Stochasticity plays a key role in many biological systems, necessitating the calibration of stochastic mathematical models to interpret associated data. For model parameters to be estimated reliably, it is typically the case that they must be structurally identifiable. Yet, while theory underlying structural identifiability analysis for deterministic differential equation models is highly developed, there are currently no tools for the general assessment of stochastic models. In this work, we present a differential algebra-based framework for the structural identifiability analysis of linear and a class of near-linear partially observed stochastic differential equation (SDE) models. Our framework is based on a deterministic recurrence relation that describes the dynamics of the statistical moments of the system of SDEs. From this relation, we iteratively form a series of necessarily satisfied equations involving only the observed moments, from which we are able to establish structurally identifiable parameter combinations. We demonstrate our framework for a suite of linear (two- and $n$-dimensional) and non-linear (two-dimensional) models. Most importantly, we define the notion of structural identifiability for SDE models and establish the effect of the initial condition on identifiability. We conclude with a discussion on the applicability and limitations of our approach, and potential future research directions in this understudied area.

翻译：随机性在众多生物系统中扮演着关键角色，这要求通过校准随机数学模型来解释相关数据。为确保模型参数能够被可靠估计，通常这些参数必须具备结构可辨识性。然而，尽管确定性微分方程模型的结构可辨识性分析理论已高度发展，目前尚缺乏适用于随机模型的通用评估工具。本研究提出了一种基于微分代数的框架，用于分析线性及一类近线性部分观测随机微分方程模型的结构可辨识性。该框架基于描述随机微分方程组统计矩动态的确定性递推关系。通过这一关系，我们迭代构建了一系列仅涉及观测矩的必然满足方程，并由此确立结构可辨识的参数组合。我们在线性模型（二维及n维）和非线性模型（二维）系列中验证了该框架的有效性。最重要的是，我们定义了随机微分方程模型的结构可辨识性概念，并阐明了初始条件对可辨识性的影响。最后，我们讨论了该方法的适用性与局限性，并展望了这一研究不足领域的潜在未来研究方向。