Random Fields based on Local Interaction Models for Spatiotemporal Data
Speaker: Dionissios T. Hristopulos, Technical University of Crete, Greece
Series: CEE Departmental Seminars
Location: Engineering Quad E219
Date/Time: Friday, December 13, 2013, 12:00 p.m. - 1:30 p.m.
This presentation will focus on the interpolation and simulation of scattered spatial observations as well as missing data on regular grids by means of Spartan spatial random fields (SSRFs). SSRFs can be derived from a Gaussian statistical field theory that includes both gradient and curvature terms, or equivalently, from stochastic (Langevin) partial differential equations driven by Gaussian white noise. SSRF covariance models are characterized by sparse structure of the precision matrix (the inverse covariance matrix), at least for data distributed on regular grids. The sparseness derives from the locality of the operators in the respective energy functional and leads to an explicit spectral density given by a rational function. At the limit of an infinite spectral cutoff, isotropic SSRF covariance functions in real space can be derived analytically by direct integration of the spectral representation, given by the Hankel transform of the spectral density. We present new expressions for three-parameter, isotropic covariance functions and discuss the parametric dependence of various correlation range measures, as well as the emergence of self-similarity. The availability of explicit, albeit approximate, expressions for both the covariance and the precision matrix can help to overcome the curse of dimensionality in the numerical procedures of parameter inference, spatial interpolation and conditional simulation. Applications of SSRFs to real and simulated data sets will be presented. Extension of the SSRF interaction-based concept for handling data with non-Gaussian probability distributions, using discretized random field models with Ising spin-type interactions will be motivated. Ongoing research efforts that extend SSRFs into the spatiotemporal domain as well as perspectives for future developments will be discussed.