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

Gianluca Frasso (), Jonathan Jaeger and Philippe Lambert
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Gianluca Frasso: Université de Liège
Jonathan Jaeger: Nestlé Research Center
Philippe Lambert: Université de Liège

AStA Advances in Statistical Analysis, 2016, vol. 100, issue 3, No 2, 259-287

Abstract: 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.

Keywords: Linear partial differential equations; Parameter estimation; Penalized tensor B-spline smoothing; State conditions (search for similar items in EconPapers)
Date: 2016
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Citations: View citations in EconPapers (2)

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DOI: 10.1007/s10182-015-0257-5

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