Skip to main content
Article thumbnail
Location of Repository

Markov Properties for Linear Causal Models with Correlated Errors

By Changsung Kang and Jin Tian

Abstract

A linear causal model with correlated errors, represented by a DAG with bi-directed edges, can be tested by the set of conditional independence relations implied by the model. A global Markov property specifies, by the d-separation criterion, the set of all conditional independence relations holding in any model associated with a graph. A local Markov property specifies a much smaller set of conditional independence relations which will imply all other conditional independence relations which hold under the global Markov property. For DAGs with bi-directed edges associated with arbitrary probability distributions, a local Markov property is given in Richardson (2003) which may invoke an exponential number of conditional independencies. In this paper, we show that for a class of linear structural equation models with correlated errors, there is a local Markov property which will invoke only a linear number of conditional independence relations. For general linear models, we provide a local Markov property that often invokes far fewer conditional independencies than that in Richardson (2003). The results have applications in testing linear structural equation models with correlated errors

Topics: Markov Properties, Linear Causal Models, Linear Structural Equation Models, Graphical Models
Year: 2010
OAI identifier: oai:CiteSeerX.psu:10.1.1.163.2925
Provided by: CiteSeerX
Download PDF:
Sorry, we are unable to provide the full text but you may find it at the following location(s):
  • http://citeseerx.ist.psu.edu/v... (external link)
  • http://www.cs.iastate.edu/~jti... (external link)
  • Suggested articles


    To submit an update or takedown request for this paper, please submit an Update/Correction/Removal Request.