Spring 2002 Seminar Series - February 12, 2002
University of Minnesota
School of Statistics
College of Liberal Arts
Design and Inference for Gaussian Random Fields
Zhengyuan Zhu
University of Chicago
(Statistics Search Candidate)
Tuesday, February 12, 2002
4:00 PM,
B10
Ford Hall
Minneapolis, East Bank Campus
Social at 3:30 PM,
300
Ford Hall
Abstract
Gaussian random fields (GRFs) can be used to model many physical processes in
space. In this talk we present two kinds of results for GRFs: spatial sampling
design and covariance parameter estimation. We study spatial sampling design
for prediction of stationary isotropic GRFs with estimated parameters of the
covariance function. The key issue is how to incorporate the parameter
uncertainty into the design criteria. Several possible design criteria are
discussed. An annealing algorithm is used to search for optimal designs of
small sample size and a two-step algorithm is proposed for moderately large
sample sizes. Simulation results are presented for the Matérn class of
covariance functions. The inference issue we consider is the asymptotic
properties of estimates of parameters of fractional Brownian motion. We give
the fixed-domain asymptotic distributions of both least square and maximum
likelihood estimates, which are different from the more standard
increasing-domain asymptotic results. We discuss why these results should still
apply when the process is not fractional Brownian motion but instead a GRF with
covariance function in the Matérn class.