  The stochastic FitzHugh-Nagumo (FHN) model considered here 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. Here, we
tackle all challenges (non-globally Lipschitz drift, non-explicit solution,
lack of available transition density, degeneracy of the noise, and partial
observations) via an intuitive and easy-to-implement sequential Monte Carlo
approximate Bayesian computation algorithm. The proposed method 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. We succeed in estimating all model
parameters 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.
