Techniques in representing high dimensional distributions
Dorota Kurowicka
Constructing and sampling distributions with given continuous invertible marginals and given rank correlation matrix, or equivalently, constructing and sampling joint uniforms with given correlation matrix is of importance in dependence modeling. Existing methods for generating joint uniform distributions appeal to the joint normal transformation, copulas, the dependence tree - copula method and to the vine-copula method. In this course the above methods will be presented, their advantages and drawbacks will be discussed.
Another very popular method of specifying joint distribution that is Bayesian Belief Nets will be briefly introduced and compared with the vine copula method. Moreover, the Uncertainty analysis software UNICORN, developed at Delft University of Technology that utilizes some of the theoretical results presented in this course will be demonstrated.