Optimal Design of Experiments for Implicit Models
成果类型：
Article
署名作者：
Duarte, Belmiro P. M.; Atkinson, Anthony C.; Granjo, Jose F. O.; Oliveira, Nuno M. C.
署名单位：
Instituto Politecnico de Coimbra (IPC); Universidade de Coimbra; Universidade de Coimbra; University of London; London School Economics & Political Science
刊物名称：
JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION
ISSN/ISSBN：
0162-1459
DOI：
10.1080/01621459.2020.1862670
发表日期：
2022
页码：
1424-1437
关键词：
programming based algorithm
nonoptimal support-points
vapor-liquid-equilibrium
minimax optimal designs
parameter-estimation
multiplicative algorithms
numerical-methods
nonlinear models
optimization
CONVERGENCE
摘要：
Explicit models representing the response variables as functions of the control variables are standard in virtually all scientific fields. For these models, there is a vast literature on the optimal design of experiments (ODoE) to provide good estimates of the parameters with the use of minimal resources. Contrarily, the ODoE for implicit models is more complex and has not been systematically addressed. Nevertheless, there are practical examples where the models relating the response variables, the parameters and the factors are implicit or hardly convertible into an explicit form. We propose a general formulation for developing the theory of the ODoE for implicit algebraic models to specifically find continuous local designs. The treatment relies on converting the ODoE problem into an optimization problem of the nonlinear programming (NLP) class which includes the construction of the parameter sensitivities and the Cholesky decomposition of the Fisher information matrix. The NLP problem generated has multiple local optima, and we use global solvers, combined with an equivalence theorem from the theory of ODoE, to ensure the global optimality of our continuous optimal designs. We consider D- and A-optimality criteria and apply the approach to five examples of practical interest in chemistry and thermodynamics. for this article are available online.