Title

Error probabilities for inference of causal directions

Document Type

Journal article

Source Publication

Synthese

Publication Date

2008

Volume

163

Issue

3

First Page

409

Last Page

418

Keywords

Bayesian network; Causal inference; Consistency; Error probability

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.

DOI

10.1007/s11229-007-9295-1

Print ISSN

00397857

E-ISSN

15730964

Publisher Statement

Copyright © 2008 Springer Netherlands.

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Recommended Citation

Zhang, J. (2008). Error probabilities for inference of causal directions. Synthese, 163(3), 409-418. doi: 10.1007/s11229-007-9295-1