Inference Methods for Interaction and Noise Intensities Using Only Spike-time Data on Coupled Oscillators

Abstract: We propose theoretical methods to infer coupling strength and noise intensity simultaneously through an observation of spike timing in two well-synchronized noisy oscillators. A phase oscillator model is applied to derive formulae relating each of the parameters to some statistics from spike-time data. Using these formulae, each parameter is inferred from a specific set of statistics. We demonstrate the methods with the FitzHugh-Nagumo model as well as the phase model. Our methods do not require any external perturbation and thus are ready for application to various experimental systems.