Primary Submission Category: Causal Inference Education
Towards Accessible Proof Techniques for Non-Identification In Causal Inference
Authors: Juan Mendez, Hadassah Lurbur, Rohit Bhattacharya,
Presenting Author: Juan Mendez*
Increasingly causal inference is becoming a staple in undergraduate and graduate curricula in fields such as computer science, (bio)statistics, economics, and epidemiology. A fundamental point that must be emphasized in these courses is why certain causal parameters cannot be computed from observed data without sufficient restrictions on the data generating process. Explanations of the non-identifiability of causal parameters, even at the graduate level, often only provide a rough intuition, or rely on specially constructed counter examples that do not generalize well if the student were interested in examining different parameters.
We explore classic identification results in causal inference and work through proofs of identification and non-identification using a general and (we hope) more accessible framework that uses concepts a student might encounter in undergraduate computer science or statistics courses-–concepts in discrete mathematics like probability distributions, bijections, and proof by contradiction—and an introductory course in probabilistic graphical models for more advanced proofs. We first present arguments of non-identification of objects like cross-world parameters (joint distributions over potential outcomes that disagree on the value of treatment assignment) and build up to other classical results in causal inference, such as necessary and sufficient conditions for identifying the effect of one variable on all other variables (Tian & Pearl, 2002).