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 non-linear regression models with covariates subject to measurement errors. Both maximum likelihood and least squares estimation are st...

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Bibliographic Details
Main Authors Konstantinou, Maria, Dette, Holger
Format Journal Article
LanguageEnglish
Published 13.05.2016
Subjects
Mathematics - Statistics Theory
Statistics - Methodology
Statistics - Theory
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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 non-linear 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 to several other designs, including the corresponding locally $D$-optimal designs, which are often used in practice.
DOI:10.48550/arxiv.1605.04055