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

Abstract

Bayesian optimality criteria provide a robust design strategy to parameter misspecification. We develop an approximate design theory for Bayesian D-optimality for nonlinear 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.

Simple Method for Incorporating Prior Parameter Information during Model-Based D-Optimal Design of Experiments for Multi-Response Chemical Process Models

“…For 79 NM reaction of acetic acid with isobutanol to produce isobutyl acetate and acetic acid Vivaldo-Lima et al 68 LE particle size distribution in suspension polymerization Omidbakhsh et al 69 LE hydrogen peroxide formulations Nabifar et al 59,70−72 LE nitroxide-mediated radical polymerization of styrene. Terejanu et al 75 NM nitridation of graphite Huan and Marzouk 80 NM shock-tube ignition of a mixture of hydrogen and oxygen Kalyanaraman et al 76 NM adsorption of carbon dioxide from flue gas using amine sorbents loaded hollow fibers Ryan et al 77,78 NM pharmacokinetics of drugs in horses and sheep Scott et al 73 LE production of nitrile butadiene rubber by emulsion copolymerization Bisetti et al 81 NM shock-tube experiments for step in hydrocarbon combustion Konstantinou and Dette 50 NM Michaelis−Menten kinetics Vohra et al 82 NM calibration of diffusivity in reactive multilayers Kalyanaraman et al 83 NM adsorption isotherm models for carbon dioxide capture using UiO-66 Walker et al 85 NM chemical reactor examples involving reaction equilibrium, adsorption and a catalytic membrane Kusumo et al 84 NM rxothermic esterification of priopionic anhydride example, Ryan et al 77 used the Metropolis−Hastings algorithm to determine optimal experimental conditions using Bayesian D-optimal design. They started by generating a candidate design, along with initial values for the parameters and associated simulated data.…”

“…In nonlinear models, the FIM can be approximated by linearizing the model around some nominal parameter values. If the nominal parameter values are noticeably different from the true parameter values, settings selected using MBDoE may lead to not-very-informative experimental data. ,,,,,,, If the modeler has little confidence in the initial parameter values, sequential design of experiments can offer robustness against poor initial guesses of the parameter values. Using a sequential MBDoE approach, where new experiments are designed in several stages, permits updating of parameters to more reliable values after each round of experimentation. ,,,,, …”