Fusion of Probabilistic Knowledge as Foundation for Sliced-Normal Approach

In many practical applications, it turns out to be efficient to use Sliced-Normal multi-D distributions, i.e., distributions for which the logarithm of the probability density function (pdf) is a polynomial -- -- to be more precise, it is a sum of squares of several polynomials. This class is a natural extension of normal distributions, i.e., distributions for which the logarithm of the pdf is a quadratic polynomial. In this paper, we provide a possible theoretical explanation for this empirical success