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On the Application, Theory and Compu...

Yu, Jing.

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On the Application, Theory and Computation of Optimal Experimental Design in the Context of Sensor Placement.

Record Type:	Electronic resources : Monograph/item
Title/Author:	On the Application, Theory and Computation of Optimal Experimental Design in the Context of Sensor Placement./
Author:	Yu, Jing.
Published:	Ann Arbor : ProQuest Dissertations & Theses, : 2019,
Description:	159 p.
Notes:	Source: Dissertations Abstracts International, Volume: 81-04, Section: B.
Contained By:	Dissertations Abstracts International81-04B.
Subject:	Applied mathematics. -
Online resource:	http://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=13858427
ISBN:	9781085789691

On the Application, Theory and Computation of Optimal Experimental Design in the Context of Sensor Placement.
Yu, Jing.

On the Application, Theory and Computation of Optimal Experimental Design in the Context of Sensor Placement. - Ann Arbor : ProQuest Dissertations & Theses, 2019 - 159 p.

Source: Dissertations Abstracts International, Volume: 81-04, Section: B.

Thesis (Ph.D.)--The University of Chicago, 2019.

This item must not be sold to any third party vendors.

Optimal experimental designs are a class of experimental designs that are optimal with respect to some statistical criterion. Sensor placement is a sampling decision on data collection which aims to minimize the uncertainty in parameter estimation. This thesis focuses on two fundamental elements: the selection of sensor locations under statistically optimal conditions, and the computation of sensor placement with an efficient algorithm. We first present a design of experiments framework for sensor placement in a natural gas pipeline system where the dynamics are described by partial differential equations, and apply sum-up rounding strategy as a heuristic to determine the sensor locations. We continue to develop convergence theory on sum-up rounding for Bayesian inverse problems, where the direct relationship is described through a discretized integral equation. We show that the integer solution from sum-up rounding is asymptotically optimal in the limit of increasingly refined meshes, for different experimental design criteria (A- and D- optimal), and demonstrate its superior performance in comparison with other standard strategies. We also propose an optimization algorithm to compute the sensor locations, based on sequential quadratic programming and Chebyshev interpolation. By providing gradient and Hessian information on the objective, we solve a sequence of quadratic programs with interior point method and achieves a complexity of O(n logs(n)), while controlling the error through choosing the number of interpolation points to satisfy a user-defined precision level.

ISBN: 9781085789691Subjects--Topical Terms:

2122814
Applied mathematics.
Subjects--Index Terms:

Bayesian inverse problem

On the Application, Theory and Computation of Optimal Experimental Design in the Context of Sensor Placement.
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245 1 0 $a On the Application, Theory and Computation of Optimal Experimental Design in the Context of Sensor Placement.
260 1 $a Ann Arbor : $b ProQuest Dissertations & Theses, $c 2019
300 $a 159 p.
500 $a Source: Dissertations Abstracts International, Volume: 81-04, Section: B.
500 $a Advisor: Anitescu, Mihai.
502 $a Thesis (Ph.D.)--The University of Chicago, 2019.
506 $a This item must not be sold to any third party vendors.
520 $a Optimal experimental designs are a class of experimental designs that are optimal with respect to some statistical criterion. Sensor placement is a sampling decision on data collection which aims to minimize the uncertainty in parameter estimation. This thesis focuses on two fundamental elements: the selection of sensor locations under statistically optimal conditions, and the computation of sensor placement with an efficient algorithm. We first present a design of experiments framework for sensor placement in a natural gas pipeline system where the dynamics are described by partial differential equations, and apply sum-up rounding strategy as a heuristic to determine the sensor locations. We continue to develop convergence theory on sum-up rounding for Bayesian inverse problems, where the direct relationship is described through a discretized integral equation. We show that the integer solution from sum-up rounding is asymptotically optimal in the limit of increasingly refined meshes, for different experimental design criteria (A- and D- optimal), and demonstrate its superior performance in comparison with other standard strategies. We also propose an optimization algorithm to compute the sensor locations, based on sequential quadratic programming and Chebyshev interpolation. By providing gradient and Hessian information on the objective, we solve a sequence of quadratic programs with interior point method and achieves a complexity of O(n logs(n)), while controlling the error through choosing the number of interpolation points to satisfy a user-defined precision level.
590 $a School code: 0330.
650 4 $a Applied mathematics. $3 2122814
650 4 $a Statistics. $3 517247
650 4 $a Operations research. $3 547123
653 $a Bayesian inverse problem
653 $a Integer programming
653 $a Optimal experimental design
653 $a Sum-up rounding
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690 $a 0364
710 2 $a The University of Chicago. $b Statistics. $3 1673632
773 0 $t Dissertations Abstracts International $g 81-04B.
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793 $a English
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