The Annals of Statistics

Bayesian $T$-optimal discriminating designs

Holger Dette, Viatcheslav B. Melas, and Roman Guchenko

Full-text: Open access

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.

Article information

Source
Ann. Statist., Volume 43, Number 5 (2015), 1959-1985.

Dates
Received: December 2014
Revised: February 2015
First available in Project Euclid: 3 August 2015

Permanent link to this document
https://projecteuclid.org/euclid.aos/1438606850

Digital Object Identifier
doi:10.1214/15-AOS1333

Mathematical Reviews number (MathSciNet)
MR3375873

Zentralblatt MATH identifier
1331.62382

Subjects
Primary: 62K05: Optimal designs

Keywords
Design of experiment Bayesian optimal design model discrimination gradient methods model uncertainty

Citation

Dette, Holger; Melas, Viatcheslav B.; Guchenko, Roman. Bayesian $T$-optimal discriminating designs. Ann. Statist. 43 (2015), no. 5, 1959--1985. doi:10.1214/15-AOS1333. https://projecteuclid.org/euclid.aos/1438606850


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