Suppose a scientist hypothesizes model GO shown in Fig. 1a with the goal of estimating the direct effect of a treatment x on an outcome y (structural coefficient λxy). 

λxy is the strength of the causal relationship, if there is no causal relationship, it's zero.

By the single-door criterion (Pearl 2000), she verifies λxy is identifiable in GO and equal to the regression estimand Ryx.z,

Another investigator, however, is suspicious that no common causes (confounders) exist between z and x in GO. She proposes an alternative model GA (Fig. 1b) such that the bidirected edge z ↔ x is included to account for that possibility.

So one question is how wrong could one be using Ryx.z to estimate λxy if the true causal model was given by graph GA?  which is an example of identification in sensitivity Analysis.

Example of Identification in Sensitivity Analysis

Informally, a model is identifiable if it is theoretically possible to learn the true values of this model's parameters after obtaining an infinite number of observations from it. 

Identification Problems are part of inferences, where we want to learn the true value of parameters from infinite observational data. When we cannot do it even through infinite data points, we fail to do identification.

University of Michigan - Ann Arbor

Sensitivity analysis refers to investigating whether the specified outcome could have resulted from alternative hypotheses and how strong those other hypotheses would need to be in order to explain the observed data.

The resulting relationships can be used to contrast the likelihoods with the original hypothesis. 

Sensitivity Analysis

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

Cornfield's inequality was the first formal method for sensitivity analysis in observational studies. It provides a way to prevent causal relationships from being immediately refuted with the assertion that a new factor is the true cause. 

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