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On the reliability of parameter estimates in a set of simultaneous nonlinear differential equations

โœ Scribed by G. Emig; L.H. Hosten

Publisher
Elsevier Science
Year
1974
Tongue
English
Weight
684 KB
Volume
29
Category
Article
ISSN
0009-2509

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โœฆ Synopsis

The evaluation of the different measures of statistical reliability for parameters in strongly nonlinear differential equations has been investigated. As an example the mathematical model for the description of the complex methanol oxidation has been used. It is shown that the individual confidence intervals, as well as the joint confidence hyperellipsoid, both based upon the assumption that the model behaves sufficiently linear in the vicinity of the least squares estimates, give a distorted picture about the reliability of the parameter estimates. The 'exact' joint confidence region appears to be strongly unsymmetrical. However, the construction of this region is subject to limits because of the large amount of computing effort and difficulties in analyzing and presenting results in the case that the dimension of the parameter space exceeds four.

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