# Making Sensitivity Analysis Computationally Efficient

arXiv: https://arxiv.org/abs/1301.3868 · HTML: https://mlsanity.com/paper/1301.3868/

## Key facts

- Cited by 7 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 16 Jan 2013.

## Built on by (most cited first, 7 of 7)

- [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)
- [Global Sensitivity Analysis of Uncertain Parameters in Bayesian Networks](https://mlsanity.com/paper/2406.05764/) (2024)
- [The diameter of a stochastic matrix: A new measure for sensitivity analysis in Bayesian networks](https://mlsanity.com/paper/2407.04667/) (2024)
- [Integrating Probabilistic Trees and Causal Networks for Clinical and Epidemiological Data](https://mlsanity.com/paper/2501.15973/) (2025)
- [Global sensitivity analysis in probabilistic graphical models](https://mlsanity.com/paper/2110.03749/) (2021)

## Abstract (arXiv)

To investigate the robustness of the output probabilities of a Bayesian network, a sensitivity analysis can be performed. A one-way sensitivity analysis establishes, for each of the probability parameters of a network, a function expressing a posterior marginal probability of interest in terms of the parameter. Current methods for computing the coefficients in such a function rely on a large number of network evaluations. In this paper, we present a method that requires just a single outward propagation in a junction tree for establishing the coefficients in the functions for all possible parameters; in addition, an inward propagation is required for processing evidence. Conversely, the method requires a single outward propagation for computing the coefficients in the functions expressing all possible posterior marginals in terms of a single parameter. We extend these results to an n-way sensitivity analysis in which sets of parameters are studied.