# Intervention and Conditioning in Causal Bayesian Networks

arXiv: https://arxiv.org/abs/2405.14728 · HTML: https://mlsanity.com/paper/2405.14728/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 3 of its 22 references that are in the map.
- First posted on arXiv 23 May 2024.

## Builds on (most cited first, 3 of 3)

- [Explaining Black-Box Algorithms Using Probabilistic Contrastive Counterfactuals](https://mlsanity.com/paper/2103.11972/) (2021)
- [Causal Explanations and XAI](https://mlsanity.com/paper/2201.13169/) (2022)
- [Causality-Guided Adaptive Interventional Debugging](https://mlsanity.com/paper/2003.09539/) (2020)

## Built on by (most cited first, 3 of 3)

- [Causal Counterfactuals Reconsidered](https://mlsanity.com/paper/2512.12804/) (2025)
- [Counterfactual identifiability beyond global monotonicity: non-monotone triangular structural causal models](https://mlsanity.com/paper/2605.04413/) (2026)
- [Actual causality in fault trees](https://mlsanity.com/paper/2607.01840/) (2026)

## Abstract (arXiv)

Causal models are crucial for understanding complex systems and identifying causal relationships among variables. Even though causal models are extremely popular, conditional probability calculation of formulas involving interventions pose significant challenges. In case of Causal Bayesian Networks (CBNs), Pearl assumes autonomy of mechanisms that determine interventions to calculate a range of probabilities. We show that by making simple yet often realistic independence assumptions, it is possible to uniquely estimate the probability of an interventional formula (including the well-studied notions of probability of sufficiency and necessity). We discuss when these assumptions are appropriate. Importantly, in many cases of interest, when the assumptions are appropriate, these probability estimates can be evaluated using observational data, which carries immense significance in scenarios where conducting experiments is impractical or unfeasible.