@conference {PooleCrowley2013,
	title = {Cyclic causal models with discrete variables: Markov chain equilibrium semantics and sample ordering},
	booktitle = {IJCAI International Joint Conference on Artificial Intelligence},
	year = {2013},
	pages = {1060{\textendash}1068},
	address = {Beijing, China},
	abstract = {We analyze the foundations of cyclic causal models for discrete variables, and compare structural equation models (SEMs) to an alternative semantics as the equilibrium (stationary) distribution of a Markov chain. We show under general conditions, discrete cyclic SEMs cannot have independent noise; even in the simplest case, cyclic structural equation models imply constraints on the noise. We give a formalization of an alternative Markov chain equilibrium semantics which requires not only the causal graph, but also a sample order. We show how the resulting equilibrium is a function of the sample ordering, both theoretically and empirically.},
	keywords = {cyclic causality, probabilistic inference},
	isbn = {9781577356332},
	issn = {10450823},
	url = {http://dl.acm.org/citation.cfm?id=2540281},
	author = {Poole, David and Crowley, Mark}
}
