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A graphical framework for representing the semantics of asymmetric models

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Anderson, Paul E. and Smith, J. Q. (2005) A graphical framework for representing the semantics of asymmetric models. Working Paper. Coventry: University of Warwick. Centre for Research in Statistical Methodology. Working papers, Vol.2005 (No.12).

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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, especially in discrete symmetric models. 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 called the chain event graph
(CEG). For symmetric models, all conditional independencies in a BN can be expressed through the topology of a CEG. However, 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. 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):

Statistics -- Graphic methods, Biological control systems -- Mathematical models

Series Name:

Working papers

Publisher:

University of Warwick. Centre for Research in Statistical Methodology

Place of Publication:

Coventry

Official Date:

2005

Dates:

Date	Event
2005	Published

Volume:

Vol.2005

Number:

No.12

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Not Peer Reviewed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)

References:

R. E. Bryant. Graph-based algorithms for Boolean
function manipulation. IEEE Transactions on Com-
puters, 35(8):677{691, 1986.
N. A. Campbell and J. B. Reece. Biology. Addison
Wesley Student Series. Benjamin Cummings, 6th
edition, 2002.
R. G. Cowell, A. P. Dawid, S. L. Laurtizen, and D. J.
Spiegelhalter. Probabilistic Networks and Expert
Systems. Springer-Verlag, 1999.
D. Geiger, D. Heckerman, and C. Meek. Asymptotic
model selection for directed networks with hidden
variables. In Proceedings of the 12th Annual Confer-
ence on Uncertainty in Artificial Intelligence (UAI-
96), pages 283{290, Portland, OR, 1996. Morgan
Kaufmann Publishers.
J. Ito and I. P. Crawford. Regulation of the Enzymes
of the Tryptophan Pathway in Escherichia Coli. Ge-
netics, 52:1303{1316, 1965.
M. Jaegar. Probabilistic decision graphs | combin-
ing verification and AI techniques for probabilis-
tic inference. Int. J. of Uncertainty, Fuzziness and
Knowledge-based Systems, 12:19{42, 2004.
S. L. Lauritzen. Causal inference from graphical mod-
els. In O. E. Barndorff-Nielsen, D. R. Cox, and
C. Kluppelberg, editors, Complex Stochastic Sys-
tems, pages 63{108. London: Chapman and Hall,
2001.
J. Pearl. Causality, models, reasoning and inference.
Cambridge University Press, 2000.
E. Riccomagno and J. Q. Smith. Chain Event Graphs
to Represent Bayesian Causal Hypotheses. Submit-
ted to J. Royal Statist. Soc. B, 2005.
M. Santillan and M. C. Mackey. Dynamic regulation
of the tryptophan operon: A modeling study and
comparison with experimental data. PNAS, 98(4):
1364{1369, 2001.
J. W. Schimd, K. Mauch, M. Reuss, E. D. Gilles, and
A. Kremling. Metabolic design based on a coupled
gene expression|metabolic network model of tryp-
tophan production in Escherichia coli. Metabolic
Engineering, 6:364{377, 2004.
G. Shafer. The Art of Causal Conjecture. Cambridge,
MA, MIT Press, 1996.
J. Q. Smith. Conditional independence and chain
event graphs. Submitted to Artificial Intelligence,
2004.
R. Somerville. The trp repressor, a ligand-activated
regulatory protein. Prog. Nucleic Acids Res. Mol.
Biol., 42:1{38, 1992.
D. J. Spiegelhalter, A. P. Dawid, S. L. Lauritzen,
and R. G. Cowell. Bayesian analysis in expert sys-
tems (with discussion). Statistical Science, 8:219{83,
1993.
P. Spirtes, C. Glymour, and R. Scheines. Causation,
Prediction, and Search. Springer-Verlag, New York,
1993.
B. Thiesson, C. Meek, D. M. Chickering, and D. Heck-
erman. Computationally Efficient Methods for Se-
lecting Among Mixtures of Graphical Models. In
Bayesian Statistics, volume 6, pages 631{656. Ox-
ford University Press, 1999.