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

arXiv: https://arxiv.org/abs/2407.04667 · HTML: https://mlsanity.com/paper/2407.04667/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 9 of its 60 references that are in the map.
- First posted on arXiv 5 Jul 2024.

## Builds on (most cited first, 9 of 9)

- [Context-Specific Independence in Bayesian Networks](https://mlsanity.com/paper/1302.3562/) (2013)
- [The R Package stagedtrees for Structural Learning of Stratified Staged Trees](https://mlsanity.com/paper/2004.06459/) (2020)
- [Labeled Directed Acyclic Graphs: a generalization of context-specific independence in directed graphical models](https://mlsanity.com/paper/1310.1187/) (2013)
- [Sensitivity and robustness analysis in Bayesian networks with the bnmonitor R package](https://mlsanity.com/paper/2107.11785/) (2021)
- [Staged trees and asymmetry-labeled DAGs](https://mlsanity.com/paper/2108.01994/) (2021)
- [Making Sensitivity Analysis Computationally Efficient](https://mlsanity.com/paper/1301.3868/) (2013)
- [A geometric characterisation of sensitivity analysis in monomial models](https://mlsanity.com/paper/1901.02058/) (2018)
- [You Only Derive Once (YODO): Automatic Differentiation for Efficient Sensitivity Analysis in Bayesian Networks](https://mlsanity.com/paper/2206.08687/) (2022)
- [The YODO algorithm: An efficient computational framework for sensitivity analysis in Bayesian networks](https://mlsanity.com/paper/2302.00364/) (2023)

## Built on by (most cited first, 1 of 1)

- [A Stable Distance Persistence Homology for Dynamic Bayesian Network Clustering](https://mlsanity.com/paper/2605.11226/) (2026)

## Abstract (arXiv)

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.