Uncertainty Quantification for Nonparametric Estimation of Probability Measures and Delay Differential Equations Driven by Colored Noise
Technical Report,15 Jul 2015,14 Jul 2018
North Carolina State University Raleigh United States
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We have continued our joint investigations on the identification of thermal degradation using probabilistic models in reflectance spectroscopy. These were carried in continued collaboration with scientists at AFRLMaterials State Awareness and Supportability Branch, Air Force Research Lab, WPAFB 45433, USA lead by Amanda K. Criner. Reflectance spectroscopy obtained from a thermally treated silicon nitride carbon based ceramic matrix composite was used to quantity the oxidation products SiO2 and SiN. Our estimation results indicate a distinguishable increase in the SiO2 present in the samples which were heat treated for 100 hours compared to 10 hours. In our consideration of several other problems of interest to DOD, we discuss two other problems where aggregate data is often mistreated as individual data. The problems, PBPK modeling and Food Chemistry Modlels and possible improvements in the associated inverse problems are discussed and summarized in separate papers.We propose in 11 a novel method which accounts for inter-individual variability in experiments where only unidentified individual data is available. Both parametric and nonparametric methods for estimating the distribution of parameters which vary among individuals are developed. These methods are illustrated using both simulated data, and data taken from a physiological experiment. Taking the approach outlined in 11 results in more accurate quantification of the uncertainty attributed to interindividual variability.
- Statistics and Probability