Bayesian Network Representation of Joint Normal Distributions - Confounding Variables Model

Abstract

This article is the second of a series discussing the Bayesian Network representation of multivariate normal distributions. In the first article we introduced a cascading regressions model leading to a Bayesian network representation of any joint normal distribution [Pap22]. A joint normal distribution being fully specified by its mean vector and its covariance matrix is not simple to interact with as its Bayesian network equivalent. Representing a joint normal distribution as a Bayesian network enables visualizing and interact the distribution through the lens of probabilistic graphical models with TKRISK®. We demonstrate in this article a simple yet powerful approach using a confounding variables model.

Keywords: Bayesian network, multivariate distribution, covariance

JEL Classification: C00, G13