Correctness is widely, but tacitly, understood in the literature on causal inference to be the primary criterion when evaluating the properties of a procedure/method of causal inference. However, I haven't found any reference that actually explains why this is so. Does anyone know an eminent work that explains why correctness should be the primary property of a procedure of causal inference, with completeness etc. following only as secondary criteria?
In the statistics literature the properties of procedures tend to be statistical ones --- like unbiasedness (of estimators of causal effects, or of tests of causal hypotheses) and other such properties. I haven't seen "correctness" or "completeness" in that literature.
Can you explain what correctness is supposed to be - I am ignorant of this.
Dear Jake and Kelvyn, many thanks for your replies.
Correctness and completeness are more commonly used in the literature on search algorithms. Various scholars introduce additional concepts (e.g., Spirtes, Glymour and Scheines (2000:289) also introduce "reliability" and "informativeness"). A procedure is correct iff what this procedure infers is causally relevant. Completeness is the inverse: a procedure is complete iff what is causally relevant is inferred by this procedure. Thus, if there is missing data, a procedure may still be correct because it does not commit causal fallacies, but it cannot be expected to be complete anymore as the data are insufficient to reveal all causally relevant components.
Spirtes, Peter, Clark N. Glymour, and Richard Scheines. 2000. Causation, prediction, and search. 2nd ed. Cambridge, MA: MIT Press.
Apologies
I have read Spirtes et al and I should have known about correctness - it was a long time ago (!) that I read about it and I have not done work in this area but I remain fascinated by it.
I suggest that if you have not already done so - that you ask the same question on
http://stackoverflow.com/
as there are many more people interested in machine learning there.
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