Estimation of dielectric parameters in composite materials using stochastic Galerkin method

This paper is concerned with uncertain qualifications of resonance wavenumbers of composite dielectric materials. The relative permittivity with a single resonance is described by the Lorentz model. Taking into account that the reflection coefficents indirectly measurable, the signal response model is given by a complex reflectance at the interface between free space and a dielectric medium. Our inverse problem is then formulated for estimating the resonance wavenumbers under noisy observations. Applying stochastic Galerkin method to the associated likelihood ratio, an approximate posteriori function is derived. A Bayesian inversion of resonance wavenumbers is implemented with the aid of the stochastic algorithm based on Hamiltonian Monte Carlo method.