Several years ago I was working with a brilliant Russian nuclear physicist. We had a problem that required computing the CDF for the multivariate normal distribution. He had a technique that he found in some book from Russia int the 80s that had a heuristic that allowed him to factorize an arbitrary high order integral, collapse it to a single dimension, and compute the integral to a high accuracy. This was his description of what he was doing, I don’t know what part of it was diversion. He was extremely secretive about it, and kept it hidden. In general he was very weird and paranoid.
This approximation was extremely fast, and it was beating all the numerical methods we had. Moreover, it was a very good approximation, and worked very well for what we wanted. We benched marked it agains lower dimensions, and it was always very accurate and computationally efficient.
I’ve been trying to look for what he does based on his vague descriptions, I have an immediate need for it. I don’t know what branch of math to look into. I’ve been looking for approximations to the multivariate distribution in high dimensions for a long time, there is nothing. All methods are either numerical methods (which I’m not a fan of), or have exponential time complexity.
Does anyone have any ideas?