随机反应网络中多个同时参数扰动的通用灵敏度方法
A general-purpose sensitivity method for multiple simultaneous parameter perturbations in stochastic reaction networks
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中文总结 AI 辅助
针对随机反应网络多参数扰动灵敏度估计的效率问题，提出多路径堆叠耦合（MSC）方法，经实验验证其在三类应用中均能实现最小均方根误差，性能优于现有方法。
中文摘要 AI 辅助
随机反应网络是用于描述相互作用种群的连续时间马尔可夫链模型，应用于生物化学、流行病学、生态学及相关领域。本文研究当单个估计器需要多条邻近参数化路径时的有限差分灵敏度估计问题。现有降方差耦合通常为成对形式，因此在多路径场景下重复使用时要么效率低下，要么需要特定于应用的选择。我们提出多路径堆叠耦合（MSC），这是一种时空泊松构造，可联合生成任意有限集合的参数化路径。MSC的每一对边际具有与对应拆分耦合对相同的分布，使现有方差界可直接转移；在有限状态场景中，我们还得到有限差分分子的均值和二阶矩的一阶展开式。我们将MSC应用于三个具有实际重要性的场景：同时估计多个一阶导数、使用更宽的有限差分模板估计单个一阶导数、以及估计高阶导数。对持续性磷酸化网络的数值实验表明，MSC在所有三个应用领域均表现出优异性能，与MSC的理论优势一致：在所有三个应用中，在测试的计算预算范围内，MSC在所考虑的方法中实现了最小的均方根误差（RMSE）。
英文摘要
Stochastic reaction networks are continuous-time Markov chain models for interacting populations, with applications in biochemistry, epidemiology, ecology, and related areas. We study finite-difference sensitivity estimation when a single estimator requires several nearby parameterized paths. Existing variance-reducing couplings are typically pairwise, so that repeated use is either inefficient or requires application-specific choices in multi-path settings. We introduce the multi-path stacked coupling (MSC), a space-time Poisson construction that jointly generates any finite collection of parameterized paths. Each pairwise marginal of MSC has the same law as the corresponding split coupling pair, allowing existing variance bounds to transfer directly; in finite-state settings, we also obtain first-order expansions for the mean and second moment of finite-difference numerators. We apply MSC in three settings of practical importance: estimating many first derivatives simultaneously, estimating a single first derivative using a wider finite-difference stencil, and estimating higher-order derivatives. Numerical experiments on a processive phosphorylation network demonstrate strong performance in each of the three application areas considered, consistent with the theoretical advantages of MSC: across all three applications, MSC achieves the smallest root mean square error (RMSE) among the methods considered over the tested computational budgets.
