Lets say I have a multivariate Gaussian. I'd like to "pack" that Gaussian full of smaller Gaussians. Intuitively, it seems like I would just sample N points from the original MV Gaussian for the means, and then set each of their covariance to 1/N of the original covariance. Is there a better/more formal way to accomplish what I'd like to do? I've attached an image of what I'm trying to get at, what is hard to show is that the density of the samples follows the original Gaussian distribution.
Thanks
