Inference for the stochastic FitzHugh-Nagumo model from real action potential data via approximate Bayesian computation

TL;DR

This paper introduces an approximate Bayesian computation method for estimating parameters of the stochastic FitzHugh-Nagumo neuron model from real action potential data, overcoming previous limitations and successfully applying it to real biological data.

Contribution

It develops a new ABC-based approach that handles partial observations, degeneracy, and non-explicit solutions, enabling parameter estimation from real neuronal data.

Findings

Successful parameter estimation from simulated data

Effective application to real rat neuron data

Broadens the model's practical applicability

Abstract

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.