The increasing availability of experimental data has intensified interest in calibrating stochastic models, raising fundamental questions about parameter identifiability. Structural identifiability determines whether parameters can be uniquely recovered from idealised, noise-free data, a prerequisite to allow for parameter estimation. However, existing methods to assess structural identifiability are not generally applicable to stochastic processes. We develop a methodology to analyse structural identifiability for a class of spatio-temporal stochastic processes. We investigate how identifiability depends on the type of available data, distinguishing between single-particle trajectories and total particle density measurements. For trajectory data, we use the individual-based model description that explicitly represents single-particle dynamics. For population-level data, we derive a partial differential equation model representation, that describes the evolution of total particle density, and apply a differential algebra approach, common to ordinary differential equations analysis. We further introduce a novel method to study the initial condition, based on characteristic equations to construct a Taylor expansion of the density evolution, enabling identification of additional identifiable parameter combinations. We apply our methodology to a model, and show it is identifiable with trajectory data but only locally identifiable with density data, and demonstrate the critical role of initial conditions in the identifiability analysis.

翻译：随着实验数据日益丰富，随机模型标定研究愈发受到关注，由此引发了参数可辨识性等基础性问题。结构可辨识性决定了在理想化无噪声数据条件下参数能否被唯一恢复，这是实现参数估计的前提条件。然而，现有评估结构可辨识性的方法通常不适用于随机过程。我们发展了一种适用于时空随机过程类别的结构可辨识性分析方法。本文探究了可辨识性如何依赖于可用数据类型，特别区分了单粒子轨迹与总粒子密度测量两种情形。针对轨迹数据，我们采用显式描述单粒子动力学的个体基模型表示；针对群体层面数据，我们推导出描述总粒子密度演化的偏微分方程模型表示，并应用常微分方程分析中常用的微分代数方法。进一步地，我们引入一种基于特征方程构建密度演化泰勒展开的创新方法来研究初始条件，从而识别出额外的可辨识参数组合。将该方法应用于某模型后表明：轨迹数据下模型全局可辨识，而密度数据下仅局部可辨识，同时证实了初始条件在可辨识性分析中的关键作用。