# Global Sensitivity Analysis of Uncertain Parameters in Bayesian Networks

arXiv: https://arxiv.org/abs/2406.05764 · HTML: https://mlsanity.com/paper/2406.05764/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 9 of its 68 references that are in the map.
- First posted on arXiv 9 Jun 2024.

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

- [Bayesian Networks in Healthcare: Distribution by Medical Condition](https://mlsanity.com/paper/2002.00224/) (2020)
- [Duality of Graphical Models and Tensor Networks](https://mlsanity.com/paper/1710.01437/) (2017)
- [Sensitivity and robustness analysis in Bayesian networks with the bnmonitor R package](https://mlsanity.com/paper/2107.11785/) (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)
- [Sensitivity Analysis for Probability Assessments in Bayesian Networks](https://mlsanity.com/paper/1303.1470/) (2013)
- [You Only Derive Once (YODO): Automatic Differentiation for Efficient Sensitivity Analysis in Bayesian Networks](https://mlsanity.com/paper/2206.08687/) (2022)
- [Fine-Tuning the Odds in Bayesian Networks](https://mlsanity.com/paper/2105.14371/) (2021)
- [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)

- [Beyond Post-hoc Explanation: Toward Glassbox AI via Probabilistic Mediation](https://mlsanity.com/paper/2606.07113/) (2026)

## Abstract (arXiv)

Traditionally, the sensitivity analysis of a Bayesian network studies the impact of individually modifying the entries of its conditional probability tables in a one-at-a-time (OAT) fashion. However, this approach fails to give a comprehensive account of each inputs' relevance, since simultaneous perturbations in two or more parameters often entail higher-order effects that cannot be captured by an OAT analysis. We propose to conduct global variance-based sensitivity analysis instead, whereby n parameters are viewed as uncertain at once and their importance is assessed jointly. Our method works by encoding the uncertainties as n additional variables of the network. To prevent the curse of dimensionality while adding these dimensions, we use low-rank tensor decomposition to break down the new potentials into smaller factors. Last, we apply the method of Sobol to the resulting network to obtain n global sensitivity indices. Using a benchmark array of both expert-elicited and learned Bayesian networks, we demonstrate that the Sobol indices can significantly differ from the OAT indices, thus revealing the true influence of uncertain parameters and their interactions.