Generalized sensitivities and optimal experimental design

被引:37
作者
Banks, H. T. [1 ]
Dediu, Sava [2 ]
Ernstberger, Stacey L. [3 ]
Kappel, Franz [4 ]
机构
[1] N Carolina State Univ, Ctr Res Sci Computat, Raleigh, NC 27695 USA
[2] Campbell & Co, Baltimore, MD 21209 USA
[3] LaGrange Coll, Dept Math, La Grange, GA 30240 USA
[4] Graz Univ, Inst Math & Sci Computat, A-8010 Graz, Austria
来源
JOURNAL OF INVERSE AND ILL-POSED PROBLEMS | 2010年 / 18卷 / 01期
关键词
Least squares inverse problems; sensitivity and generalized sensitivity functions; Fisher information matrix; design of experiments;
D O I
10.1515/JIIP.2010.002
中图分类号
O29 [应用数学];
学科分类号
070104 ;
摘要
We consider the problem of estimating amodeling parameter theta using a weighted least squares criterion J(d) (y, theta) = Sigma(n)(i=1) 1/sigma(t(i))(2)(y(t(i))-f(t(i), theta))(2) for given data y by introducing an abstract framework involving generalized measurement procedures characterized by probability measures. We take an optimal design perspective, the general premise (illustrated via examples) being that in any data collected, the information content with respect to estimating theta may vary considerably from one time measurement to another, and in this regard some measurements may be much more informative than others. We propose mathematical tools which can be used to collect data in an almost optimal way, by specifying the duration and distribution of time sampling in the measurements to be taken, consequently improving the accuracy (i.e., reducing the uncertainty in estimates) of the parameters to be estimated. We recall the concepts of traditional and generalized sensitivity functions and use these to develop a strategy to determine the "optimal" final time T for an experiment; this is based on the time evolution of the sensitivity functions and of the condition number of the Fisher information matrix. We illustrate the role of the sensitivity functions as tools in optimal design of experiments, in particular in finding "best" sampling distributions. Numerical examples are presented throughout to motivate and illustrate the ideas.
引用
收藏
页码:25 / 83
页数:59
相关论文
共 34 条
[1]   SENSITIVITY ANALYSIS OF DISCRETE STRUCTURAL SYSTEMS [J].
ADELMAN, HM ;
HAFTKA, RT .
AIAA JOURNAL, 1986, 24 (05) :823-832
[2]  
[Anonymous], 1993, OPTIMAL DESIGN EXPT
[3]  
[Anonymous], 2000, WILEY SERIES PROBABI
[4]  
[Anonymous], 1994, Theory of Sensitivity in Dynamic Systems
[5]  
[Anonymous], 2005, PARAMETER ESTIMATION, DOI DOI 10.1016/C2015-0-02458-3
[6]  
Bai P, 2007, MATH BIOSCI ENG, V4, P373
[7]  
Banks HT, 2007, MATH BIOSCI ENG, V4, P403
[8]  
Banks H. T., 2005, Journal of Inverse and ILL-Posed Problems, V13, P103, DOI 10.1163/1569394053978515
[9]  
Banks H. T., 2007, Journal of Inverse and ILL-Posed Problems, V15, P683, DOI 10.1515/JIIP.2007.038
[10]  
Banks H.T., 2006, J. Inv. Ill-posed Problems, V15, P1