# Bayesian Model Averaging for Causality Estimation and its Approximation based on Gaussian Scale Mixture Distributions

arXiv: https://arxiv.org/abs/2103.08195 · HTML: https://mlsanity.com/paper/2103.08195/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Builds on 3 of its 28 references that are in the map.
- First posted on arXiv 15 Mar 2021.

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

- [Learning Bayesian Networks: The Combination of Knowledge and Statistical Data](https://mlsanity.com/paper/1302.6815/) (2013)
- [Benchmarking Framework for Performance-Evaluation of Causal Inference Analysis](https://mlsanity.com/paper/1802.05046/) (2018)
- [A Note on the Estimation Method of Intervention Effects based on Statistical Decision Theory](https://mlsanity.com/paper/1901.05186/) (2019)

## Built on by (most cited first, 4 of 4)

- [Causal Entropy Optimization](https://mlsanity.com/paper/2208.10981/) (2022)
- [Effective Bayesian Causal Inference via Structural Marginalisation and Autoregressive Orders](https://mlsanity.com/paper/2402.14781/) (2024)
- [Horseshoe Forests for High-Dimensional Causal Survival Analysis](https://mlsanity.com/paper/2507.22004/) (2025)
- [Robust Weighted Triangulation of Causal Effects Under Model Uncertainty](https://mlsanity.com/paper/2603.01119/) (2026)

## Abstract (arXiv)

In the estimation of the causal effect under linear Structural Causal Models (SCMs), it is common practice to first identify the causal structure, estimate the probability distributions, and then calculate the causal effect. However, if the goal is to estimate the causal effect, it is not necessary to fix a single causal structure or probability distributions. In this paper, we first show from a Bayesian perspective that it is Bayes optimal to weight (average) the causal effects estimated under each model rather than estimating the causal effect under a fixed single model. This idea is also known as Bayesian model averaging. Although the Bayesian model averaging is optimal, as the number of candidate models increases, the weighting calculations become computationally hard. We develop an approximation to the Bayes optimal estimator by using Gaussian scale mixture distributions.