Formulation and solution of stochastic inverse problems for science and engineering models
The stochastic inverse problem of determining probability structures on input parameters for a physics model corresponding to a given probability structure on the output of the model forms the core of scientific inference and engineering design. We describe a formulation and solution method for stochastic inverse problems that is based on functional analysis, differential geometry, and probability/measure theory. This approach yields a computationally tractable problem while avoiding alterations of the model like regularization and ad hoc assumptions about the probability structures. We present several examples, including a high-dimensional application to determination of parameter fields in storm surge models. We also describe work aimed at defining a notion of condition for stochastic inverse problems and tackling the related problem of designing sets of optimal observable quantities.
Don Estep is the Director of CANSSI and a professor in the Department of Statistics and Actuarial Science at Simon Fraser University. Previously, he was a University Distinguished Professor, University Interdisciplinary Research Scholar, and Chair of the Department of Statistics at Colorado State University. Before that, he was a professor in the School of Mathematics at Georgia Tech for 13 years. He has also spent significant amounts of time at Chalmers University of Technology in Göteborg, Sweden and Caltech.