质量-作用系统准平稳分布的灵敏度分析

IF 2.1 3区工程技术 Q2 MATHEMATICS, INTERDISCIPLINARY APPLICATIONS

Siam-Asa Journal on Uncertainty Quantification Pub Date : 2023-10-20 DOI:10.1137/22m1535875

Yao Li, Yaping Yuan

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引用次数: 0

摘要

本文研究了质量作用系统对其扩散近似的敏感性分析，特别是对种群大小的依赖。作为一个连续时间马尔可夫链，质量-作用系统可以用一个由有限多个泊松过程驱动的方程来描述，该泊松过程具有路径智能匹配的扩散近似。在质量作用系统中，噪声的大小与分子数/分子数的平方根成正比，这使得大量的质量作用系统除了具有不变的概率测度外，还具有准平稳分布(qsd)。在本文中，我们改进了基于耦合的技术。杜布森，李勇，翟志强，SIAM/ASA J.不确定。Quantif。[j]， 9 (2021)， pp. 135-162]估计两个qsd之间1-Wasserstein距离的上界。给出了不同种群大小下的敏感性数值结果。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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Sensitivity Analysis of Quasi-Stationary Distributions (QSDs) of Mass-Action Systems

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.

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来源期刊

Siam-Asa Journal on Uncertainty Quantification Mathematics-Statistics and Probability

CiteScore

3.70

自引率

0.00%

发文量

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.