Decomposition of permittivity contributions from reflectance using mechanism models

Abstract

Abstract-In this paper, we investigate the properties of a complex nonmagnetic material through the reflectance, where the permittivity is described by a mechanism model in which an unknown probability measure is placed on the model parameters. Specifically, we consider whether or not this unknown probability measure can be determined from the reflectance or the derivatives of the reflectance, and we also investigate the effect of measurement noise on the estimation. The numerical results demonstrate that if only the reflectance can be observed, then the distribution form cannot be recovered even in the case where the measurement noise level is small. However, if both the reflectance and the derivative of the reflectance can be observed, then the estimated distribution is reasonably close to the true one even in the case where the measurement noise level is relatively high.

Asymptotic Properties of Probability Measure Estimators in a Nonparametric Model

“…[4,8,9,10,15]). However, it was demonstrated in [5] that if the sought-after probability measure is absolutely continuous, then the spline-based approximation methods converge much faster than do the Dirac measure approximation methods (in terms of the value of M).…”

“…Equation (1.1) is often referred to as a nonparametric model (a model with all the unknown parameters being in an infinite-dimensional parameter space) in the statistics literature. Such models are motivated by a number of applications arising in biology and physics, for example, in modeling mosquitofish populations [9] and shrimp populations [6], in wave propagation in biotissue [15], in modeling of a complex nonmagnetic dielectric materials [4,10], and in HIV cellular models [3]. Here we only elaborate one of the motivating examples, a recent project investigated by our group.…”