Bayesian D‐optimal designs for error‐in‐variables models

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 studi...

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Bibliographic Details
Published inApplied stochastic models in business and industry Vol. 33; no. 3; pp. 269 - 281
Main Authors Konstantinou, Maria, Dette, Holger
Format Journal Article
LanguageEnglish
Published Bognor Regis Wiley Subscription Services, Inc 01.05.2017
Subjects
Bayesian analysis
Bayesian optimal designs
classical errors
Design parameters
D‐optimality
Economic models
error‐in‐variables models
Least squares method
Maximum likelihood estimation
Optimality criteria
Optimization
Regression analysis
Robust design
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Summary: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.
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ISSN:1524-1904
1526-4025
DOI:10.1002/asmb.2226