Inverse Problems for Physics-Based Process Models

Abstract

We describe and compare two formulations of inverse problems for a physics-based process model in the context of uncertainty and random variability: the Bayesian inverse problem and the stochastic inverse problem. We describe the foundations of the two problems in order to create a context for interpreting the applicability and solutions of inverse problems important for scientific and engineering inference. We conclude by comparing them to statistical approaches to related problems, including Bayesian calibration of computer models. Expected final online publication date for the Annual Review of Statistics and Its Application, Volume 11 is March 2024. Please see http://www.annualreviews.org/page/journal/pubdates for revised estimates.