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

Abstract

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 (−1,1) n 2 →C(n) ( 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.