Today, there is a talk jointly organized between the departments of Computer Science, Economics, Mathematics, Philosophy, Public Health Sciences and Statistics, by Judea Pearl who is a professor of Department of Computer Science at UCLA. Professor Pearl just was awarded an honorary doctorate degree at University of Toronto today. He is the father of journalist Daniel Pearl. His talk today is about the Mathematics of Causal Inference. He says that the explanation of causal inference is actually really simple and common sense.
Causal analysis deals with changes (dynamics) whereas probability and statistics deal with static relations. Causal and statistical concepts do not mix. Statistical concepts can be computed given the joint probability distribution. For example, regression and association/independence are statistical concepts. Statistical assumptions and data and causal assumptions combine to form causal conclusions. Causal assumptions cannot be expressed in the mathematical language of standard statistics. Causality then needs special mathematics. In high school algebra, we weren't allowed to wipe out equations, but in causality, you need to wipe out equations. Professor Pearl just mentioned that Computer Science is the science of daydreaming (amid smiles and laughter in the audience).
To make causality mathematical, we need to introduce counterfactuals.
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