classification, meet sampling

At astronomy meets applied math group meeting (Goodman, Hou, Foreman-Mackey, Fadely, myself) we discussed Hou's insertion of Goodman's stretch move (the basis of our popular product emcee) into Brewer's nested sampling. We think we have some improvements for the method, and Hou is meeting our functional tests, so we are about to apply the method to exoplanet systems. After that we discussed an idea we have been kicking around for a year or so: If a MCMC sampler is stuck in a small number of optima and can't easily transition from one optimum to another, then we should split the parameter space up into regions such that there is only one optimum per region. Then we can sample each region independently and recombine the individual-region samplings into one full sampling. We worked out a method that involves k-means (to do the clustering to find optima) and SVM (to do the splitting of the space). In principle we could make a very general, very flexible sampler this way.