Gaussian Process: A stochastic process in which any finite collection of random variables has a joint Gaussian distribution, commonly used for non-parametric modelling.

We will begin with a thorough review of basic probability theory including probability spaces, random variables, probabilistic inequalities, and laws of large numbers. We then will study a number of ...

SIAM Journal on Applied Mathematics, Vol. 18, No. 4 (Jun., 1970), pp. 721-737 (17 pages) The probability density functions of products of independent beta, gamma and central Gaussian random variables ...

We discuss properties of distributions that are multivariate totally positive of order two (MTP2) related to conditional independence. In particular, we show that any independence model generated by ...

In the first part of the course, we will start with an introduction to the Gaussian free field (GFF), which is an object which has been at the heart of some recent groundbreaking developments in ...