A Short Note on a Flexible Cholesky Parameterization of Correlation Matrices

TL;DR

This paper introduces a flexible, differentiable Cholesky-based parameterization of correlation matrices that enables easier incorporation of prior restrictions and boundary constraints, improving random sampling methods like MCMC.

Contribution

It presents a novel Cholesky parameterization that allows for a priori restrictions and boundary constraints on correlation matrices, aiding Bayesian sampling techniques.

Findings

Enables smooth and differentiable transformations of correlation matrices.

Facilitates boundary constraints in MCMC sampling.

Improves random sampling under positivity constraints.

Abstract

We propose a Cholesky factor parameterization of correlation matrices that facilitates a priori restrictions on the correlation matrix. It is a smooth and differentiable transform that allows additional boundary constraints on the correlation values. Our particular motivation is random sampling under positivity constraints on the space of correlation matrices using MCMC methods.