Markov Properties for Linear Causal Models with Correlated Errors Markov Properties for Linear Causal Models with Correlated Errors
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BibTeX
@MISC{Kang_markovproperties,
author = {Changsung Kang and Jin Tian},
title = {Markov Properties for Linear Causal Models with Correlated Errors Markov Properties for Linear Causal Models with Correlated Errors},
year = {}
}
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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 the local Markov property will invoke only 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.
