Noninvasive inference methods for interaction and noise intensities of coupled oscillators using only spike time data

Measurements of interaction intensity are generally achieved by observing responses to perturbations. In biological and chemical systems, external stimuli tend to deteriorate their inherent nature, and thus, it is necessary to develop noninvasive inference methods. In this paper, we propose theoretical methods to infer coupling strength and noise intensity simultaneously in two well-synchronized noisy oscillators through observations of spontaneously fluctuating events such as neural spikes. A phase oscillator model is applied to derive formulae relating each of the parameters to spike time statistics. Using these formulae, each parameter is inferred from a specific set of statistics. We verify these methods using the FitzHugh-Nagumo model as well as the phase model. Our methods do not require external perturbations and thus can be applied to various experimental systems.