Estimating varying coefficients for partial differential equation models

Biometrics. 2017 Sep;73(3):949-959. doi: 10.1111/biom.12646. Epub 2017 Jan 11.

Abstract

Partial differential equations (PDEs) are used to model complex dynamical systems in multiple dimensions, and their parameters often have important scientific interpretations. In some applications, PDE parameters are not constant but can change depending on the values of covariates, a feature that we call varying coefficients. We propose a parameter cascading method to estimate varying coefficients in PDE models from noisy data. Our estimates of the varying coefficients are shown to be consistent and asymptotically normally distributed. The performance of our method is evaluated by a simulation study and by an empirical study estimating three varying coefficients in a PDE model arising from LIDAR data.

Keywords: B-splines; Dynamical models; Inverse problems; LIDAR data; Parameter cascading; System identification.

MeSH terms

  • Computer Simulation
  • Models, Theoretical*