{"title":"Sensitivity Analysis of Quasi-Stationary Distributions (QSDs) of Mass-Action Systems","authors":"Yao Li, Yaping Yuan","doi":"10.1137/22m1535875","DOIUrl":null,"url":null,"abstract":"This paper studies the sensitivity analysis of mass-action systems against their diffusion approximations, particularly the dependence on population sizes. As a continuous-time Markov chain, a mass-action system can be described by an equation driven by finitely many Poisson processes, which has a diffusion approximation that can be pathwisely matched. The magnitude of noise in mass-action systems is proportional to the square root of the molecule count/population, which makes a large class of mass-action systems have quasi-stationary distributions (QSDs) besides invariant probability measures. In this paper, we modify the coupling-based technique developed in [M. Dobson, Y. Li, and J. Zhai, SIAM/ASA J. Uncertain. Quantif., 9 (2021), pp. 135–162] to estimate an upper bound of the 1-Wasserstein distance between two QSDs. Some numerical results of sensitivity with different population sizes are provided.","PeriodicalId":56064,"journal":{"name":"Siam-Asa Journal on Uncertainty Quantification","volume":"5 1","pages":"0"},"PeriodicalIF":2.1000,"publicationDate":"2023-10-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Siam-Asa Journal on Uncertainty Quantification","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1137/22m1535875","RegionNum":3,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATHEMATICS, INTERDISCIPLINARY APPLICATIONS","Score":null,"Total":0}
引用次数: 0
Abstract
This paper studies the sensitivity analysis of mass-action systems against their diffusion approximations, particularly the dependence on population sizes. As a continuous-time Markov chain, a mass-action system can be described by an equation driven by finitely many Poisson processes, which has a diffusion approximation that can be pathwisely matched. The magnitude of noise in mass-action systems is proportional to the square root of the molecule count/population, which makes a large class of mass-action systems have quasi-stationary distributions (QSDs) besides invariant probability measures. In this paper, we modify the coupling-based technique developed in [M. Dobson, Y. Li, and J. Zhai, SIAM/ASA J. Uncertain. Quantif., 9 (2021), pp. 135–162] to estimate an upper bound of the 1-Wasserstein distance between two QSDs. Some numerical results of sensitivity with different population sizes are provided.
期刊介绍：
SIAM/ASA Journal on Uncertainty Quantification (JUQ) publishes research articles presenting significant mathematical, statistical, algorithmic, and application advances in uncertainty quantification, defined as the interface of complex modeling of processes and data, especially characterizations of the uncertainties inherent in the use of such models. The journal also focuses on related fields such as sensitivity analysis, model validation, model calibration, data assimilation, and code verification. The journal also solicits papers describing new ideas that could lead to significant progress in methodology for uncertainty quantification as well as review articles on particular aspects. The journal is dedicated to nurturing synergistic interactions between the mathematical, statistical, computational, and applications communities involved in uncertainty quantification and related areas. JUQ is jointly offered by SIAM and the American Statistical Association.
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