A stochastic programming approach for the Bayesian experimental design of nonlinear systems. (2nd January 2015)

• Record Type: Journal Article
• Authors: Laínez-Aguirre, José M.; Mockus, Linas; Reklaitis, Gintaras V.
• Is Part Of: Computers & chemical engineering. Volume 72(2015)
• Page Start: 312
• Page End: 324
• Publication Date: 2015-01-02
• Subjects: Design of experiments -- Stochastic programming -- NLP -- MINLP; Chemical engineering -- Data processing -- Periodicals; 660.0285
• DOI: 10.1016/j.compchemeng.2014.06.006
• Languages: English
• ISSNs: 0098-1354

Abstract

Abstract: Several approaches for the Bayesian design of experiments have been proposed in the literature (e.g., D-optimal, E-optimal, A-optimal designs). Most of these approaches assume that the available prior knowledge is represented by a normal probability distribution. In addition, most nonlinear design approaches involve assuming normality of the posterior distribution and approximate its variance using the expected Fisher information matrix. In order to be able to relax these assumptions, we address and generalize the problem by using a stochastic programming formulation. Specifically, the optimal Bayesian experimental design is mathematically posed as a three-stage stochastic program, which is then discretized using a scenario based approach. Given the prior probability distribution, a Smolyak rule (sparse-grids) is used for the selection of scenarios. Two retrospective case studies related to population pharmacokinetics are presented. The benefits and limitations of the proposed approach are demonstrated by comparing the numerical results to those obtained by implementing a more exhaustive experimentation and the D-optimal design.