The stochastic FitzHugh-Nagumo (FHN) model is a two-dimensional nonlinear stochastic differential equation with additive degenerate noise, whose first component, the only one observed, describes the membrane voltage evolution of a single neuron. Due to its low-dimensionality, its analytical and numerical tractability and its neuronal interpretation, it has been used as a case study to test the performance of different statistical methods in estimating the underlying model parameters. Existing methods, however, often require complete observations, non-degeneracy of the noise or a complex architecture (e.g., to estimate the transition density of the process, "recovering" the unobserved second component) and they may not (satisfactorily) estimate all model parameters simultaneously. Moreover, these studies lack real data applications for the stochastic FHN model. The proposed method tackles all challenges (non-globally Lipschitz drift, non-explicit solution, lack of available transition density, degeneracy of the noise and partial observations). It is an intuitive and easy-to-implement sequential Monte Carlo approximate Bayesian computation algorithm, which relies on a recent computationally efficient and structure-preserving numerical splitting scheme for synthetic data generation and on summary statistics exploiting the structural properties of the process. All model parameters are successfully estimated from simulated data and, more remarkably, real action potential data of rats. The presented novel real-data fit may broaden the scope and credibility of this classic and widely used neuronal model.

翻译：随机FitzHugh-Nagumo（FHN）模型是一个具有加性退化噪声的二维非线性随机微分方程，其第一个分量（也是唯一被观测的分量）描述了单个神经元的膜电压演化。由于其低维性、解析与数值易处理性以及神经学解释，该模型常被用作案例研究来检验不同统计方法在估计底层模型参数时的性能。然而，现有方法通常需要完整观测数据、噪声的非退化性或复杂架构（例如需估计过程的转移密度、"重构"未观测的第二个分量），且可能无法（令人满意地）同时估计所有模型参数。此外，这些研究缺乏随机FHN模型在真实数据中的应用。本文提出的方法解决了所有挑战（非全局Lipschitz漂移项、无显式解、转移密度不可得、噪声退化及部分观测）。这是一种直观且易于实现的序贯蒙特卡洛近似贝叶斯计算算法，其依赖于近期提出的计算高效且保持结构特性的数值分裂方案来生成合成数据，并利用过程的结构特性构建摘要统计量。所有模型参数均成功从模拟数据中估计得出，更显著的是，该方法成功应用于大鼠的真实动作电位数据。这种新颖的真实数据拟合方法有望拓展这一经典且广泛使用的神经元模型的应用范围与可信度。