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Theory and Methods for Large Spatial...

Mullen, Z.

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Theory and Methods for Large Spatial Data.

Record Type:	Electronic resources : Monograph/item
Title/Author:	Theory and Methods for Large Spatial Data./
Author:	Mullen, Z.
Published:	Ann Arbor : ProQuest Dissertations & Theses, : 2018,
Description:	83 p.
Notes:	Source: Dissertations Abstracts International, Volume: 80-04, Section: B.
Contained By:	Dissertations Abstracts International80-04B.
Subject:	Applied Mathematics. -
Online resource:	http://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=10928440
ISBN:	9780438384378

Theory and Methods for Large Spatial Data.
Mullen, Z.

Theory and Methods for Large Spatial Data. - Ann Arbor : ProQuest Dissertations & Theses, 2018 - 83 p.

Source: Dissertations Abstracts International, Volume: 80-04, Section: B.

Thesis (Ph.D.)--University of Colorado at Boulder, 2018.

This item must not be added to any third party search indexes.

Correlated Gaussian processes are of central importance to the study of time series, spatial statistics, computer experiments, and many machine learning models. Large spatially or temporally indexed datasets bring with them a host of computational and mathematical challenges. Parameter estimation of these processes often relies on maximum likelihood, which for Gaussian processes involves manipulations of the covariance matrix including solving systems of equations and determinant calculations. The score function, on the other hand, avoids direct calculation of the determinant, but still requires solving a large number of linear equations. We propose an equivalent kernel approximation to the score function of a stationary Gaussian process. A nugget effect is required for the approximation. We suggest two approximations, and for large sample sizes, our proposals are fast, accurate, and compare well against existing approaches. We then present a method for simulating time series of high frequency wind data calibrated by real data. The method provides and fits a parametric model for local wind directions by embedding them into the angular projection of a bivariate normal. Incorporating a temporal autocorrelation structure in that normal induces a continuous angular correlation over time in the simulated wind directions. The final joint model for speed and direction can be decomposed into the simulation of a single multivariate normal and a series of transformations thereof, allowing for fast and easy repeated generations of long time series. This is compared to a state of the art approach for simulating angular time series of swapping between discrete regimes of wind direction, a method that does not fully translate to high frequency data.

ISBN: 9780438384378Subjects--Topical Terms:

1669109
Applied Mathematics.
Subjects--Index Terms:

Circular data

Theory and Methods for Large Spatial Data.
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100 1 $a Mullen, Z. $3 3543578
245 1 0 $a Theory and Methods for Large Spatial Data.
260 1 $a Ann Arbor : $b ProQuest Dissertations & Theses, $c 2018
300 $a 83 p.
500 $a Source: Dissertations Abstracts International, Volume: 80-04, Section: B.
500 $a Publisher info.: Dissertation/Thesis.
500 $a Advisor: Kleiber, William.
502 $a Thesis (Ph.D.)--University of Colorado at Boulder, 2018.
506 $a This item must not be added to any third party search indexes.
506 $a This item must not be sold to any third party vendors.
520 $a Correlated Gaussian processes are of central importance to the study of time series, spatial statistics, computer experiments, and many machine learning models. Large spatially or temporally indexed datasets bring with them a host of computational and mathematical challenges. Parameter estimation of these processes often relies on maximum likelihood, which for Gaussian processes involves manipulations of the covariance matrix including solving systems of equations and determinant calculations. The score function, on the other hand, avoids direct calculation of the determinant, but still requires solving a large number of linear equations. We propose an equivalent kernel approximation to the score function of a stationary Gaussian process. A nugget effect is required for the approximation. We suggest two approximations, and for large sample sizes, our proposals are fast, accurate, and compare well against existing approaches. We then present a method for simulating time series of high frequency wind data calibrated by real data. The method provides and fits a parametric model for local wind directions by embedding them into the angular projection of a bivariate normal. Incorporating a temporal autocorrelation structure in that normal induces a continuous angular correlation over time in the simulated wind directions. The final joint model for speed and direction can be decomposed into the simulation of a single multivariate normal and a series of transformations thereof, allowing for fast and easy repeated generations of long time series. This is compared to a state of the art approach for simulating angular time series of swapping between discrete regimes of wind direction, a method that does not fully translate to high frequency data.
590 $a School code: 0051.
650 4 $a Applied Mathematics. $3 1669109
650 4 $a Statistics. $3 517247
653 $a Circular data
653 $a Equivalent kernel
653 $a Gaussian processes
653 $a Spatial statistics
653 $a Stochastic weather generators
653 $a Wind modeling
690 $a 0364
690 $a 0463
710 2 $a University of Colorado at Boulder. $b Applied Mathematics. $3 1030307
773 0 $t Dissertations Abstracts International $g 80-04B.
790 $a 0051
791 $a Ph.D.
792 $a 2018
793 $a English
856 4 0 $u http://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=10928440