HR: 08:00h
AN: H21G-01 INVITED     [Abstracts]
TI: New Vistas in Geostatistical and Bayesian Methods in Interpolation and Inverse Problems
AU: * Kitanidis, P K
EM: peterk@stanford.edu
AF: Stanford University, Civil and Environmental Engineering, Stanford, CA 94305-4020 United States
AB: If any stochastic methodology for the solution of interpolation and inverse problems can be considered general, I believe that it is the Bayesian one. Among other features that illustrate it generality, the Bayesian approach produces the familiar kriging and co-kriging results of geostatistics as special cases. It also provides satisfactory approaches to the vexing problems of estimating parameters of semivariograms; selecting among semivariograms; and accounting for uncertainty in semivariograms. In inverse problems, Bayesian methods with appropriate generalized covariance functions yield the most popular regularization methods, such as Tikhonov-type regularization, while also suggesting how to weigh the various terms in the objective function. Most important of all, the Bayesian approach may be the only general and systematic approach to solve problems that are clearly outside of the realm served by classical methods that trace their roots to least squares. That is, interpolation and inverse problems that are best formulated as strongly non-linear and non-Gaussian stochastic inference problems. Although Bayesian methods are not new, they have been under-utilized in the solution of inverse problems because of the discouragingly high computational cost associated with their implementation. However, the tremendous improvement in computer power over the last few years has opened up new and exciting avenues. What is most thrilling about new methods is that they allow us to formulate a problem in ways that utilize all available information. We review some of the progress that has been made and some of the promising methods that can be used.
DE: 1816 Estimation and forecasting
SC: Hydrology [H]
MN: Fall Meeting 2005