We define $G_O$ as model of the the original hypothesis. $G_A$ is the model made to account for confounders. $G_B$ is another variation of $G_O$.

Sensitivity analysis, Identification : models

PUSH-FORWARD Theorem

Algorithm for Sensitivity Curves

Image : Sensitivity Analyses

1. Introduce formal sensitivity analysis for linear SCMs and reduce it to a non-zero constrained identification problem.
2. Introduce graphical process PUSH-FORWARD to simplify identification - which can they be solved by a number of algorithms
3. Develop graph-based constrained identification solving algorithm that returns sensitivity curve.

University of Michigan - Ann Arbor

Pearl, Judea, et al. “Sensitivity Analysis of Linear Structural Causal Models.”

http://proceedings.mlr.press/v97/cinelli19a/cinelli19a.pdf

Sensitivity Analysis of Linear Structural Causal Models

Keele, L. (2015). The Statistics of Causal Inference: A View from Political Methodology. Political Analysis, 23(3), 313–335. doi: 10.1093/pan/mpv007

The Statistics of Causal Inference: A View from Political Methodology. Political Analysis

Causal inferences need a formal method to quantify sensitivity to causal assumptions. There is no all-purpose algorithm to determine sensitivity. 
This paper aims to find a general method that works for finding the sensitivity of all arbitrary linear SCMs.

Key Idea of Paper

Contributions of Paper

The research on sensitivity analysis of linear structural causal models (SCMs) yielded two primary conclusions:
1. It generated a general framework for conducting sensitivity analyses specifically in linear SCMs.
2. Future research should explore extensions into different models to develop techniques applicable to more general models.

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