Thank you for the clarification, and yes, most of what I gave as an example could be characterized as forward probabilistic methods. - Start with a value + div

Thank you for the clarification, and yes, most of what I gave as an example could be characterized as forward probabilistic methods. - Start with a value + divergence and then propagate that state through your transforms to get a mean + divergent final state. I should note that in the given example the base divergences need to be found through some method, which is usually running a Monte-carlo around some baseline state, and then making the significant assumption that new calculations (with small deltas) follow roughly the same statistical behavior. For the backwards case, that can be a significantly more challenging case, as it basically comes down to performing approximate eigenvalue decomposition. However, there are a lot of SOTA tools like pretty much anything from this list: - http://en.wikipedia.org/wiki/Pattern_recognition#Algorithms http://en.wikipedia.org/wiki/Pattern_recognition#Algorithms IE, the crater example is fairly close to the setup for a Hidden Markov Model, where we get final data, and assume that it is based on a set of hidden states. Or for lighter reading, almost any of the major tools used in the Netflix recommendation contest, which is effectively an enormous version of this problem.