Sensitivity of Causal Effect Estimates Under Assumed Gaussian Noise to the True Latent Noise Distribution

Estimating causal effects from observational data is frequently challenged by the presence of unobserved confounders. The ρ-GNF estimator addresses this challenge by using deep generative models to perform sensitivity analysis, parametrizing the latent confounding structure using a Gaussian copula. However, the reliability of this estimator when the true underlying latent distribution deviates from the Gaussian copula assumption remains a critical open question. This thesis systematically evaluates the robustness of the ρ-GNF to misspecified latent structures. Utilizing a controlled simulation based strategy, we tested the model against data generating processes exhibiting non-linear (quadratic) and asymmetric tail-dependent (Clayton copula) latent structures. The analysis focused on whether the estimator could determine an "effective" sensitivity parameter that recovers the true Average Causal Effect (ACE) despite the distributional mismatch. Our results demonstrate that the ρ-GNF is remarkably robust to structural misspecification. In both non-linear and tail-dependent scenarios, the model consistently yielded a specific sensitivity parameter that compensated for the bias, aligning the estimated ACE with the ground truth. Furthermore, the estimator exhibited high stability and monotonicity across repeated experiments. These findings suggest that the Gaussian copula serves as a flexible functional proxy for complex dependency structures, extending the practical applicability of the ρ-GNF beyond strictly Gaussian copula environments.