Department of Statistics Seminar
North Carolina State University

presents

Montserrat Fuentes

University of Chicago

"Prediction of Random Fields Combining Different Sources of Data"

ABSTRACT

The Southern Great Plains (SGP) site is a field measurement site of the Atmospheric Radiation Measurement (ARM) program. It covers approximately 55,000 square miles in north-Central Oklahoma and south Central Kansas. The site consists of 30 instrument arrays. Argonne National Laboratories collects Advanced Very High Resolution Radiometer (AVHRR) satellite data once a day for the entire SGP region. I will present a Bayesian imputation technique for the satellite data, to estimate the surface characteristics where we have clouds. I have developed methods for combining the two sources of information, ground and satellite, to get better predictions of these surface characteristics. I also have explored methods of constructing and implementing efficient algorithms to estimate the variability in these spatial-temporal data. I will present a kriging procedure as the prediction technique of the surface characteristics. Surface variables play an important role in the General Circulation Models (GCMs) that predict the climate. I will demonstrate that the kriging predictors of numerical integrals of random fields obtain a more reasonable parameterization for the GCMs.

In the second part of my talk I will consider a distinct topic, the prediction of the integral of a diffusion process Z() in a bounded interval, based on the observations Z[n] = (Z(t1n),...,Z(tnn)) where t1n,...,tnn is a dense sequence of points in the bounded interval. Let Zn(t)=E(Z(t)|Z[n]) be the conditional mean for Z(). I predict the integral of Z(t) over the set A with the integral of Zn(t) over the set A, the optimal predictor of the integral of Z(t) in terms of minimizing the mse. I have obtained that under certain circumstances, the standardized conditional prediction error is approximately Gaussian with mean zero and variance 1, even if the underlying process is non-Gaussian. Since this optimal predictor is hard to calculate exactly for most diffusion, I propose an easy computed approximation to it that is a function of the diffusion parameters and is asymptotically optimal. The Best Linear Predictor is generally not asymptotically optimal.

Key Words: AVHRR data, diffusion process, infill asymptotics, kriging, spatial-temporal process, variogram.

Tuesday, January 27, 1998

8:00 - 9:00 am

124 Dabney Hall

Refreshments will be served in 124 Dabney Hall at 7:45.