Statistical and Applied Mathematical Sciences Institute
19 T. W. Alexander Drive
P.O. Box 14006
Research Triangle Park, NC 27709-4006
Tel: 919.685.9350 FAX: 919.685.9360
[email protected]

Inverse Problem Methodology In Complex Stochastic Models
September 2002 - January 2003

Opening Workshop, September 21-24, 2002

Program

This will be the kickoff Workshop for the 2002-2003 SAMSI Focused Study Program on Inverse Problem Methodology in Complex Stochastic Models. The Workshop will be devoted to catalyzing new interdisciplinary research thrusts and collaborations focused on inverse and estimation problems in the context of uncertainty and stochasticity in models and data. It will offer keynote lectures and invited presentations by leading researchers involved in modeling of complex systems, statistical modeling and computation, and disciplinary science.

Keynote lectures will include a number of overview presentations illustrating common challenges in parameter estimation across several areas of science via testbed examples including modeling of polymers (material sciences), dielectric materials (electromagnetics), molecular mechanisms in HIV dynamics (biology), and tomography (physics and medicine). Mathematical modeling and statistical inferential issues and the need for an integrated framework will be described in some detail.

A special feature of the Workshop will be introductory tutorials during the first day on differential equation modeling, statistical inference and modeling, and computational techniques.

The Workshop is intended for applied mathematicians; statisticians; physicists; engineers; and domain scientists from biology and medicine, materials, and electromagnetics. Financial support for travel and lodging is available for participants. Young investigators (graduate students, postdocs, and faculty in the early stages of their careers) and members of underrepresented groups are especially encouraged to participate.

Because of space limitations, registration for the workshop closed on August 23, 2002. Copies of presentations and related materials will be available on the SAMSI Web site.

Program and Schedule of Events

Saturday, September 21--North Carolina Biotechnology Center

      12:45-1:30: Registration

      1:30-3:30: Tutorial on Differential Equation Modeling and Inverse Problems
      H. T. Banks

This tutorial will focus on modeling and inverse problem concepts for complex dynamical systems. Topics include ordinary and partial differential equation modeling; time, space, and state dependent coefficient estimation; nonlinear mechanisms; identifiability, ill-posedness, stability, and regularization in inverse problems. Computational methods to be discussed are finite differences, finite elements and modal approximations; reduced order modeling including Proper Orthogonal Decomposition (POD) / Principal Component Analysis (PCA) based techniques. A review of related available software will be given.

       3:30-4:00: Coffee Break

      4:00-6:00: Tutorial on Statistical Modeling and Inference
      M. Davidian

This tutorial will provide an overview of considerations underlying statistical approaches to taking appropriate account of uncertainty in fitting nonlinear mathematical models to data and to making formal statistical inference. Sources of variation in different data structures will be discussed, including situations where repeated observations on a system are available for a single sample or individual and on multiple such samples or individuals. Consequences of failure to acknowledge variation appropriately will be elucidated. Incorporation of deterministic mathematical models within appropriate statistical frameworks that explicitly represent relevant sources of variation, including nonlinear fixed and random effects models, will be outlined. Associated methods for parameter estimation and inference both by frequentist and Bayesian approaches will be discussed. Available software will be reviewed and demonstrated, and its limitations for incorporation of complex dynamical systems highlighted.

      6:00 - 8:00: Welcome Reception at the NISS/SAMSI Building

Sunday, September 22-- Radisson Governors Inn

Morning: HIV Dynamics

Afternoon: Electromagnetics

Monday, September 23, Radisson Governors Inn

Morning: Polymers

Mid-Morning: Tomography

Late Morning: Physiologically Based Pharmacokinetics

Afternoon: Parameter Estimation and Inverse Problems
Statistics Perspective

Tuesday, September 24, Radisson Governors Inn

Morning: Parameter Estimation and Inverse Problems
Applied Mathematics Perspective

Afternoon

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