Modelling and estimating uncertainty in parameter estimation
Open Access
- 8 January 2001
- journal article
- Published by IOP Publishing in Inverse Problems
- Vol. 17 (1) , 95-111
- https://doi.org/10.1088/0266-5611/17/1/308
Abstract
In this paper we discuss questions related to reliability or variability of estimated parameters in deterministic least-squares problems. By viewing the parameters for the inverse problem as realizations for a random variable we are able to use standard results from probability theory to formulate a tractable probabilistic framework to treat this uncertainty. We discuss method stability and approximate problems and are able to show convergence of solutions of the approximate problems to those of the original problem. The efficacy of our approach is demonstrated in numerical examples involving estimation of constant parameters in differential equations.Keywords
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