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Bayesian representations using chain event graphs

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Anderson, Paul E. and Smith, J. Q. (2006) Bayesian representations using chain event graphs. Working Paper. Coventry: University of Warwick. Centre for Research in Statistical Methodology. Working papers, Vol.2006 (No.8).

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Official URL: http://www2.warwick.ac.uk/fac/sci/statistics/crism...

Abstract

Bayesian networks (BNs) are useful for coding conditional independence statements between a given set of measurement variables.
On the other hand, event trees (ETs) are convenient for representing asymmetric structure and how situations unfold. In this paper
we report the development of a new graphical framework for discrete
probability models called the Chain Event Graph (CEG). The class of
CEG models contains finite BNs as a special case. Unlike the BN, the
CEG is equally appropriate for representing conditional independencies in asymmetric systems and does not need dependent variables to
be specified in advance. As with the BN, it also provides a framework
for learning relevant conditional probabilities and propagation. Furthermore, being a function of an ET, the CEG is a more
exible way of
representing various causal hypotheses than the BN. This new framework is illustrated throughout by a biological regulatory network: the
tryptophan metabolic pathway in the bacterium E. coli.

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), Biological control systems -- Mathematical models, Escherichia coli -- Mathematical models, Bayesian statistical decision theory

Series Name:

Working papers

Publisher:

University of Warwick. Centre for Research in Statistical Methodology

Place of Publication:

Coventry

Official Date:

2006

Dates:

Date	Event
2006	Published

Volume:

Vol.2006

Number:

No.8

Number of Pages:

Status:

Not Peer Reviewed

Access rights to Published version:

Open Access

Funder:

Engineering and Physical Sciences Research Council (EPSRC), Biotechnology and Biological Sciences Research Council (Great Britain) (BBSRC), BioSim

References:

[1] C. Boutilier, N. Friedman, M. Goldszmidt, and D. Koller. Context-
Specific Independence in Bayesian Networks. In Proceedings of the 12th
Annual Conference on Uncertainty in Artificial Intelligence (UAI-96),
pages 115{123, San Francisco, CA, 1996. Morgan Kaufmann Publishers.
[2] R. E. Bryant. Graph-based algorithms for Boolean function manipula-
tion. IEEE Transactions on Computers, 35(8):677{691, 1986.
[3] H. J. Call and W. A. Miller. A Comparison of Approaches and Imple-
mentations for Automating Decision Analysis. Reliability Engineering
and System Safety, 30:115{162, 1990.
[4] N. A. Campbell and J. B. Reece. Biology. Addison Wesley Student
Series. Benjamin Cummings, 6th edition, 2002.
[5] R. G. Cowell, A. P. Dawid, S. L. Laurtizen, and D. J. Spiegelhalter.
Probabilistic Networks and Expert Systems. Springer-Verlag, 1999.
[6] D. Geiger, D. Heckerman, and C. Meek. Asymptotic model selection
for directed networks with hidden variables. In Proceedings of the 12th
Annual Conference on Uncertainty in Artificial Intelligence (UAI-96),
pages 283{290, Portland, OR, 1996. Morgan Kaufmann Publishers.
[7] J. Ito and I. P. Crawford. Regulation of the Enzymes of the Tryptophan
Pathway in Escherichia Coli. Genetics, 52:1303{1316, 1965.
[8] M. Jaeger. Probabilistic decision graphs | combining verification and
AI techniques for probabilistic inference. Int. J. of Uncertainty, Fuzzi-
ness and Knowledge-based Systems, 12:19{42, 2004.
[9] S. L. Lauritzen. Causal inference from graphical models. In O. E.
Barndorff-Nielsen, D. R. Cox, and C. Kluppelberg, editors, Complex
Stochastic Systems, pages 63{108. London: Chapman and Hall, 2001.
[10] David McAllester, Michael Collins, and Fernando Pereira. Case-Factor
Diagrams for Structured Probability Modelling. In Proceedings of the
20th Annual Conference on Uncertainty in Artificial Intelligence (UAI-
04), pages 382{391, 2004.
[11] S. M. Olmsted. On representing and solving decision problems. PhD
thesis, Engineering-Economic Systems, Stanford University, 1983.
[12] J. Pearl. Causality, models, reasoning and inference. Cambridge Uni-
versity Press, 2000.
[13] David Poole and Nevin Lianwen Zhang. Exploiting Contextual Inde-
pendence in Probabilistic Inference. Journal of Artificial Intelligence
Research, 18:263{313, 2003.
[14] E. Riccomagno and J. Q. Smith. Chain Event Graphs to Represent
Bayesian Causal Hypotheses. CRiSM paper, Department of Statistics,
University of Warwick, 2006.
[15] M. Santillan and M. C. Mackey. Dynamic regulation of the trypto-
phan operon: A modeling study and comparison with experimental data.
PNAS, 98(4):1364{1369, 2001.
[16] J. W. Schimd, K. Mauch, M. Reuss, E. D. Gilles, and A. Kremling.
Metabolic design based on a coupled gene expression | metabolic net-
work model of tryptophan production in Escherichia coli. Metabolic
Engineering, 6:364{377, 2004.
[17] G. Shafer. The Art of Causal Conjecture. Cambridge, MA, MIT Press,
1996.
[18] Jim Q. Smith and Paul E. Anderson. Conditional independence and
chain event graphs. Artificial Intelligence, 2006. Accepted, subject to
revision.
[19] R. Somerville. The trp repressor, a ligand-activated regulatory protein.
Prog. Nucleic Acids Res. Mol. Biol., 42:1{38, 1992.
[20] D. J. Spiegelhalter, A. P. Dawid, S. L. Lauritzen, and R. G. Cowell.
Bayesian analysis in expert systems (with discussion). Statistical Sci-
ence, 8:219{83, 1993.
[21] P. Spirtes, C. Glymour, and R. Scheines. Causation, Prediction, and
Search. Springer-Verlag, New York, 1993.
[22] B. Thiesson, C. Meek, D. M. Chickering, and D. Heckerman. Compu-
tationally Efficient Methods for Selecting Among Mixtures of Graphical
Models. In Bayesian Statistics, volume 6, pages 631{656. Oxford Uni-
versity Press, 1999.
[23] P. Thwaites and J. Q. Smith. Non-symmetric Models, Chain Event
Graphs and Propagation. In Proceedings of IPMU, July 2006. To appear.