A High Performance Bayesian Computing Framework for Spatiotemporal Uncertainty Modeling

Abstract:

All types of spatiotemporal measurements are subject to uncertainty. With 
spatiotemporal data becomes increasingly involved in scientific research 
and decision making, it is important to appropriately model the impact of 
uncertainty. Quantitatively modeling spatiotemporal uncertainty, however, 
is a challenging problem considering the complex dependence and data
heterogeneities.

State-space models provide a unifying and intuitive framework for 
dynamic systems modeling. In this paper, we aim to 
extend the conventional state-space models for uncertainty modeling in 
space-time contexts while accounting for spatiotemporal effects and data 
heterogeneities. Gaussian Markov Random Field (GMRF) models, also known 
as conditional autoregressive models, are arguably the most commonly 
used methods for modeling of spatially dependent data. GMRF models 
basically assume that a geo-referenced variable primarily depends on its 
neighborhood (Markov property), and the spatial dependence structure 
is described via a precision matrix. Recent study has shown that GMRFs 
are efficient approximation to the commonly used Gaussian fields (e.g., 
Kriging), and compared with Gaussian fields, GMRFs enjoy a series of 
appealing features, such as fast computation and easily accounting for 
heterogeneities in spatial data (e.g, point and areal). This paper 
represents each spatial dataset as a GMRF and integrates them into a 
state-space form to statistically model the temporal dynamics. Different 
types of spatial measurements (e.g., categorical, count or continuous), 
can be accounted for by according link functions. A fast alternative to 
MCMC framework, so-called Integrated Nested Laplace Approximation (INLA), 
was adopted for model inference.

Preliminary case studies will be conducted to showcase the advantages 
of the described framework. In the first case, we apply the proposed 
method for modeling the water table elevation of Ogallala aquifer 
over the past decades. In the second case, we analyze the drought 
impacts in Texas counties in the past years, where the spatiotemporal 
dynamics are represented in areal data.