A Monte Carlo based analysis of optimal design criteria

H. T. Banks, Kathleen J. Holm, Franz Kappel
2012 Journal of Inverse and Ill-Posed Problems  
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 [8]) 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
more » ... d 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 [10] and the standard harmonic oscillator model [10] . Public reporting burden for the collection of information is estimated to average 1 hour per response, including the time for reviewing instructions, searching existing data sources, gathering and maintaining the data needed, and completing and reviewing the collection of information. Send comments regarding this burden estimate or any other aspect of this collection of information, including suggestions for reducing this burden, to Washington Headquarters Services, Directorate for Information Operations and Reports, 1215 Jefferson Davis Highway, Suite 1204, Arlington VA 22202-4302. Respondents should be aware that notwithstanding any other provision of law, no person shall be subject to a penalty for failing to comply with a collection of information if it does not display a currently valid OMB control number.
doi:10.1515/jip-2012-0201 fatcat:ct43aqvvxjcgdcu5kpsigt7fsq