The diameter of a stochastic matrix: A new measure for sensitivity analysis in Bayesian networks

TL;DR

This paper introduces the diameter, a new measure of dependence in Bayesian networks, to improve robustness analysis by providing transparent bounds on sensitivity to model misspecification.

Contribution

It proposes the diameter as a novel dependence measure for Bayesian networks, enabling more interpretable robustness bounds based on total variation distance.

Findings

Diameter offers a simple, formal robustness bound.

Bounds are more transparent than Kullback-Leibler measures.

Method integrates seamlessly into Bayesian network construction.

Abstract

Bayesian networks are one of the most widely used classes of probabilistic models for risk management and decision support because of their interpretability and flexibility in including heterogeneous pieces of information. In any applied modelling, it is critical to assess how robust the inferences on certain target variables are to changes in the model. In Bayesian networks, these analyses fall under the umbrella of sensitivity analysis, which is most commonly carried out by quantifying dissimilarities using Kullback-Leibler information measures. In this paper, we argue that robustness methods based instead on the familiar total variation distance provide simple and more valuable bounds on robustness to misspecification, which are both formally justifiable and transparent. We introduce a novel measure of dependence in conditional probability tables called the diameter to derive such bounds. This measure quantifies the strength of dependence between a variable and its parents. We demonstrate how such formal robustness considerations can be embedded in building a Bayesian network.