Probabilistic Constraints for Inverse Problems

The authors previous work on probabilistic constraint reasoning assumes the uncertainty of numerical variables within given bounds, characterized by a priori probability distributions. It propagates such knowledge through a network of constraints, reducing the uncertainty and providing a posteriori probability distributions. An inverse problem aims at estimating parameters from observed data, based on some underlying theory about a system behavior. This paper describes how nonlinear inverse problems can be cast into the probabilistic constraint framework, highlighting its ability to deal with all the uncertainty aspects of such problems.