Data-Driven Inference for Jump-Diffusion Models of Neuroscientific Data

Detailed biophysical models are often used to describe neuroscientific data. They can, however, suffer from high-dimensional and poorly constrained parameter spaces. This makes it difficult to draw meaningful conclusions about the associated neural systems. Alternatively, a data-driven approach can be used where the observed fluctuations are captured by a single diffusion process. The resulting model is non-parametric, low-dimensional, and relies only on a minimal set of working assumptions. This approach has been applied to data such as membrane potential and EEG recordings. In some cases, however, these data exhibit abrupt jumps, or discontinuities, that must be disentangled from the diffusional fluctuations in order to fully understand the underlying dynamics. To address this, we develop an inference procedure that results in a fully specified jump-diffusion stochastic differential equation. This is done by first implementing a detection scheme for the jumps, taking into account the presence of false positives. The diffusion and drift functions are then obtained from the Kramers-Moyal coefficient and the differential Chapman-Kolmogorov equation, respectively. We successfully apply this procedure to data associated with membrane noise and active sensing in electric fish.