What is do-calculus Pearl?

Do-calculus is a formal set of rules developed by Judea Pearl for deriving causal effects from observational data using graphical models (e.g., Bayesian networks).

The main idea of do-calculus is to analyze how intervention (the do operation) affects the distribution of variables in a system, distinguishing correlation from causality.

The rules of do-calculus allow transforming expressions with the do operation (e.g., P(Y | do(X))) into expressions without do, if possible, using the structure of the causal model. This is important for estimating causal effects from data where direct experimental intervention is not possible.

Applications:

• Estimating treatment effects in medicine without randomization.
• Analyzing causal relationships in economics and social sciences.
• Uplift modeling — identifying the effect of interventions on user behavior.

Thus, do-calculus is a powerful tool for formally deriving causal effects from observational data, based on graphs and probabilistic models.