The Chemical Master Equation (CME) is a set of linear differential equations that describes the evolution of the probability distribution on all possible configurations of a (bio-)chemical reaction system. Since the number of configurations and therefore the dimension of the CME rapidly increases with the number of molecules, its applicability is restricted to small systems. A widely applied remedy for this challenge is moment-based approaches which consider the evolution of the first few moments of the distribution as summary statistics for the complete distribution. Here, we investigate the performance of two moment-estimation methods for reaction systems whose equilibrium distributions encounter fat-tailedness and do not possess statistical moments.We show that estimation via stochastic simulation algorithm (SSA) trajectories lose consistency over time and estimated moment values span a wide range of values even for large sample sizes. In comparison, the method of moments returns smooth moment estimates but is not able to indicate the non-existence of the allegedly predicted moments. We furthermore analyze the negative effect of a CME solution’s fat-tailedness on SSA run times and explain inherent difficulties. While moment-estimation techniques are a commonly applied tool in the simulation of (bio-)chemical reaction networks, we conclude that they should be used with care, as neither the system definition nor the moment-estimation techniques themselves reliably indicate the potential fat-tailedness of the CME’s solution.
%0 Journal Article
%1 10.1093/bioinformatics/btad205
%A Wagner, Vincent
%A Radde, Nicole
%D 2023
%J Bioinformatics
%K exc2075 myown
%N Supplement_1
%P i440-i447
%R 10.1093/bioinformatics/btad205
%T The impossible challenge of estimating non-existent moments of the Chemical Master Equation
%U https://doi.org/10.1093/bioinformatics/btad205
%V 39
%X The Chemical Master Equation (CME) is a set of linear differential equations that describes the evolution of the probability distribution on all possible configurations of a (bio-)chemical reaction system. Since the number of configurations and therefore the dimension of the CME rapidly increases with the number of molecules, its applicability is restricted to small systems. A widely applied remedy for this challenge is moment-based approaches which consider the evolution of the first few moments of the distribution as summary statistics for the complete distribution. Here, we investigate the performance of two moment-estimation methods for reaction systems whose equilibrium distributions encounter fat-tailedness and do not possess statistical moments.We show that estimation via stochastic simulation algorithm (SSA) trajectories lose consistency over time and estimated moment values span a wide range of values even for large sample sizes. In comparison, the method of moments returns smooth moment estimates but is not able to indicate the non-existence of the allegedly predicted moments. We furthermore analyze the negative effect of a CME solution’s fat-tailedness on SSA run times and explain inherent difficulties. While moment-estimation techniques are a commonly applied tool in the simulation of (bio-)chemical reaction networks, we conclude that they should be used with care, as neither the system definition nor the moment-estimation techniques themselves reliably indicate the potential fat-tailedness of the CME’s solution.
@article{10.1093/bioinformatics/btad205,
abstract = {{The Chemical Master Equation (CME) is a set of linear differential equations that describes the evolution of the probability distribution on all possible configurations of a (bio-)chemical reaction system. Since the number of configurations and therefore the dimension of the CME rapidly increases with the number of molecules, its applicability is restricted to small systems. A widely applied remedy for this challenge is moment-based approaches which consider the evolution of the first few moments of the distribution as summary statistics for the complete distribution. Here, we investigate the performance of two moment-estimation methods for reaction systems whose equilibrium distributions encounter fat-tailedness and do not possess statistical moments.We show that estimation via stochastic simulation algorithm (SSA) trajectories lose consistency over time and estimated moment values span a wide range of values even for large sample sizes. In comparison, the method of moments returns smooth moment estimates but is not able to indicate the non-existence of the allegedly predicted moments. We furthermore analyze the negative effect of a CME solution’s fat-tailedness on SSA run times and explain inherent difficulties. While moment-estimation techniques are a commonly applied tool in the simulation of (bio-)chemical reaction networks, we conclude that they should be used with care, as neither the system definition nor the moment-estimation techniques themselves reliably indicate the potential fat-tailedness of the CME’s solution.}},
added-at = {2023-11-24T10:02:53.000+0100},
author = {Wagner, Vincent and Radde, Nicole},
biburl = {https://puma.ub.uni-stuttgart.de/bibtex/2d9f50320acfea6c088804d94af731c83/vincentwagner},
doi = {10.1093/bioinformatics/btad205},
eprint = {https://academic.oup.com/bioinformatics/article-pdf/39/Supplement\_1/i440/50741574/btad205.pdf},
interhash = {61d8f0a594585ba150702cb0b6fc9537},
intrahash = {d9f50320acfea6c088804d94af731c83},
issn = {1367-4811},
journal = {Bioinformatics},
keywords = {exc2075 myown},
month = {06},
number = {Supplement_1},
pages = {i440-i447},
timestamp = {2023-11-24T10:02:53.000+0100},
title = {The impossible challenge of estimating non-existent moments of the Chemical Master Equation},
url = {https://doi.org/10.1093/bioinformatics/btad205},
volume = 39,
year = 2023
}
