Statistical parameter estimation of dielectric materials using MCMC for nonlinear hierarchical models

Abstract

This paper is concerned with material interrogation methods for homogeneous dielectric materials using statistical inversion. Frequency dispersions for homogeneous dielectric materials can be described by a classical Lorentz model. Taking into account that the reflection coefficients are indirectly measurable, the signal response model is given by a complex reflectance at the interface between free space and the dielectric medium. The problem considered here is to quantify uncertainties of the estimated dielectric parameters from the measurements obtained by a reflective interferometer. A computational method using Hamiltonian Monte Carlo sampling based on nonlinear hierarchical models is tested.