相互作用区室内反应网络模型的参数敏感性分析
Parametric Sensitivity Analysis for Models of Reaction Networks within Interacting Compartments
AI总结：
针对相互作用区室内反应网络模型，提出了基于Girsanov变换和耦合的有限差分参数敏感性分析方法，并通过数值实验验证其性能与标准随机反应网络一致，代码已开源。
摘要：
相互作用区室内的反应网络模型（RNIC）是随机反应网络的推广。最自然的理解是将相互作用的区室视为“细胞”，这些细胞可以出现、降解、分裂甚至合并，每个细胞内包含底层随机反应网络的一个演化副本。此类模型具有多个参数，包括与内部化学模型相关的参数以及与区室相互作用相关的参数，因此自然希望有高效的计算方法来数值估计模型统计量对这些参数的敏感性。受过去几十年随机反应网络参数敏感性分析计算方法广泛研究的启发，我们在基本RNIC设置中提供了多种方法。所提供的方法包括（无偏的）Girsanov变换方法（也称为似然比方法）以及多种用于实现有限差分的耦合方法，每种方法都受到先前与随机反应网络相关工作的启发。我们提供了几个数值示例，在新设置中比较各种方法。我们发现每种方法的相对性能与其在“标准”随机反应网络设置中的对应方法一致。我们已将用于实现各种方法的所有Matlab代码免费提供下载。
英文摘要：
Models of reaction networks within interacting compartments (RNIC) are a generalization of stochastic reaction networks. It is most natural to think of the interacting compartments as "cells" that can appear, degrade, split, and even merge, with each cell containing an evolving copy of the underlying stochastic reaction network. Such models have a number of parameters, including those associated with the internal chemical model and those associated with the compartment interactions, and it is natural to want efficient computational methods for the numerical estimation of sensitivities of model statistics with respect to these parameters. Motivated by the extensive work on computational methods for parametric sensitivity analysis in the context of stochastic reaction networks over the past few decades, we provide a number of methods in the basic RNIC setting. Provided methods include the (unbiased) Girsanov transformation method (also called the Likelihood Ratio method) and a number of coupling methods for the implementation of finite differences, each motivated by methods from previous work related to stochastic reaction networks. We provide several numerical examples comparing the various methods in the new setting. We find that the relative performance of each method is in line with its analog in the "standard" stochastic reaction network setting. We have made all of the Matlab code used to implement the various methods freely available for download.
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