The causal manipulation of chain event graphs
Riccomagno, Eva and Smith, J. Q., 1953- (2007) The causal manipulation of chain event graphs. Working Paper. University of Warwick. Centre for Research in Statistical Methodology, Coventry.
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Discrete Bayesian Networks (BN’s) have been very successful as a framework both for inference and for expressing certain causal hypotheses. In this paper we present a class of graphical models called the chain event graph (CEG) models, that generalises the class of discrete BN models. It provides a flexible and expressive framework for representing and analysing the implications of causal hypotheses, expressed in terms of the effects of a manipulation of the generating underlying system.We prove that, as for a BN, identifiability analyses of causal effects can be performed through examining the topology of the CEG graph, leading to theorems analogous to the back-door theorem for the BN.
|Item Type:||Working or Discussion Paper (Working Paper)|
|Subjects:||Q Science > QA Mathematics|
|Divisions:||Faculty of Science > Statistics|
|Library of Congress Subject Headings (LCSH):||Graphical modeling (Statistics), Bayesian statistical decision theory|
|Series Name:||Working papers|
|Publisher:||University of Warwick. Centre for Research in Statistical Methodology|
|Place of Publication:||Coventry|
|Number of Pages:||49|
|Status:||Not Peer Reviewed|
|Access rights to Published version:||Open Access|
|References:|| P. Anderson and J.Q. Smith (2005). A graphical framework for representing the semantics of asymmetric models. Technical report 05-12, CRiSM, Department of Statistics, The University of Warwick.  T. Bedford and R. Cooke (2001). Probabilistic risk analysis: foundations and methods. Cambridge University Press, Cambridge.  C. Boutilier, N. Freidman, M. Goldszmidt and D. Koller (1996). Context-specific independence in Bayesian networks. In Proceedings of UAI - 96 115-123.  R.E. Bryant (1986). Graphical algorithms for Boolean function manipulation. IEEE Transactions of Computers C-35 677-691.  G.A. Churchill (1995). Accurate restoration of DNA sequences. In C. Gatsaris et al. (eds.) Case Studies in Bayesian Statistics vol. II, Springer-Verlag, New-York, 90-148.  A.P. Dawid (2002). Infuence Diagrams for Causal Modelling and Inference. International Statistical Reviews, 70:161 - 89.  A.P. Dawid, J. Mortera, V.L. Pascali and D. W. van Boxel (2002). Probabilistic expert systems for forensic inference from genetic markers. Scand. J. Statist., 29:577595.  N. Freidman and M. Goldszmidt (1999). Learning Bayesian networks with local structure. In M.I. Jordan (ed.) Learning in Graphical Models MIT Press, 421-459.  S. French (ed.) (1989). Readings in Decision analysis. Chapman and Hall/CRC, London.  L.D. Garcia, M. Stillman and B. Sturmfels (2005). Algebraic geometry of Bayesian networks, Journal of Symbolic Computation, 39(3-4):331-355.  D. Glymour and G.F. Cooper (1999). Computation, Causation, and Discovery. MIT Press, Cambridge, MA.  D. Hausman (1998). Causal Asymmetries, Cambridge University Press, Cambridge.  M. Jaeger (2004). Probabilistic decision graphs - combining verification and AI techniques for probabilistic inference. Int.J. of Uncertainty, Fuzziness and Knowledge-based Systems, 12:19-42.  S.L. Lauritzen (1996). Graphical models. Oxford Science Press, Oxford, 1st edition.  R. Lyons (1990). Random walks and percolation on trees. Annals of Probability, 18:931-958.  D. McAllester, M. Collins and F. Pereira (2004). Case-factor diagrams for structured probability models. In Proceedings of UAI - 2004 382-391.  J. Pearl (1995). Causal diagrams for empirical research. Biometrika, 82:669-710.  J. Pearl (2000). Causality. models, reasoning and inference. Cambridge University Press, Cambridge.  J. Pearl (2003). Statistics and Causal Inference: A Review (with discussion). Test, 12(2):281-345.  G. Pistone, E. Riccomagno and H.P. Wynn (2001). Algebraic Statistics. Chapman & Hall/CRC, Boca Raton.  D. Poole and N.L. Zhang (2003). Exploiting contextual independence in probabilistic inference. Journal of Artificial Intelligence research, 18:263-313.  E. Riccomagno and J.Q. Smith (2003). Non-Graphical Causality: a generalisation of the concept of a total cause. Research report series No. 394, Dept of Statistics, The University of Warwick.  E. Riccomagno and J.Q. Smith (2004). Identifying a cause in models which are not simple Bayesian networks. In Proceedings of the 10th Conference on Information Processing and Management of Uncertainty in Knowledge-Based Systems, 1315-1322.  E. Riccomagno and J.Q. Smith (2007). The geometry of causal probability trees that are algebraically constrained. In L Pronzato and A A Zigljavsky (eds.) In Search for Optimality in Design and Statistics: Algebraic and Dynamical System Methods Springer 131-152.  G. Shafer (1996). The Art of Causal Conjecture. MIT Press, Cambridge, MA.  R. Settimi and J.Q. Smith (1998). On the geometry of Bayesian graphical models with hidden variables. In G. Cooper and S. Moral (eds.) Proceedings of the Fourteenth Conference on Uncertainty in Artificial Intelligence, Morgan Kaufmann Publishers, S. Francisco, 472–479.  R. Settimi and J.Q. Smith (2000). Geometry, moments and conditional independence trees with hidden variables. The Annals of Statistics, 28(4):1179-1205.  J.Q. Smith and E. E. Anderson (2006). Conditional independence and Chain Event Graphs. Artificial Intelligence, to appear.  J.Q. Smith and J. Croft (2003). Bayesian networks for discrete multivariate data: An algebraic approach to inference. J. of Multivariate Analysis, 84(2):387-402.  P. Spirtes, C. Glymour and R. Scheines (1993). Causation, Prediction, and Search. Springer-Verlag, New York.|
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