  Employing both Bayesian statistics and the theory of nonlinear dynamics, we
present a practically efficient method to extract a phase description of weakly
coupled limit-cycle oscillators directly from time series observed in a
rhythmic system. As a practical application, we numerically demonstrate that
this method can retrieve all the interaction functions from the fluctuating
rhythmic neuronal activity exhibited by a network of asymmetrically coupled
neurons. This method can be regarded as a type of statistical phase reduction
method that requires no detailed modeling, and as such, it is a very practical
and reliable method in application to data-driven studies of rhythmic systems.
