A Tutorial on Inverse Theory
Organizer: Vicki Lancaster
(vlancast@neptuneandco.com)
Neptune and Company, Inc.

Description:
Inverse theory addresses problems in making inferences about a phenomenon from indirect or incomplete information. Statistical estimation and model building are examples of inverse problems familiar to us from our statistical education. This tutorial will deal with inverse problems that do not have a unique or stable solution. These are called ill-posed inverse problems. Our problem is to somehow choose a solution which is consistent with the data and with our prior knowledge of the process. We will use examples to illustrate different techniques developed to incorporate prior information in inverse problems and study the performance of the estimates.

Format:
The entire session will be devoted to the tutorial with time for questions at the end of the session.

Participants:
Luis Tenorio (presentation, A Tutorial on Statistical Inverse Theory)
Luis Tenorio is in the Department of Mathematical and Computer Sciences at the Colorado School of Mines. He received his Ph.D. in Mathematics from the University of California, Berkley in 1992. Since completion of his degree, he has worked with the George Smoot's astrophysics group at the Space Science Laboratory, the Universidad Carlos III in Madrid, and the Space Science Laboratory and Center for Particle Physic Astrophysics in Berkeley. Luis has numerous publications dealing with the use of prior information in ill-posed inverse problems. His most recent paper "Bigger Uncertainties and the Big Bang" (Inverse Problems 15 (1999) 329-341), deals with the use of Bayesian hierarchical models and recent results for the theory of minimax confidence interval estimation to study the effect of prior information in a cosmological inverse problem.

Alberto Villarreal (poster, Velocity Estimation in Exploration Geophysics, a Bootstrap Approach)
Colorado School of Mines

Luis Tenorio and Alberto Villarreal (poster, Generalizing Wiener-Levinson Deconvolution)
Colorado School of Mines

Albena Mateeva (poster, Estimating the Influence of Random Noise on Measured Travel Times)
Colorado School of Mines