Techniques for generic probabilistic inversion

Probabilistic inversion problems are defined, existing algorithms for solving such problems are discussed, and new algorithms based on iterative re-weighting of a sample are introduced. One of these is the well-known iterative proportional fitting whose properties were already studied (Csiszar, Ann. Probab. (3) (1975) 146). A variant on this is shown to have fixed points minimizing an information functional, even if the problem is not feasible, and is shown to have only feasible fixed points if the problem is feasible. The algorithm is not shown to converge, but the relative information of successive iterates is shown to converge to zero. Applications to atmospheric dispersion and environmental transport are discussed.