Sequential Model-Based A-Optimal Design of Experiments When the Fisher Information Matrix Is Noninvertible

2018 ◽  
Vol 58 (3) ◽  
pp. 1244-1261 ◽  
Author(s):  
Ali Shahmohammadi ◽  
Kimberley B. McAuley
Keyword(s):  
Optimal Design ◽  
Design Of Experiments ◽  
Fisher Information ◽  
Fisher Information Matrix ◽  
Information Matrix ◽  
Sequential Model ◽  
Optimal Design Of Experiments ◽  
Model Based

scholarly journals Optimal design for population pk/pd models

2012 ◽  
Vol 51 (1) ◽  
pp. 115-130
Author(s):  
Sergei Leonov ◽  
Alexander Aliev
Keyword(s):  
Optimal Design ◽  
Fisher Information ◽  
Fisher Information Matrix ◽  
Information Matrix ◽  
Optimal Sampling ◽  
Design Algorithm ◽  
Sampling Schemes ◽  
Population Pk ◽  
Different Types

ABSTRACT We provide some details of the implementation of optimal design algorithm in the PkStaMp library which is intended for constructing optimal sampling schemes for pharmacokinetic (PK) and pharmacodynamic (PD) studies. We discuss different types of approximation of individual Fisher information matrix and describe a user-defined option of the library.

scholarly journals Optimal Design of Experiments for Liquid–Liquid Equilibria Characterization via Semidefinite Programming

Processes ◽  
2019 ◽  
Vol 7 (11) ◽  
pp. 834 ◽  
Author(s):  
Belmiro P.M. Duarte ◽  
Anthony C. Atkinson ◽  
José F.O. Granjo ◽  
Nuno M.C. Oliveira
Keyword(s):  
Optimal Design ◽  
Design Of Experiments ◽  
Semidefinite Programming ◽  
Information Matrix ◽  
Ternary Systems ◽  
Initial Mixture ◽  
Optimality Criteria ◽  
Optimal Design Of Experiments ◽  
Optimization Formulation ◽  
Considerable Work

Liquid–liquid equilibria (LLE) characterization is a task requiring considerable work and appreciable financial resources. Notable savings in time and effort can be achieved when the experimental plans use the methods of the optimal design of experiments that maximize the information obtained. To achieve this goal, a systematic optimization formulation based on Semidefinite Programming is proposed for finding optimal experimental designs for LLE studies carried out at constant pressure and temperature. The non-random two-liquid (NRTL) model is employed to represent species equilibria in both phases. This model, combined with mass balance relationships, provides a means of computing the sensitivities of the measurements to the parameters. To design the experiment, these sensitivities are calculated for a grid of candidate experiments in which initial mixture compositions are varied. The optimal design is found by maximizing criteria based on the Fisher Information Matrix (FIM). Three optimality criteria (D-, A- and E-optimal) are exemplified. The approach is demonstrated for two ternary systems where different sets of parameters are to be estimated.

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