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We propose theoretical methods to infer coupling strength and noise intensitysimultaneously through an observation of spike timing in two well-synchronizednoisy oscillators. A phase oscillator model is applied to derive formulaerelating each of the parameters to some statistics from spike-time data. Usingthese formulae, each parameter is inferred from a specific set of statistics.We demonstrate the methods with the FitzHugh-Nagumo model as well as the phasemodel. Our methods do not require any external perturbation and thus are readyfor application to various experimental systems.

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