Bayesian $D$-optimal designs for error-in-variables models

Maria Konstantinou; Holger Dette

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arXiv · 1605.04055

Bayesian $D$-optimal designs for error-in-variables models

Maria Konstantinou·Holger Dette

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Abstract

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.

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Maria Konstantinou, Holger Dette. 2016-05-13. Bayesian $D$-optimal designs for error-in-variables models. https://arxiv.org/abs/1605.04055

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