Posterior Sampling using Particle Swarm Optimizers and Model Reduction Techniques

Inverse problems are ill-posed and posterior sampling is a way of providing an estimate of the uncertainty based on a finite set of the family of models that fit the observed data within the same tolerance. Monte Carlo methods are used for this purpose but are highly inefficient. Global optimization methods address the inverse problem as a sampling problem, particularly Particle Swarm, which is a very interesting algorithm that is typically used in an exploitative form. Although PSO has not been designed originally to perform importance sampling, the authors show practical applications in the domain of environmental geophysics, where it provides a proxy for the posterior distribution when it is used in its explorative form. Finally, this paper presents a hydrogeological example how to perform a similar task for inverse problems in high dimensional spaces through the combined use with model reduction techniques.