Hierarchical Additive Spatial and Spatio-Temporal Process Models for Massive Datasets
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University of Cincinnati / OhioLINK
2018
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ndltd-OhioLink-oai-etd.ohiolink.edu-ucin15356351935810962021-08-03T07:08:29Z Hierarchical Additive Spatial and Spatio-Temporal Process Models for Massive Datasets Ma, Pulong Statistics Fused Gaussian process Statistical Downscaling Spatial and Spatio-Temporal Modeling Nonstationarity Nonseparability Massive datasets Many geophysical processes evolve in space and time, resulting in complicated data including nonstationary and nonseparable covariance structures, and highly complex dynamics. With the advance of new remote-sensing technologies, massive amount of these datasets can be collected at very high spatial resolutions each day from satellite instruments. These data are often noisy and irregularly observed with incompatible supports as well. These challenges require new statistical methods to account for both model flexibility and computational efficiency. In this dissertation, three novel approaches are proposed: 1) the covariance function model that incorporates low-rank representation and spatial graphical model, to allow nonstationarity and robust predictive performance. This leads to a kriging methodology called fused Gaussian process (FGP); 2) the downscaling framework based on FGP to carry out conditional simulation to generate high-resolution fields; 3) the low-cost Bayesian inference framework for an additive covariance function model that combines any type of computational-complexity-reduction methods (e.g., low-rank representation) and separable covariance structure together, to allow nonseparability and good predictive performance. This leads to another kriging methodology called additive approximate Gaussian process (AAGP).The methodology in FGP relies on a small set of fixed spatial basis functions and random weights to model large-scale variation of a nonstationary process, and a Gaussian graphical model to capture remaining variation. This method is applied to analyze massive amount of remotely-sensed sea surface temperature data. Another important application based on FGP is to generate high-resolution nature runs in global observing system simulation experiments, which have been widely used to guide the development of new observing systems, and to evaluate the performance of new data assimilation algorithms. The change-of-support problem is handled explicitly to account for the resolution difference between the numerical model outputs and synthetic observations in data assimilation algorithms. As an extension, a spatio-temporal model based on FGP is also proposed to obtain filtering, smoothing, and forecasting of the spatio-temporal processes in a dynamic modeling framework. The resulting methodology is called dynamic fused Gaussian process (DFGP). The DFGP model is applied to analyze massive amount of daily sea surface temperature data at different spatial resolutions from two different instruments. In contrast to dynamic modeling approach in DFGP, the methodology in AAGP takes a multivariate modeling approach in a Bayesian framework, which allows fast inference by utilizing a hierarchical representation of the covariance function model that admits an additive structure. The covariance function in AAGP explicitly models nonseparable and separable variations according to the underlying structure of the geophysical processes. A novel conditional Markov chain Monte Carlo method is proposed to allow fast Bayesian inference based on the fully hierarchical representation of the model in AAGP. This methodology is applied to analyze Eastern U.S. ozone data over a three-month period. 2018-10-29 English text University of Cincinnati / OhioLINK http://rave.ohiolink.edu/etdc/view?acc_num=ucin1535635193581096 http://rave.ohiolink.edu/etdc/view?acc_num=ucin1535635193581096 unrestricted This thesis or dissertation is protected by copyright: some rights reserved. It is licensed for use under a Creative Commons license. Specific terms and permissions are available from this document's record in the OhioLINK ETD Center. |
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NDLTD |
| language |
English |
| sources |
NDLTD |
| topic |
Statistics Fused Gaussian process Statistical Downscaling Spatial and Spatio-Temporal Modeling Nonstationarity Nonseparability Massive datasets |
| spellingShingle |
Statistics Fused Gaussian process Statistical Downscaling Spatial and Spatio-Temporal Modeling Nonstationarity Nonseparability Massive datasets Ma, Pulong Hierarchical Additive Spatial and Spatio-Temporal Process Models for Massive Datasets |
| author |
Ma, Pulong |
| author_facet |
Ma, Pulong |
| author_sort |
Ma, Pulong |
| title |
Hierarchical Additive Spatial and Spatio-Temporal Process Models for Massive Datasets |
| title_short |
Hierarchical Additive Spatial and Spatio-Temporal Process Models for Massive Datasets |
| title_full |
Hierarchical Additive Spatial and Spatio-Temporal Process Models for Massive Datasets |
| title_fullStr |
Hierarchical Additive Spatial and Spatio-Temporal Process Models for Massive Datasets |
| title_full_unstemmed |
Hierarchical Additive Spatial and Spatio-Temporal Process Models for Massive Datasets |
| title_sort |
hierarchical additive spatial and spatio-temporal process models for massive datasets |
| publisher |
University of Cincinnati / OhioLINK |
| publishDate |
2018 |
| url |
http://rave.ohiolink.edu/etdc/view?acc_num=ucin1535635193581096 |
| work_keys_str_mv |
AT mapulong hierarchicaladditivespatialandspatiotemporalprocessmodelsformassivedatasets |
| _version_ |
1719454620202303488 |