{"ID":2883153,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2508.08752","arxiv_id":"2508.08752","title":"Sensitivity Analysis to Unobserved Confounding with Copula-based Normalizing Flows","abstract":"We propose a novel method for sensitivity analysis to unobserved confounding in causal inference. The method builds on a copula-based causal graphical normalizing flow that we term $ρ$-GNF, where $ρ\\in [-1,+1]$ is the sensitivity parameter. The parameter represents the non-causal association between exposure and outcome due to unobserved confounding, which is modeled as a Gaussian copula. In other words, the $ρ$-GNF enables scholars to estimate the average causal effect (ACE) as a function of $ρ$, accounting for various confounding strengths. The output of the $ρ$-GNF is what we term the $ρ_{curve}$, which provides the bounds for the ACE given an interval of assumed $ρ$ values. The $ρ_{curve}$ also enables scholars to identify the confounding strength required to nullify the ACE. We also propose a Bayesian version of our sensitivity analysis method. Assuming a prior over the sensitivity parameter $ρ$ enables us to derive the posterior distribution over the ACE, which enables us to derive credible intervals. Finally, leveraging on experiments from simulated and real-world data, we show the benefits of our sensitivity analysis method.","short_abstract":"We propose a novel method for sensitivity analysis to unobserved confounding in causal inference. The method builds on a copula-based causal graphical normalizing flow that we term $ρ$-GNF, where $ρ\\in [-1,+1]$ is the sensitivity parameter. The parameter represents the non-causal association between exposure and outcom...","url_abs":"https://arxiv.org/abs/2508.08752","url_pdf":"https://arxiv.org/pdf/2508.08752v1","authors":"[\"Sourabh Balgi\",\"Marc Braun\",\"Jose M. Peña\",\"Adel Daoud\"]","published":"2025-08-12T08:57:30Z","proceeding":"stat.ME","tasks":"[\"stat.ME\",\"cs.LG\",\"stat.ML\"]","methods":"[]","has_code":false}