| Contents |
| In this presentation we investigate the properties of materials through the reflectivity, where the permittivity is described by the
Lorentz model in which an unknown probability measure is placed on the model parameters. We summarize the computational and theoretical methodology (consistency of the probability measure estimator, the bias due to the approximation and the point-wise asymptotic normality of the
approximated probability measure estimator) developed by our group in the past two decades for nonparametric estimation of probability measures using a least-squares method under the {\underline{\em Prohorov Metric Framework}}. We demonstrate the feasibility of our proposed methods by numerical results.
\medskip\noindent{\bf References.}\newline
[1] H.T. Banks, J. Catenacci, S. Hu, and Z.R. Kenz, Decomposition of permittivity contributions from reflectance using mechanism models, Tech. Report CRSC-TR13-11, N. C. State University, Raleigh, NC, September, 2013; {\em Proceedings 2014 American Control Conference}, Portland, OR.
[2] H. T. Banks, S. Hu, and W. Clayton Thompson, {\em Modeling and Inverse Problems in the Presence of Uncertainty}, CRC Press/Taylor and Frances, Boca Raton, April, 2014. |
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