### Abstract

Original language | English |
---|---|

Pages (from-to) | 409-418 |

Number of pages | 10 |

Journal | Synthese |

Volume | 163 |

Issue number | 3 |

DOIs | |

Publication status | Published - 1 Jan 2008 |

Externally published | Yes |

### Fingerprint

### Keywords

- Bayesian network; Causal inference; Consistency; Error probability

### Cite this

*Synthese*,

*163*(3), 409-418. https://doi.org/10.1007/s11229-007-9295-1

}

*Synthese*, vol. 163, no. 3, pp. 409-418. https://doi.org/10.1007/s11229-007-9295-1

**Error probabilities for inference of causal directions.** / ZHANG, Jiji.

Research output: Journal Publications › Journal Article (refereed)

TY - JOUR

T1 - Error probabilities for inference of causal directions

AU - ZHANG, Jiji

PY - 2008/1/1

Y1 - 2008/1/1

N2 - 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.

AB - 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.

KW - Bayesian network; Causal inference; Consistency; Error probability

UR - http://commons.ln.edu.hk/sw_master/4151

U2 - 10.1007/s11229-007-9295-1

DO - 10.1007/s11229-007-9295-1

M3 - Journal Article (refereed)

VL - 163

SP - 409

EP - 418

JO - Synthese

JF - Synthese

SN - 0039-7857

IS - 3

ER -