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Marginal process framework: A model reduction tool for Markov jump processes

Bronstein, L. and Koeppl, H. (2018):
Marginal process framework: A model reduction tool for Markov jump processes.
In: Physical Review E, American Physical Society, E 97, 062147, ISSN 2470-0045,
DOI: 10.1103/PhysRevE.97.062147,
[Online-Edition: https://journals.aps.org/pre/abstract/10.1103/PhysRevE.97.06...],
[Article]

Abstract

Markov jump process models have many applications across science. Often, these models are defined on a state-space of product form and only one of the components of the process is of direct interest. In this paper, we extend the marginal process framework, which provides a marginal description of the component of interest, to the case of fully coupled processes. We use entropic matching to obtain a finite-dimensional approximation of the filtering equation which governs the transition rates of the marginal process. The resulting equations can be seen as a combination of two projection operations applied to the full master equation, so that we obtain a principled model reduction framework. We demonstrate the resulting reduced description on the totally asymmetric exclusion process. An important class of Markov jump processes are stochastic reaction networks, which have applications in chemical and biomolecular kinetics, ecological models and models of social networks. We obtain a particularly simple instantiation of the marginal process framework for mass-action systems by using product-Poisson distributions for the approximate solution of the filtering equations. We investigate the resulting approximate marginal process analytically and numerically.

Item Type: Article
Erschienen: 2018
Creators: Bronstein, L. and Koeppl, H.
Title: Marginal process framework: A model reduction tool for Markov jump processes
Language: English
Abstract:

Markov jump process models have many applications across science. Often, these models are defined on a state-space of product form and only one of the components of the process is of direct interest. In this paper, we extend the marginal process framework, which provides a marginal description of the component of interest, to the case of fully coupled processes. We use entropic matching to obtain a finite-dimensional approximation of the filtering equation which governs the transition rates of the marginal process. The resulting equations can be seen as a combination of two projection operations applied to the full master equation, so that we obtain a principled model reduction framework. We demonstrate the resulting reduced description on the totally asymmetric exclusion process. An important class of Markov jump processes are stochastic reaction networks, which have applications in chemical and biomolecular kinetics, ecological models and models of social networks. We obtain a particularly simple instantiation of the marginal process framework for mass-action systems by using product-Poisson distributions for the approximate solution of the filtering equations. We investigate the resulting approximate marginal process analytically and numerically.

Journal or Publication Title: Physical Review E
Volume: E 97, 062147
Publisher: American Physical Society
Uncontrolled Keywords: Markov jump processes; marginal process framework; model reduction tool; asymmetric exclusion process; networks
Divisions: 18 Department of Electrical Engineering and Information Technology
18 Department of Electrical Engineering and Information Technology > Institute for Telecommunications > Bioinspired Communication Systems
18 Department of Electrical Engineering and Information Technology > Institute for Telecommunications
Date Deposited: 22 May 2018 09:11
DOI: 10.1103/PhysRevE.97.062147
Official URL: https://journals.aps.org/pre/abstract/10.1103/PhysRevE.97.06...
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