A Robust Bayesian Approach for Causal Inference Problems

Basu, Tathagata; Troffaes, Matthias C. M.; Einbeck, Jochen

Abstract

Causal inference concerns finding the treatment effect on subjects along with causal links between the variables and the outcome. However, the underlying heterogeneity between subjects makes the problem practically unsolvable. Additionally, we often need to find a subset of explanatory variables to understand the treatment effect. Currently, variable selection methods tend to maximise the predictive performance of the underlying model, and unfortunately, under limited data, the predictive performance is hard to assess, leading to harmful consequences. To address these issues, in this paper, we consider a robust Bayesian analysis which accounts for abstention in selecting explanatory variables in the high dimensional regression model. To achieve that, we consider a set of spike and slab priors through prior elicitation to obtain a set of posteriors for both the treatment and outcome model. We are specifically interested in the sensitivity of the treatment effect in high dimensional causal inference as well as identifying confounder variables. However, confounder selection can be deceptive in this setting, especially when a predictor is strongly associated with either the treatment or the outcome. To avoid that we apply a post-hoc selection scheme, attaining a smaller set of confounders as well as separate sets of variables which are only related to treatment or outcome model. Finally, we illustrate our method to show its applicability.

Citation

Basu, T., Troffaes, M. C. M., & Einbeck, J. (2023, September). A Robust Bayesian Approach for Causal Inference Problems. Presented at ECSQARU 2023, Arras, France

• Presentation Conference Type: Conference Paper (published)
• Conference Name: ECSQARU 2023
• Start Date: Sep 19, 2023
• End Date: Sep 22, 2023
• Acceptance Date: Sep 19, 2023
• Online Publication Date: Nov 19, 2023
• Publication Date: 2023
• Deposit Date: Nov 26, 2024
• Publicly Available Date: Nov 26, 2024
• Publisher: Springer Nature
• Peer Reviewed: Peer Reviewed
• Pages: 359-371
• Series Title: Lecture Notes in Computer Science
• Book Title: Symbolic and Quantitative Approaches to Reasoning with Uncertainty
• ISBN: 9783031456077; 9783031456084
• DOI: https://doi.org/10.1007/978-3-031-45608-4_27
• Public URL: https://durham-repository.worktribe.com/output/3106504