Comparison of Optimal Design Methods in Inverse Problems
NORTH CAROLINA STATE UNIV AT RALEIGH CENTER FOR RESEARCH IN SCIENTIFIC COMPUTATION
Pagination or Media Count:
Typical optimal design methods for inverse or parameter estimation problems are designed to choose optimal sampling distributions through minimization of a specific cost function related to the resulting error in parameter estimates. It is hoped that the inverse problem will produce parameter estimates with increased accuracy using data from the optimal sampling distribution. We present a new Prohorov metric based theoretical framework that permits one to treat succinctly and rigorously any optimal design criteria based on the Fisher Information Matrix FIM. A fundamental approximation theory is also included in this framework. A new optimal design SE-optimal design standard error optimal design, is then introduced in the context of this framework. We compare this new design criteria 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 the standard errors for parameters are computed using asymptotic theory or bootstrapping and the optimal mesh. We use three examples to illustrate ideas the Verhulst-Pearl logistic population model 7, the standard harmonic oscillator model 7 and a popular glucose regulation model 10, 13, 21.
- Theoretical Mathematics