Bayesian D‐optimal designs for error‐in‐variables models‡. (10th February 2017)

• Record Type: Journal Article
• Authors: Konstantinou, Maria; Dette, Holger
• Other Names: Soyer Refik guestEditor.; Verdinelli Isabella guestEditor.
• Is Part Of: Applied stochastic models in business and industry. Volume 33:Number 3(2017)
• Page Start: 269
• Page End: 281
• Publication Date: 2017-02-10
• Subjects: error‐in‐variables models -- classical errors -- Bayesian optimal designs -- D‐optimality; Stochastic analysis -- Periodicals; Stochastic processes -- Periodicals; Business mathematics -- Periodicals; Finance -- Mathematical models -- Periodicals; Industrial management -- Mathematical models -- Periodicals; 338.00151923
• DOI: 10.1002/asmb.2226
• Languages: English
• ISSNs: 1524-1904

Abstract

Abstract : Bayesian optimality criteria provide a robust design strategy to parameter misspecification. We develop an approximate design theory for Bayesian D ‐optimality for nonlinear regression models with covariates subject to measurement errors. Both maximum likelihood and least squares estimation are studied, and explicit characterisations of the Bayesian D ‐optimal saturated designs for the Michaelis–Menten, Emax and exponential regression models are provided. Several data examples are considered for the case of no preference for specific parameter values, where Bayesian D ‐optimal saturated designs are calculated using the uniform prior and compared with several other designs, including the corresponding locally D ‐optimal designs, which are often used in practice. Copyright © 2017 John Wiley & Sons, Ltd.