got it!

Adrian Price-Whelan (Flatiron) and I spent time this past week trying to factorize products of Gaussians into new products of different Gaussians. The context is Bayesian inference, where you can factor the joint probability of the data and your parameters into a likelihood times a prior or else into an evidence (what we here call the FML) times a posterior. The factorization was causing us pain this week, but I finally got it this weekend, in the woods. The trick I used (since I didn't want to expand out enormous quadratics) was to use a determinant theorem to get part of the way, and some particularly informative terms in the quadratic expansion to get the rest of the way. Paper (or note or something) forthcoming...