Date:

Monday, January 28, 2002

Speaker:

Doug Nychka

Affiliation:

Geophysical Statistics Project
National Center for Atmospheric Research
Boulder, CO.

Web site

www.cgd.ucar.edu/~nychka

Title:

Wavelet representations for nonstationary spatial fields

Abstract:

Spatial analysis for large nonstationary processes poses challenges in both modeling and computation. A promising way to represent nonstationary covariance structure is by expanding the field in terms of a wavelet basis and then building a simple, sparse model for correlations and variances among the wavelet coefficients. The sparse structure is important for computing statistical estimates for large spatial problems using iterative methods for sloving linear systems. In this talk a nonorthogonal wavelet basis (the W-transform) is presented that not only appears to fit a variety of standard covariance models but is well suited to the computation of Kriging estimates and conditional distributions. From a more conventional perspective, this wavelet-based model provides an reasonable blending between an EOF representation (principle components of the sample covariance matrix) and a stationary, parametric family. This approach is illustrated using output from a run of the Regional Oxidant Model, an EPA pollution simulation.