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L4-07 · Identification before estimation

Show how two models can fit the same observations and disagree about an intervention.

Level 4 icon Level 4 · Undergraduate
Objective. Show how two models can fit the same observations and disagree about an intervention.
Before this lesson. L4-01, L4-04, L4-05
Hands-on lab. Confounding and intervention

Learn

Identification asks whether the target causal quantity is uniquely determined by the available distributions and assumptions. Estimation asks how to approximate an identified quantity from finite data. A larger dataset can improve estimation, but cannot resolve a causal ambiguity that remains even with exact observational probabilities.

In a fully observed causal DAG with suitable independent disturbances, an intervention removes the factors for the intervened variables from the observational factorization. This is called the truncated factorization. With hidden variables, this simple observed-variable calculation may fail. Identification then needs another justified argument or additional information.

Do-calculus provides graphical rules for exchanging observations, actions, and irrelevant terms under specified separation conditions. It is not permission to delete a do symbol whenever convenient. State the graph, target, available distributions, and assumptions first. A valid derivation must justify every transformation.

Practice

Solution

Model A gives probability zero because Y follows the set value of X. Model B gives probability one half because U stays fair. Their observational distributions are identical, so observations alone cannot choose between them.

Check your understanding

What can solve an identification failure caused by observationally equivalent causal models?

Show the answer

C. Adding justified assumptions or informative interventions

Different models can agree on an exact observational distribution. New causal assumptions or relevant intervention data can distinguish their causal answers.

Sources

This lesson draws on Pearl, 2009Peters et al., 2017.

Next: L4-08 · Causal discovery and its limits

References
  1. Pearl, J. (2009). Causal inference in statistics: An overview. Statistics Surveys, 3(none), 96–146. 10.1214/09-ss057
  2. Peters, J., Janzing, D., & Scholkopf, B. (2017). Elements of Causal Inference. https://mitpress.mit.edu/9780262037310/elements-of-causal-inference/
  3. Bareinboim, E. (2025). Causal Artificial Intelligence: A Roadmap for Building Causally Intelligent Systems. https://causalai-book.net/