The modeling of spatio-temporal and multivariate spatial random fields has been
an important and growing area of research due to the increasing availability of spacetime-referenced data in a large number of scientific applications. In geostatistics, the
covariance function plays a crucial role in describing the spatio-temporal dependence
in the data and is key to statistical modeling, inference, stochastic simulation and
prediction. Therefore, the development of flexible covariance models, which can accomodate the inherent variability of the real data, is necessary for an advantageous
modeling of random fields. This thesis is composed of four significant contributions
in the development and applications of new covariance models for stationary multivariate spatial processes, and nonstationary spatial and spatio-temporal processes.
The first focus of the thesis is on modeling of stationary multivariate spatial
random fields through flexible multivariate covariance functions. Chapter 2 proposes a
semiparametric approach for multivariate covariance function estimation with flexible
specification of the cross-covariance functions via their spectral representations. The
proposed method is applied to model and predict the bivariate data of particulate
matter concentration (PM2.5) and wind speed (WS) in the United States. Chapter 3
introduces a parametric class of multivariate covariance functions with asymmetric
cross-covariance functions. The proposed covariance model is applied to analyze the
asymmetry and perform prediction in a trivariate data of PM2.5, WS and relative
humidity (RH) in the United States.
The second focus of the thesis is on nonstationary spatial and spatio-temporal
random fields. Chapter 4 presents a space deformation method which imparts nonstationarity to any stationary covariance function. The proposed method utilizes
the functional data registration algorithm and classical multidimensional scaling to
estimate the spatial deformation. The application of the proposed method is demonstrated on a precipitation data. Finally, chapter 5 proposes a parametric class of
time-varying spatio-temporal covariance functions, which are nonstationary in time.
The proposed class is a time-varying generalization of an existing nonseparable stationary class of spatio-temporal covariance functions. The proposed time-varying
model is then used to study the seasonality effect and perform space-time predictions
in the daily PM2.5 data from Oregon, United States.
|Date of Award
|Jun 6 2021
- Computer, Electrical and Mathematical Sciences and Engineering
|Ying Sun (Supervisor)
- spatial statistics
- stochastic processes
- non stationary