{"id":{"repo_id":"ncsu","oai_identifier":"oai:repository.lib.ncsu.edu:1840.16/5401"},"canonical_url":"https://search.dev.ndltd.org/etd/ncsu/oai:repository.lib.ncsu.edu:1840.16/5401","repository":{"repo_id":"ncsu","name":"North Carolina State University","base_url":"https://repository.lib.ncsu.edu/server/oai/request"},"display":{"title":"Uncertainty Quantification in the Estimation of Probability Distributions on Parameters in Size-Structured Population Models","abstract":"We consider ordinary least squares (OLS) parameter estimation problems in which the underlying dynamics are described by partial differential equations and the unknown parameter of interest is a probability distribution describing the variability of growth rates across a size-structured population. The focus of our work is the development of an inverse problem computational methodology for the estimation of functional parameters in the presence of (model and data) uncertainty. Since this optimization problem involves both an infinite-dimensional state space and an infinite-dimensional parameter space, computationally efficient approximation methods for both parametric and non-parametric versions of the OLS inverse problem are developed and discussed. The approximation methods that we present are applicable to a variety of inverse problems, including Type II problems in which only aggregate or population level longitudinal data is available. We compare computational and statistical results of a delta function approximation method, a spline based approximation method, and a standard parametric OLS formulation. The latter uses an a priori probability distribution in the inverse problem for estimation of distributions of growth rates in size-structured marine populations. After summarizing the underlying theoretical framework, we present several numerical examples as validation of the theory. Convergence as well as sensitivity of the estimates with respect to noise in the data is discussed for both approximation methods. A computational framework for quantification of uncertainty associated with the estimated parameters is given and sample numerical findings are presented. We demonstrate how to construct \"functional\" confidence bands that will aid in quantifying the uncertainty in estimated probability distributions by extending the standard asymptotic theory for finite-dimensional OLS estimators. Using our inverse problem methodology, we present results for the estimation of growth rate distributions in size-structured marine populations illustrating the strengths and weaknesses associated with the three different computational schemes.","abstract_html":"We consider ordinary least squares (OLS) parameter estimation problems in which the underlying dynamics are described by partial differential equations and the unknown parameter of interest is a probability distribution describing the variability of growth rates across a size-structured population. The focus of our work is the development of an inverse problem computational methodology for the estimation of functional parameters in the presence of (model and data) uncertainty. Since this optimization problem involves both an infinite-dimensional state space and an infinite-dimensional parameter space, computationally efficient approximation methods for both parametric and non-parametric versions of the OLS inverse problem are developed and discussed. The approximation methods that we present are applicable to a variety of inverse problems, including Type II problems in which only aggregate or population level longitudinal data is available. We compare computational and statistical results of a delta function approximation method, a spline based approximation method, and a standard parametric OLS formulation. The latter uses an a priori probability distribution in the inverse problem for estimation of distributions of growth rates in size-structured marine populations. After summarizing the underlying theoretical framework, we present several numerical examples as validation of the theory. Convergence as well as sensitivity of the estimates with respect to noise in the data is discussed for both approximation methods. A computational framework for quantification of uncertainty associated with the estimated parameters is given and sample numerical findings are presented. We demonstrate how to construct "functional" confidence bands that will aid in quantifying the uncertainty in estimated probability distributions by extending the standard asymptotic theory for finite-dimensional OLS estimators. Using our inverse problem methodology, we present results for the estimation of growth rate distributions in size-structured marine populations illustrating the strengths and weaknesses associated with the three different computational schemes.","abstract_has_math":false,"creators":["Davis, Jimena Lamanda"],"institution":null,"degree_name":null,"degree_level":null,"degree_discipline":null,"degree_department":null,"school":null,"contributors":[],"advisors":["Dr. Marie Davidian, Committee Member","Dr. Alun L. Lloyd, Committee Member","Dr. H.T. Banks, Committee Chair","Dr. Hien T. Tran, Committee Member"],"committee_chairs":[],"committee_members":[],"year":2008,"date_issued":"2008-07-21","date_published":"2008-07-21","updated_at":"2026-08-21T22:21:56Z","subjects":["Inverse Problem","Probability Distributions","Confidence Bands","Uncertainty","Size-Structured Population Models"],"languages":[],"rights":["I hereby certify that, if appropriate, I have obtained and attached hereto a written permission statement from the owner(s) of each third party copyrighted matter to be included in my thesis, dis sertation, or project report, allowing distribution as specified below. I certify that the version I submitted is the same as that approved by my advisory committee. I hereby grant to NC State University or its agents the non-exclusive license to archive and make accessible, under the conditions specified below, my thesis, dissertation, or project report in whole or in part in all forms of media, now or hereafter known. I retain all other ownership rights to the copyright of the thesis, dissertation or project report. I also retain the right to use in future works (such as articles or books) all or part of this thesis, dissertation, or project report."],"rights_urls":[],"identifier_entries":[{"key":"dc:identifier.other","label":"Dc Identifier Other","values":["etd-07182008-151056"],"render_values":[{"text":"etd-07182008-151056","href":null,"code":true}]}]},"links":{"outbound_url":"http://www.lib.ncsu.edu/resolver/1840.16/5401","outbound_label":"Repository record","outbound_source":"dc:identifier.uri"},"source_record":{"url":"https://repository.lib.ncsu.edu/server/oai/request?verb=GetRecord&metadataPrefix=dim&identifier=oai%3Arepository.lib.ncsu.edu%3A1840.16%2F5401","prefix":"dim"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor.advisor","label":"Advisor","values":["Dr. Marie Davidian, Committee Member","Dr. Alun L. Lloyd, Committee Member","Dr. H.T. 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I certify that the version I submitted is the same as that approved by my advisory committee. I hereby grant to NC State University or its agents the non-exclusive license to archive and make accessible, under the conditions specified below, my thesis, dissertation, or project report in whole or in part in all forms of media, now or hereafter known. I retain all other ownership rights to the copyright of the thesis, dissertation or project report. I also retain the right to use in future works (such as articles or books) all or part of this thesis, dissertation, or project report."]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier.other","label":"Dc Identifier Other","values":["etd-07182008-151056"]},{"key":"dc:identifier.uri","label":"Identifier URI","values":["http://www.lib.ncsu.edu/resolver/1840.16/5401"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description","label":"Description","values":["North Carolina State University Theses Mathematics."]},{"key":"dc:description.abstract","label":"Abstract","values":["We consider ordinary least squares (OLS) parameter estimation problems in which the underlying dynamics are described by partial differential equations and the unknown parameter of interest is a probability distribution describing the variability of growth rates across a size-structured population. The focus of our work is the development of an inverse problem computational methodology for the estimation of functional parameters in the presence of (model and data) uncertainty. Since this optimization problem involves both an infinite-dimensional state space and an infinite-dimensional parameter space, computationally efficient approximation methods for both parametric and non-parametric versions of the OLS inverse problem are developed and discussed. The approximation methods that we present are applicable to a variety of inverse problems, including Type II problems in which only aggregate or population level longitudinal data is available. We compare computational and statistical results of a delta function approximation method, a spline based approximation method, and a standard parametric OLS formulation. The latter uses an a priori probability distribution in the inverse problem for estimation of distributions of growth rates in size-structured marine populations. After summarizing the underlying theoretical framework, we present several numerical examples as validation of the theory. Convergence as well as sensitivity of the estimates with respect to noise in the data is discussed for both approximation methods. A computational framework for quantification of uncertainty associated with the estimated parameters is given and sample numerical findings are presented. We demonstrate how to construct \"functional\" confidence bands that will aid in quantifying the uncertainty in estimated probability distributions by extending the standard asymptotic theory for finite-dimensional OLS estimators. Using our inverse problem methodology, we present results for the estimation of growth rate distributions in size-structured marine populations illustrating the strengths and weaknesses associated with the three different computational schemes."]},{"key":"dc:format","label":"Dc Format","values":["Thesis (Ph.D.)--North Carolina State University."]},{"key":"dc:title","label":"Title","values":["Uncertainty Quantification in the Estimation of Probability Distributions on Parameters in Size-Structured Population Models"]}]}],"canonical_facts":{"dc:contributor.advisor":["Dr. Marie Davidian, Committee Member","Dr. Alun L. Lloyd, Committee Member","Dr. H.T. Banks, Committee Chair","Dr. Hien T. Tran, Committee Member"],"dc:creator":["Davis, Jimena Lamanda"],"dc:date.accessioned":["2010-04-02T19:13:13Z"],"dc:date.available":["2010-04-02T19:13:13Z"],"dc:date.issued":["2008-07-21"],"dc:description":["North Carolina State University Theses Mathematics."],"dc:description.abstract":["We consider ordinary least squares (OLS) parameter estimation problems in which the underlying dynamics are described by partial differential equations and the unknown parameter of interest is a probability distribution describing the variability of growth rates across a size-structured population. The focus of our work is the development of an inverse problem computational methodology for the estimation of functional parameters in the presence of (model and data) uncertainty. Since this optimization problem involves both an infinite-dimensional state space and an infinite-dimensional parameter space, computationally efficient approximation methods for both parametric and non-parametric versions of the OLS inverse problem are developed and discussed. The approximation methods that we present are applicable to a variety of inverse problems, including Type II problems in which only aggregate or population level longitudinal data is available. We compare computational and statistical results of a delta function approximation method, a spline based approximation method, and a standard parametric OLS formulation. The latter uses an a priori probability distribution in the inverse problem for estimation of distributions of growth rates in size-structured marine populations. After summarizing the underlying theoretical framework, we present several numerical examples as validation of the theory. Convergence as well as sensitivity of the estimates with respect to noise in the data is discussed for both approximation methods. A computational framework for quantification of uncertainty associated with the estimated parameters is given and sample numerical findings are presented. We demonstrate how to construct \"functional\" confidence bands that will aid in quantifying the uncertainty in estimated probability distributions by extending the standard asymptotic theory for finite-dimensional OLS estimators. Using our inverse problem methodology, we present results for the estimation of growth rate distributions in size-structured marine populations illustrating the strengths and weaknesses associated with the three different computational schemes."],"dc:format":["Thesis (Ph.D.)--North Carolina State University."],"dc:identifier.other":["etd-07182008-151056"],"dc:identifier.uri":["http://www.lib.ncsu.edu/resolver/1840.16/5401"],"dc:rights":["I hereby certify that, if appropriate, I have obtained and attached hereto a written permission statement from the owner(s) of each third party copyrighted matter to be included in my thesis, dis sertation, or project report, allowing distribution as specified below. I certify that the version I submitted is the same as that approved by my advisory committee. I hereby grant to NC State University or its agents the non-exclusive license to archive and make accessible, under the conditions specified below, my thesis, dissertation, or project report in whole or in part in all forms of media, now or hereafter known. I retain all other ownership rights to the copyright of the thesis, dissertation or project report. I also retain the right to use in future works (such as articles or books) all or part of this thesis, dissertation, or project report."],"dc:subject":["Inverse Problem","Probability Distributions","Confidence Bands","Uncertainty","Size-Structured Population Models"],"dc:title":["Uncertainty Quantification in the Estimation of Probability Distributions on Parameters in Size-Structured Population Models"]},"updated_at":"2026-08-21T22:21:56Z"}