Doctor of Philosophy / Department of Statistics / Juan Du / It is common to assume the spatial or spatio-temporal data are realizations of underlying
random elds or stochastic processes. E ective approaches to modelling of the
underlying autocorrelation structure of the same random eld and the association among
multiple processes are of great demand in many areas including atmospheric sciences, meteorology and agriculture. To this end, this dissertation studies methods and application
of the spatial modeling of large-scale dependence structure and spatio-temporal regression
modelling.
First, variogram and variogram matrix functions play important roles in modeling
dependence structure among processes at di erent locations in spatial statistics. With
more and more data collected on a global scale in environmental science, geophysics, and
related elds, we focus on the characterizations of the variogram models on spheres of
all dimensions for both stationary and intrinsic stationary, univariate and multivariate
random elds. Some e cient approaches are proposed to construct a variety of variograms
including simple polynomial structures. In particular, the series representation
and spherical behavior of intrinsic stationary random elds are explored in both theoretical
and simulation study. The applications of the proposed model and related theoretical
results are demonstrated using simulation and real data analysis.
Second, knowledge of the influential factors on the number of days suitable for fieldwork
(DSFW) has important implications on timing of agricultural eld operations, machinery
decision, and risk management. To assess how some global climate phenomena
such as El Nino Southern Oscillation (ENSO) a ects DSFW and capture their complex
associations in space and time, we propose various spatio-temporal dynamic models under
hierarchical Bayesian framework. The Integrated Nested Laplace Approximation (INLA)
is used and adapted to reduce the computational burden experienced when a large number
of geo-locations and time points is considered in the data set. A comparison study
between dynamics models with INLA viewing spatial domain as discrete and continuous
is conducted and their pros and cons are evaluated based on multiple criteria. Finally a
model with time- varying coefficients is shown to reflect the dynamic nature of the impact and lagged effect of ENSO on DSFW in US with spatio-temporal correlations accounted.
| Identifer | oai:union.ndltd.org:KSU/oai:krex.k-state.edu:2097/38749 |
| Date | January 1900 |
| Creators | Li, Xintong |
| Publisher | Kansas State University |
| Source Sets | K-State Research Exchange |
| Language | en_US |
| Detected Language | English |
| Type | Dissertation |
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