  A new method is introduced for analysis of interactions between
time-dependent coupled oscillators, based on the signals they generate. It
distinguishes unsynchronized dynamics from noise-induced phase slips, and
enables the evolution of the coupling functions and other parameters to be
followed. It is based on phase dynamics, with Bayesian inference of the
time-evolving parameters achieved by shaping the prior densities to incorporate
knowledge of previous samples. The method is tested numerically and applied to
reveal and quantify the time-varying nature of cardiorespiratory interactions.
