A parameterization of positive definite matrices in terms of partial correlation vines

We present a parameterization of the class PD(n) of positive definite n×n matrices using regular vines and partial correlations. Using a bijection from (C(n) is the class of n×n correlation matrices) with a clear probabilistic interpretation [Ann. Statist. 30 (4) (2002) 1031], we suggest a new approach to various problems involving positive definiteness.