A Time-Varying Low-Dimensional Representation for Spatio-Temporal Data
We were motivated by the two major limitations of the current research approaches on the North Atlantic Oscillation (NAO) based on empirical orthogonal functions (EOF) analysis: (i) long-term stationary assumptions; (ii) lack of measures of uncertainty, and proposed and developed a time-varying low-...
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ftcdlib:qt4v59183q 2023-05-15T17:33:10+02:00 A Time-Varying Low-Dimensional Representation for Spatio-Temporal Data Tian, Xu 157 2014-01-01 application/pdf http://www.escholarship.org/uc/item/4v59183q http://n2t.net/ark:/13030/m57w7sd2 en eng eScholarship, University of California http://www.escholarship.org/uc/item/4v59183q qt4v59183q http://n2t.net/ark:/13030/m57w7sd2 public Tian, Xu. (2014). A Time-Varying Low-Dimensional Representation for Spatio-Temporal Data. UC Irvine: Statistics. Retrieved from: http://www.escholarship.org/uc/item/4v59183q Statistics covariance matrix EOF NAO state space model dissertation 2014 ftcdlib 2016-10-07T22:55:08Z We were motivated by the two major limitations of the current research approaches on the North Atlantic Oscillation (NAO) based on empirical orthogonal functions (EOF) analysis: (i) long-term stationary assumptions; (ii) lack of measures of uncertainty, and proposed and developed a time-varying low-dimensional representation for spatio-temporal data in this thesis. The low-dimensional representation is based on a structured spatial covariance matrix using a certain number of structured basis functions with certain parametric forms. Initially, we developed the Parametric Basis Function (PBF) spatial covariance model in a stationary scenario and provided the statistical inference in both maximum likelihood and Bayesian analysis frameworks. We further extended the model by introducing time-varying parameters to develop the time-varying parametric basis function (TV-PBF) model in the state space model framework. The Bayesian approach with MCMC techniques was used to make inference for the TV-PBF model. The model is able to provide smoothly changing patterns of the 1st EOFs NAO over time which can serve as an alternative representation for the spatio-temporal NAO data. Doctoral or Postdoctoral Thesis North Atlantic North Atlantic oscillation University of California: eScholarship |
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Open Polar |
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University of California: eScholarship |
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language |
English |
topic |
Statistics covariance matrix EOF NAO state space model |
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Statistics covariance matrix EOF NAO state space model Tian, Xu A Time-Varying Low-Dimensional Representation for Spatio-Temporal Data |
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Statistics covariance matrix EOF NAO state space model |
description |
We were motivated by the two major limitations of the current research approaches on the North Atlantic Oscillation (NAO) based on empirical orthogonal functions (EOF) analysis: (i) long-term stationary assumptions; (ii) lack of measures of uncertainty, and proposed and developed a time-varying low-dimensional representation for spatio-temporal data in this thesis. The low-dimensional representation is based on a structured spatial covariance matrix using a certain number of structured basis functions with certain parametric forms. Initially, we developed the Parametric Basis Function (PBF) spatial covariance model in a stationary scenario and provided the statistical inference in both maximum likelihood and Bayesian analysis frameworks. We further extended the model by introducing time-varying parameters to develop the time-varying parametric basis function (TV-PBF) model in the state space model framework. The Bayesian approach with MCMC techniques was used to make inference for the TV-PBF model. The model is able to provide smoothly changing patterns of the 1st EOFs NAO over time which can serve as an alternative representation for the spatio-temporal NAO data. |
format |
Doctoral or Postdoctoral Thesis |
author |
Tian, Xu |
author_facet |
Tian, Xu |
author_sort |
Tian, Xu |
title |
A Time-Varying Low-Dimensional Representation for Spatio-Temporal Data |
title_short |
A Time-Varying Low-Dimensional Representation for Spatio-Temporal Data |
title_full |
A Time-Varying Low-Dimensional Representation for Spatio-Temporal Data |
title_fullStr |
A Time-Varying Low-Dimensional Representation for Spatio-Temporal Data |
title_full_unstemmed |
A Time-Varying Low-Dimensional Representation for Spatio-Temporal Data |
title_sort |
time-varying low-dimensional representation for spatio-temporal data |
publisher |
eScholarship, University of California |
publishDate |
2014 |
url |
http://www.escholarship.org/uc/item/4v59183q http://n2t.net/ark:/13030/m57w7sd2 |
op_coverage |
157 |
genre |
North Atlantic North Atlantic oscillation |
genre_facet |
North Atlantic North Atlantic oscillation |
op_source |
Tian, Xu. (2014). A Time-Varying Low-Dimensional Representation for Spatio-Temporal Data. UC Irvine: Statistics. Retrieved from: http://www.escholarship.org/uc/item/4v59183q |
op_relation |
http://www.escholarship.org/uc/item/4v59183q qt4v59183q http://n2t.net/ark:/13030/m57w7sd2 |
op_rights |
public |
_version_ |
1766131580111159296 |