@article{banks_holm_kappel_2012, title={A Monte Carlo based analysis of optimal design criteria}, volume={20}, ISSN={["1569-3945"]}, DOI={10.1515/jip-2012-0201}, abstractNote={Abstract. 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.}, number={1}, journal={JOURNAL OF INVERSE AND ILL-POSED PROBLEMS}, author={Banks, H. T. and Holm, Kathleen J. and Kappel, Franz}, year={2012}, month={Mar}, pages={1–37} } @article{banks_holm_kappel_2011, title={Comparison of optimal design methods in inverse problems}, volume={27}, number={7}, journal={Inverse Problems}, author={Banks, H. T. and Holm, K. and Kappel, F.}, year={2011} } @article{banks_holm_robbins_2010, title={Standard error computations for uncertainty quantification in inverse problems: Asymptotic theory vs. bootstrapping}, volume={52}, ISSN={["0895-7177"]}, DOI={10.1016/j.mcm.2010.06.026}, abstractNote={We computationally investigate two approaches for uncertainty quantification in inverse problems for nonlinear parameter dependent dynamical systems. We compare the bootstrapping and asymptotic theory approaches for problems involving data with several noise forms and levels. We consider both constant variance absolute error data and relative error which produces non-constant variance data in our parameter estimation formulations. We compare and contrast parameter estimates, standard errors, confidence intervals, and computational times for both bootstrapping and asymptotic theory methods.}, number={9-10}, journal={MATHEMATICAL AND COMPUTER MODELLING}, author={Banks, H. T. and Holm, Kathleen and Robbins, Danielle}, year={2010}, month={Nov}, pages={1610–1625} }