Conditional Independence Beyond Domain Separability: Discussion of Engelke and Hitz (2020)

TL;DR

This paper discusses a new, general definition of conditional independence for multivariate distributions, extending beyond extreme value theory and including prior definitions as special cases.

Contribution

It proposes a broad, context-independent framework for independence and conditional independence applicable to general random variables.

Findings

Introduces a new definition of conditional independence for multivariate distributions.

Includes the authors' extreme value theory definition as a special case.

Highlights the importance of independence concepts beyond extreme value contexts.

Abstract

We congratulate Engelke and Hitz on a thought-provoking paper on graphical models for extremes. A key contribution of the paper is the introduction of a novel definition of conditional independence for a multivariate Pareto distribution. Here, we outline a proposal for independence and conditional independence of general random variables whose support is a general set Omega in multidimensional real number space. Our proposal includes the authors' definition of conditional independence, and the analogous definition of independence as special cases. By making our proposal independent of the context of extreme value theory, we highlight the importance of the authors' contribution beyond this particular context.