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

TL;DR

This paper develops an approximate Bayesian $D$-optimal design theory for non-linear regression models with measurement errors, providing explicit designs for common models and comparing them to traditional methods.

Contribution

It introduces a new Bayesian $D$-optimal design framework for error-in-variables models, with explicit characterizations for several nonlinear models and practical comparisons.

Findings

Explicit Bayesian $D$-optimal saturated designs for Michaelis-Menten, Emax, and exponential models.

Comparison of Bayesian $D$-optimal designs with locally $D$-optimal designs.

Demonstration of the robustness of Bayesian designs through data examples.

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.