Algebraic discrete causal models
Riccomagno, Eva, Smith, J. Q., 1953- and Thwaites, Peter (2010) Algebraic discrete causal models. Working Paper. University of Warwick. Centre for Research in Statistical Methodology, Coventry.
WRAP_Riccomagno_10-11w.pdf - Published Version - Requires a PDF viewer such as GSview, Xpdf or Adobe Acrobat Reader
Official URL: http://www2.warwick.ac.uk/fac/sci/statistics/crism...
The main feature of the paper is to show that Algebraic Statistics is a natural framework to address issues of causality and to help discern a total cause. Indeed identifiability of an effect of a cause in discrete models is almost algebraic rather than graphical in nature. It is useful to think of it as such and it leads to the definition of a large class of discrete models which comprises popular ones.
|Item Type:||Working or Discussion Paper (Working Paper)|
|Subjects:||Q Science > QA Mathematics|
|Divisions:||Faculty of Science > Statistics|
|Library of Congress Subject Headings (LCSH):||Causation -- Statistical methods, Causation -- Mathematical models, Mathematical statistics|
|Series Name:||Working papers|
|Publisher:||University of Warwick. Centre for Research in Statistical Methodology|
|Place of Publication:||Coventry|
|Number of Pages:||19|
|Status:||Not Peer Reviewed|
|Access rights to Published version:||Open Access|
|References:||Allman, E. S. and Rhodes, J. A. (2003). Phylogenetic invariants for the general Markov model of sequence mutation. Math. Biosci. 186, no. 2, 113–144. Allman, E. S., An´e, C., Rhodes, J. A. (2008). Identifiability of a Markovian model of molecular evolution with gamma-distributed rates. Adv. in Appl. Probab. 40, no. 1, 229–249. Anderson, P.E., Smith, J.Q. (2005). A graphical framework for representing the semantics of asymmetric models. Technical report 05-12, CRiSM. Cox, D., Little, J. & OShea, D. (2008). Ideals, Varieties, and Algorithms 3edn. Springer- Verlag, New York. awid, A.P. (2002). Influence diagrams for causal modelling and inference. International Statistical Review, 70, 161–189. Dawid, A.P., Studen´y, M. (1999). Conditional products: an alternative approach to conditional independence. In D. Heckerman, J. Whittaker (Eds.), Artificial Intelligence and Statistics 99 (pp. 32–40) Morgan Kaufmann Publishers, S. Francisco. Drton, M., Sullivant, S. (2007). Algebraic statistical models. Statist. Sinica 17 (2007), no. 4, 1273–1297. Garcia, L. D., Stillman, M., Sturmfels, B. (2005). Algebraic geometry of Bayesian networks. J. Symbolic Comput. 39, no. 3-4, 331–355. Glymour, D., Cooper, G.F. (1999). Computation, Causation, and Discovery. MIT Press, Cambridge. Hausman, D. (1998). Causal asymmetries. Cambridge University Press, Cambridge. Kang, C., Tian, J. (2007). Polynomial Constraints in Causal Bayesian Networks. In Proceedings of the Conference on UAI (pp. 200–208), AUAI Press. M. Kuroki, Graphical identifiability criteria for causal effects in studies with an unobserved treatment/response variable, Biometrika 94(1) 37–47, 2007. Lauritzen, S. (2000). Graphical models for causal inference. In O.E. Barndorff-Nielsen, D. Cox, and C. Kluppelberg (Eds.), Complex Stochastic Systems (pp. 67–112), Chapman and Hall/CRC Press, London. McAllester, D., Collins, M., Periera, F. (2004). Case factor diagrams for structured probabilistic modeling. In Proceedings of the 20th Conference on Uncertainty in Artificial Intelligence (pp. 382–391), AUAI Press. D.M.Q. Mond, J.Q. Smith and D. Van Straten, Stochastic factorisations, sandwiched simplices and the topology of the space of explanations, Proc. R. Soc. London. A 459: 2821-2845, 2003. Pearl, J. (2000). Causality: Models, Reasoning and Inference. Cambridge University Press, Cambridge. Riccomagno, E., Smith, J.Q. (2009). The geometry of causal probability trees that are algebraically constrained. In L. Pronzato and A. A. Zhigljavsky (Eds.), Search for Optimality in Design and Statistics (pp. 133–154), Springer-Verlag, Berlin. Riccomagno, E., Smith, J.Q. (2004). Identifying a cause in models which are not simple Bayesian networks. In IPMU 2004 (pp. 1315–1322). Riccomagno, E., Smith, J.Q. (2005). The causal manipulation and Bayesian estimation of chain event graphs, http://arxiv.org/abs/0709.3380. Riccomagno, E., Smith, J.Q., Thwaites, P.A. (submitted). Causal analysis with chain event graphs. Robins, J.M. (1997). Causal inference from complex longitudinal data. In M. Berkane (Ed.), Latent variable modeling and applications to causality (pp. 69–117), Springer, New York. R. Settimi and J.Q. Smith, Geometry, moments and conditional independence trees with hidden variables, The Annals of Statistics, 28(4):1179-1205, 2000. Shafer, G. (1996). The Art of Casual Conjecture MIT Press. Smith, J.Q., Anderson, P.E. (2008). Conditional independence and Chain Event Graphs. Artificial Intelligence, 172, 42–68. Spirtes, P., Glymour, C., Scheines, R. (1993). Causation, Prediction, and Search. Springer- Verlag, New York. Studen´y, M. (2004). Probabilistic Conditional Independence Structures. Springer-Verlag, London. Thwaites, P.A., Smith, J.Q., Cowell, R.G. (2008). Propagation using Chain event graphs. In Proceedings of the 24th Conference on UAI, Helsinki. Tian, J., Pearl, J. (2002). On the testable implications of causal models with hidden variables. In Proceedings of UAI 2002, pp.567–573. Zwiernik, P. and Smith, J.Q. (2009). The Geometry of Conditional Independence Tree Models with Hidden Variables (submitted to Annals of Statistics).|
Actions (login required)