Parameter estimation and inference in dynamic systems described by linear partial differential equations

Frasso, Gianluca;Jaeger, Jonathan;Lambert, Philippe
(2016) A St A - Advances in Statistical Analysis — Vol. 100, n° 3, p. 259-287 (2016)

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Abstract
Differential equations (DEs) are commonly used to describe dynamic systems evolving in one (ordinary differential equations or ODEs) or in more than one dimensions (partial differential equations or PDEs). In real data applications, the parameters involved in the DE models are usually unknown and need to be estimated from the available measurements together with the state function. In this paper, we present frequentist and Bayesian approaches for the joint estimation of the parameters and of the state functions involved in linear PDEs.We also propose two strategies to include state (initial and/or boundary) conditions in the estimation procedure.We evaluate the performances of the proposed strategy through simulated examples and a real data analysis involving (known and necessary) state conditions.
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Frasso, G., Jaeger, J., & Lambert, P. (2016). Parameter estimation and inference in dynamic systems described by linear partial differential equations. A St A - Advances in Statistical Analysis, 100(3), 259-287. https://doi.org/10.1007/s10182-015-0257-5 (Original work published 2016)