Modeling for spatial and spatio-temporal data with applications

Abstract

It is common to assume the spatial or spatio-temporal data are realizations of underlying random fields or stochastic processes. Effective approaches to modeling of the underlying autocorrelation structure of the same random field 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 different locations in spatial statistics. With more and more data collected on a global scale in environmental science, geophysics, and related fields, we focus on the characterizations of the variogram models on spheres of all dimensions for both stationary and intrinsic stationary, univariate and multivariate random fields. Some effcient 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 fields 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 field operations, machinery decision, and risk management. To assess how some global climate phenomena such as El Nino Southern Oscillation (ENSO) affects 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.