields to discrimination design problems for more than 100 competing models. A new efficient method is developed to deal with problems of this type. It combines some features of the classical exchange type algorithm with the gradient methods. Convergence is proved, and it is demonstrated that the new method can find Bayesian optimal discriminating designs in situations where all currently available procedures fail.

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Holger Dette. Viatcheslav B. Melas. Roman Guchenko. "Bayesian $T$-optimal discriminating designs." Ann. Statist. 43 (5) 1959 - 1985, October 2015. https://doi.org/10.1214/15-AOS1333

Information

Received: 1 December 2014; Revised: 1 February 2015; Published: October 2015
First available in Project Euclid: 3 August 2015

zbMATH: 1331.62382
MathSciNet: MR3375873
Digital Object Identifier: 10.1214/15-AOS1333

Subjects:
Primary: 62K05

Keywords: Bayesian optimal design , design of experiment , gradient methods , model discrimination , model uncertainty

Rights: Copyright © 2015 Institute of Mathematical Statistics

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Vol.43 • No. 5 • October 2015
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