Optimal experimental design

Abstract

estimators). He found that the points of the optimum design lie on the least ellipsoid which contains the design region, an insight further developed by Silvey and Titterington. 4 Guest 5 shows that, for the G-optimal design for the polynomial of order m, support points are roots of the derivatives of the (m − 1)th Legendre polynomial plus end points. Hoel 6 constructed D-optimal designs and commented that his designs are same as those of Guest. Two years later, Kiefer and Wolfowitz 7,8 proved the equivalence of G-and D-optimality and have started to treat experimental design as a particular area of convex optimization theory on the space of probability measures. The later direction is explored by Karlin and Studden 9 and by Fedorov. 10,11 Chernoff 12,13 went beyond the linear regression introducing locally optimal designs. Box and Lucas 14 use some of his ideas to find locally D-optimum designs for the single response of nonlinear models arising in chemical kinetics. Box and Hunter 15 develop an adaptive strategy in the Bayesian setting for updating the design one trial at a time as observations become available. Closely related approach based on the use of the Shannon information measure was initiated by Lindley 16 and elaborated by Fedorov and Pázman, 17 Caselton and Zidek, 18 Caselton et al. 19 , and recently revisited by Sebastiani and Wynn. 20 More on design for nonlinear models mainly in the Bayesian setting can be found in the studies of Ermakov, 21 Pilz, 22 Chaloner and Verdinelli. 23 Box and Hunter 15 show that an observation added at the point, where the variance of prediction using the linearized model is a maximum, is the most informative in the D-criterion sense. It is a short step to consider the same adaptive design generation for linear models, into which the parameter values do not enter, and so to obtain the (first order) algorithm for the iterative construction; see Fedorov, 11 Wynn,24 Fedorov and Malyutov. 25 These results evolved, cf., for instance, Atwood, 26 Fedorov and Uspensky, 27Vo lu me 2,

Optimal designs for pairwise calculation: An application to free energy perturbation in minimizing prediction variability

“…In practices, D‐optimal designs are best suited to minimize average MSE of while A‐optimal designs are best suited to minimize average MSE of . In this work, both D‐optimal and A‐optimal designs are obtained through the Fedorov‐exchange algorithm …”

Data-Driven Measurement Models for Active Localization in Sparse Environments

“…Lemma 1: The expected information of an environment measurement model with respect to a transformation g(θ) is given by (7) where I(s) = ∂Γ ∂s T Σ −1 ∂Γ ∂s is the Fisher information with respect to the search space of the robot, p(θ) is the belief of the parameter θ, and Doptimality [12,19] (determinant) is chosen a measure of information.…”

A statistical perspective on oxygen diffusion and surface exchange experiments: Sensitivity analysis, parameter estimation and robust optimal experimental design

“…Typically ϕ(V) indicates some geometrical feature of the confidence region itself and in the literature various criteria are utilized [38,40] each corresponding to specific geometrical properties of the asymptotic confidence ellipsoid, see Fig. 2.…”