1. For implementation by a programmed computer-based circuit, a method for computing probability densities of a set of data representing multivariate Gaussians, the method comprising the steps of: generating cavity-local univariate truncated Gaussians by truncating cavity-local univariate Gaussians for the set of data; selecting site-local univariate Gaussians based on a determination that the moments of the products of the cavity-local univariate Gaussians and the selected site-local univariate Gaussians match the moments of the cavity-local univariate truncated Gaussians; and in response to a current global Gaussian based on the site-local univariate Gaussians matching a previous global Gaussian, generating Gaussian probability density data corresponding to the set of data.