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Uncertainty Quantification for Mixed...

Schmidt, Kathleen Lynn.

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Uncertainty Quantification for Mixed-Effects Models with Applications in Nuclear Engineering.

Record Type:	Electronic resources : Monograph/item
Title/Author:	Uncertainty Quantification for Mixed-Effects Models with Applications in Nuclear Engineering./
Author:	Schmidt, Kathleen Lynn.
Published:	Ann Arbor : ProQuest Dissertations & Theses, : 2016,
Description:	103 p.
Notes:	Source: Dissertation Abstracts International, Volume: 78-08(E), Section: B.
Contained By:	Dissertation Abstracts International78-08B(E).
Subject:	Applied mathematics. -
Online resource:	http://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=10583544
ISBN:	9781369622232

Uncertainty Quantification for Mixed-Effects Models with Applications in Nuclear Engineering.
Schmidt, Kathleen Lynn.

Uncertainty Quantification for Mixed-Effects Models with Applications in Nuclear Engineering. - Ann Arbor : ProQuest Dissertations & Theses, 2016 - 103 p.

Source: Dissertation Abstracts International, Volume: 78-08(E), Section: B.

Thesis (Ph.D.)--North Carolina State University, 2016.

Mixed-effects models include two types of parameters: fixed effects, which characterize the nominal parameter value for a population, and random effects, which characterize the variation amongindividual data sets. Whereas this type of model is routinely used in a variety of scientific fields, there has been little consideration for quantifying the associated uncertainties. In this dissertation, we explore techniques for performing uncertainty quantification (UQ) on mixed-effects models, focusing on the tasks of model calibration and parameter selection. To aid in model calibration, we introduce a novel version of the Delayed Rejection Adaptive Metropolis (DRAM) algorithm for mixed-effects models.Moreover, we employ this new technique to calibrate nuclear engineering models, including a parameterized version of theDittus-Boelter model. We also utilize the modified DRAM algorithm for radiation source localization in an urban setting based on detector responses. We consider this inverse problem for both stationary and mobile detectors, and we incorporate mixed-effects modeling to account for the variation in background radiation among detector locations. The parameterizations of mixed-effects models that serve to incorporate the population and individual effects are often unidentifiable in the sense that parameters are not uniquely specified by the data, but traditional parameter selection techniques are ineffective. As a result, current literature focuses on model selection, by which insensitive parameters are fixed or removed from the model.Model selection methods that employ information criteria are applicable to both linear and nonlinear mixed effects models, but such techniques are limited in that they are computationally prohibitive for large problems due to the number of possible models that must be tested. To limit the scope of possible models for model selection via information criteria, we introduce a parameter subset selection (PSS) algorithm for mixed-effects models, which orders the parameters by their significance.We provide examples to verify the effectiveness of the PSS algorithm and to test the performance of mixed-effects model selection that makes use of parameter subset selection.

ISBN: 9781369622232Subjects--Topical Terms:

2122814
Applied mathematics.

Uncertainty Quantification for Mixed-Effects Models with Applications in Nuclear Engineering.
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245 1 0 $a Uncertainty Quantification for Mixed-Effects Models with Applications in Nuclear Engineering.
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300 $a 103 p.
500 $a Source: Dissertation Abstracts International, Volume: 78-08(E), Section: B.
500 $a Adviser: Ralph Smith.
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520 $a Mixed-effects models include two types of parameters: fixed effects, which characterize the nominal parameter value for a population, and random effects, which characterize the variation amongindividual data sets. Whereas this type of model is routinely used in a variety of scientific fields, there has been little consideration for quantifying the associated uncertainties. In this dissertation, we explore techniques for performing uncertainty quantification (UQ) on mixed-effects models, focusing on the tasks of model calibration and parameter selection. To aid in model calibration, we introduce a novel version of the Delayed Rejection Adaptive Metropolis (DRAM) algorithm for mixed-effects models.Moreover, we employ this new technique to calibrate nuclear engineering models, including a parameterized version of theDittus-Boelter model. We also utilize the modified DRAM algorithm for radiation source localization in an urban setting based on detector responses. We consider this inverse problem for both stationary and mobile detectors, and we incorporate mixed-effects modeling to account for the variation in background radiation among detector locations. The parameterizations of mixed-effects models that serve to incorporate the population and individual effects are often unidentifiable in the sense that parameters are not uniquely specified by the data, but traditional parameter selection techniques are ineffective. As a result, current literature focuses on model selection, by which insensitive parameters are fixed or removed from the model.Model selection methods that employ information criteria are applicable to both linear and nonlinear mixed effects models, but such techniques are limited in that they are computationally prohibitive for large problems due to the number of possible models that must be tested. To limit the scope of possible models for model selection via information criteria, we introduce a parameter subset selection (PSS) algorithm for mixed-effects models, which orders the parameters by their significance.We provide examples to verify the effectiveness of the PSS algorithm and to test the performance of mixed-effects model selection that makes use of parameter subset selection.
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