Seminars and Events - Research Colloquia

Special Colloquia, Department of Statistics

Wednesday, February 20, 2002
4:30 PM in CL50 129

Mr. Zhengyuan Zhu
University of Chicago

will speak on

Design and Inference for Gaussian Random Fields

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 Mat ern 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 Matern class.