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

2016/05/13 by Maria Konstantinou, Holger Dette, Konstantinou, Maria +1
Mathematics · #FOS: Computer and information sciences #FOS: Mathematics #Methodology (stat.ME) #Statistics Theory (math.ST) #math.ST #stat.ME #stat.TH

paper · pdf · doi:10.48550/arxiv.1605.04055

Keywords: error-in-variables models, classical errors, Bayesian optimal designs, D-optimality AMS Subject Classification: 62K05

arxiv created 2016/05/13 · arxiv updated 2016/05/16

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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