Banks, H. T.; Holm, Kathleen J.; Kappel, Franz A Monte Carlo based analysis of optimal design criteria. (English) Zbl 1279.93056 J. Inverse Ill-Posed Probl. 20, No. 1, 1-37 (2012). Summary: Optimal design methods (designed to choose optimal sampling distributions through minimization of a specific cost function related to the resulting error in parameter estimates) for inverse or parameter estimation problems are considered. We compare a recent design criteria, SE-optimal design (standard error optimal design) with the more traditional D-optimal and E-optimal designs. The optimal sampling distributions from each design are used to compute and compare standard errors; here the standard errors for parameters are computed using the optimal mesh along with Monte Carlo simulations as compared to asymptotic theory based standard errors. We illustrate ideas with two examples: the Verhulst-Pearl logistic population model and the standard harmonic oscillator model. MSC: 93B51 Design techniques (robust design, computer-aided design, etc.) 62B10 Statistical aspects of information-theoretic topics 62B15 Theory of statistical experiments 62G08 Nonparametric regression and quantile regression 62H12 Estimation in multivariate analysis 90C31 Sensitivity, stability, parametric optimization 65C05 Monte Carlo methods Keywords:Optimal design methods; least squares inverse problems; Fisher information matrix; D-optimal; E-optimal; SE-optimal; Monte Carlo analysis PDFBibTeX XMLCite \textit{H. T. Banks} et al., J. Inverse Ill-Posed Probl. 20, No. 1, 1--37 (2012; Zbl 1279.93056) Full Text: DOI Link