Error probabilities for inference of causal directions

Synthese 163 (3):409 - 418 (2008)
Abstract
A main message from the causal modelling literature in the last several decades is that under some plausible assumptions, there can be statistically consistent procedures for inferring (features of) the causal structure of a set of random variables from observational data. But whether we can control the error probabilities with a finite sample size depends on the kind of consistency the procedures can achieve. It has been shown that in general, under the standard causal Markov and Faithfulness assumptions, the procedures can only be pointwise but not uniformly consistent without substantial background knowledge. This implies the impossibility of choosing a finite sample size to control the worst case error probabilities. In this paper, I consider the simpler task of inferring causal directions when the skeleton of the causal structure is known, and establish a similarly negative result concerning the possibility of controlling error probabilities. Although the result is negative in form, it has an interesting positive implication for causal discovery methods.
Keywords Bayesian network  Causal inference  Consistency  Error probability
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References found in this work BETA
Frank Arntzenius (1992). The Common Cause Principle. PSA: Proceedings of the Biennial Meeting of the Philosophy of Science Association 1992:227 - 237.
DM Hausman & J. Woodward (1999). Independence, Invariance and the Causal Markov Condition. British Journal for the Philosophy of Science 50 (4):521-583.
Michael McDermott (1995). Redundant Causation. British Journal for the Philosophy of Science 46 (4):523-544.

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