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August 2010 Stochastic kinetic models: Dynamic independence, modularity and graphs
Clive G. Bowsher
Ann. Statist. 38(4): 2242-2281 (August 2010). DOI: 10.1214/09-AOS779


The dynamic properties and independence structure of stochastic kinetic models (SKMs) are analyzed. An SKM is a highly multivariate jump process used to model chemical reaction networks, particularly those in biochemical and cellular systems. We identify SKM subprocesses with the corresponding counting processes and propose a directed, cyclic graph (the kinetic independence graph or KIG) that encodes the local independence structure of their conditional intensities. Given a partition [A, D, B] of the vertices, the graphical separation AB|D in the undirected KIG has an intuitive chemical interpretation and implies that A is locally independent of B given A ∪ D. It is proved that this separation also results in global independence of the internal histories of A and B conditional on a history of the jumps in D which, under conditions we derive, corresponds to the internal history of D. The results enable mathematical definition of a modularization of an SKM using its implied dynamics. Graphical decomposition methods are developed for the identification and efficient computation of nested modularizations. Application to an SKM of the red blood cell advances understanding of this biochemical system.


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Clive G. Bowsher. "Stochastic kinetic models: Dynamic independence, modularity and graphs." Ann. Statist. 38 (4) 2242 - 2281, August 2010.


Published: August 2010
First available in Project Euclid: 11 July 2010

zbMATH: 1203.92033
MathSciNet: MR2676889
Digital Object Identifier: 10.1214/09-AOS779

Primary: 62-09 , 62P10
Secondary: 60G55 , 92C37 , 92C40 , 92C45

Keywords: counting and point processes , dynamic and local independence , graphical decomposition , kinetic independence graph , Reaction networks , Stochastic kinetic model , systems biology

Rights: Copyright © 2010 Institute of Mathematical Statistics


Vol.38 • No. 4 • August 2010
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