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

Abstract

Bayesian optimality criteria provide a robust design strategy to parameter misspeci- fication. 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.