Errata: older papers by Shpitser, Tian, and Pearl

[rjc955]

While implementing a set of algorithms by Correa, Lee, and Bareinboim, we reviewed sections of some papers they cited and uncovered a few errata.

Errata

A. Shpitser and Pearl 2008: Complete Identification Methods for the Causal Hierarchy

1. p. 1953: the last line reads, "Putting everything together, we obtain: $P_{x}{(y_{1},y{2}) = \Sigma_{w_{2}}{P(y_{1},w_{2})}\Sigma_{w_1}}{P(y_{1}|x,w_{1})P(w_{1})}$." We think it should read: $P_{x}{(y_{1},y{2}) = \Sigma_{w_{2}}{P(y_{2},w_{2})}\Sigma_{w_1}}{P(y_{1}|x,w_{1})P(w_{1})}$.

B. Tian and Pearl 2003: On the Identification of Causal Effects

1. p. 26: the Identify() function technically requires an additional parameter, $G$, in order to compute $A=An(C){G{T}}$ at one point. Later publications, such as Correa and Barenboim 2020, pick up on this fact.

C. Inconsistencies in terminology across papers

1. (Restated from Issue Errata: "Counterfactual Transportability: A Formal Approach" and "General Transportability of Soft Interventions: Completeness Results" #206) There seems to be an inconsistency in how different authors use the term "c-factor." Tian and Pearl (2002) define "c-factor" as follows: "We will call $Q[S_{i}]$ the c-factor corresponding to the c-component $S_{i}$." In the rest of the paper, each time they refer to a "c-factor" it is to apply the $Q$ function to a c-component. In "General Transportability of Soft Interventions: Completeness Results," (page 6), Correa and Bareinboim cite Tian and Pearl's paper in referencing "the concept of C-factors and C-components," and they use "C-factor" to denote the Q function applied to any set of vertices in a graph. In the "Causal Effect" R package, Santu Tikka denotes the compute.c.factor() function to only apply to c-components. The confusion may originate in the ambiguity of Tian and Pearl's original definition of "c-factor": did they intend for "c-factor" to denote the function $Q$, or did they intend for the $Q$ function to be a "c-factor" only when applied to a c-component?