Abstract #300199

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JSM 2003 Abstract #300199
Activity Number: 35
Type: Invited
Date/Time: Sunday, August 3, 2003 : 4:00 PM to 5:50 PM
Sponsor: Section on Bayesian Stat. Sciences
Abstract - #300199
Title: Relaxed Controls, Preisach Hysteresis, and Mixing Distributions in Statistical Inverse Problems
Author(s): H. T. Banks*+
Companies: Center for Research in Scientific Computation
Address: Box 8205 N.C. State University, Raleigh, NC, 27695-8205,
Keywords: inverse problems ; mixing distributions ; relaxed controls ; Preisach Hysteresis
Abstract:

In numerous applications in the biological and engineering sciences, one encounters inverse problems where the uncertainty and/or variability in parameters and mechanisms to be modeled are a fundamental part of the problem formulation. This is in addition to the data-driven uncertainty that arises naturally in most inverse problems. We discuss a theoretical framework and an associated computational methodology for such problems. In statistical inverse problems this approach is usually discussed in the context of "mixing distributions," but the mathematical foundations can be found in much earlier work on relaxed controls (sliding regimes, chattering controls) of Young, Filippov, Warga, and more recently in the treatment of Preisach hysteresis in smart materials. We outline these connections and present results from our recent efforts using these ideas in several biological applications.

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