Standard errors and confidence intervals in inverse problems: sensitivity and associated pitfalls. (English) Zbl 1124.34002
Summary: We review the asymptotic theory for standard errors in classical ordinary least squares inverse or parameter estimation problems involving general nonlinear dynamical systems where sensitivity matrices can be used to compute the asymptotic covariance matrices. We discuss possible pitfalls in computing standard errors in regions of low parameter sensitivity and/or near a steady state solution of the underlying dynamical system.
MSC:
| 34A55 | Inverse problems involving ordinary differential equations |
| 65L09 | Numerical solution of inverse problems involving ordinary differential equations |
Keywords:
inverse problems; standard errors; dynamical systems; parameter estimation; sensitivity matrices; asymptotic theoryReferences:
| [1] | Adelman H. M., A.I.A.A. Journal 24 pp 823– (1986) |
| [2] | DOI: 10.1007/s00285-004-0299-x · Zbl 1083.92025 · doi:10.1007/s00285-004-0299-x |
| [3] | DOI: 10.1515/1569394053978515 · doi:10.1515/1569394053978515 |
| [4] | DOI: 10.1016/S0025-5564(02)00218-3 · Zbl 1011.92037 · doi:10.1016/S0025-5564(02)00218-3 |
| [5] | DOI: 10.1016/j.jmaa.2005.09.084 · Zbl 1103.93025 · doi:10.1016/j.jmaa.2005.09.084 |
| [6] | DOI: 10.2307/1403510 · Zbl 0825.62860 · doi:10.2307/1403510 |
| [7] | DOI: 10.1214/aoms/1177697731 · Zbl 0193.47201 · doi:10.1214/aoms/1177697731 |
| [8] | Kot M., Cambridge pp 7– (2001) |
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