Stochastic kinetic models: Dynamic independence, modularity and graphs

CG Bowsher

Research output: Contribution to journalArticle (Academic Journal)peer-review

10 Citations (Scopus)

Abstract

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 A ⊥ B|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.
Translated title of the contributionStochastic kinetic models: Dynamic independence, modularity and graphs
Original languageEnglish
Pages (from-to)2242 - 2281
Number of pages40
JournalAnnals of Statistics
Volume38
Issue number4
DOIs
Publication statusPublished - Aug 2010

Fingerprint Dive into the research topics of 'Stochastic kinetic models: Dynamic independence, modularity and graphs'. Together they form a unique fingerprint.

Cite this