Density deconvolution with epi-splines
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Authors
Carbaugh, James C.
Subjects
Deconvolution
Probability Density Estimation
Epi-splines
Optimization
Functional Approximation
Non- Parametric Statistics
Uncertainty Quantification
Probability Density Estimation
Epi-splines
Optimization
Functional Approximation
Non- Parametric Statistics
Uncertainty Quantification
Advisors
Royset, Johannes O.
Kang, Wei
Date of Issue
2015-09
Date
Sep-15
Publisher
Monterey, California: Naval Postgraduate School
Language
Abstract
Analysts tasked with developing probability density estimates may obtain data in sets of varying quality and quantity. Often low-fidelity data contaminated with measurement error, or noise, may be abundant, but the cost of obtaining data free of these errors will limit the amount of high-fidelity data available. In such a scenario, the problem is to identify an estimate of a probability density function given scarce high-fidelity observations, knowledge of measurement errors, abundant noisy data, and available user knowl-edge of the density apart from empirical data. We solve this rich class of deconvolution problems through constrained optimization with first-order epi-splines, which are used for the first time to approximate densities to an arbitrarily high level of precision.We limit our scope to univariate densities where measurement errors are homoscedastic. Demonstrations come from a benchmark from the literature, historical medical data, and a scenario in uncertainty quantification in fluid dynamics. Results show that deconvolution via epi-splines is viable, comparable with a widely available deconvolution method, and shows potential for savings in resource budgets for data collection.
Type
Thesis
Description
Series/Report No
Department
Operations Research
Applied Mathematics
Operations Research
Applied Mathematics
Organization
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NPS Report Number
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Distribution Statement
Approved for public release; distribution is unlimited.
Rights
This publication is a work of the U.S. Government as defined in Title 17, United States Code, Section 101. Copyright protection is not available for this work in the United States.