  In view of the current availability and variety of measured data, there is an
increasing demand for powerful signal processing tools that can cope
successfully with the associated problems that often arise when data are being
analysed. In practice many of the data-generating systems are not only
time-variable, but also influenced by neighbouring systems and subject to
random fluctuations (noise) from their environments. To encompass problems of
this kind, we present a tutorial about the dynamical Bayesian inference of
time-evolving coupled systems in the presence of noise. It includes the
necessary theoretical description and the algorithms for its implementation.
For general programming purposes, a pseudocode description is also given.
Examples based on coupled phase and limit-cycle oscillators illustrate the
salient features of phase dynamics inference. State domain inference is
illustrated with an example of coupled chaotic oscillators. The applicability
of the latter example to secure communications based on the modulation of
coupling functions is outlined. MatLab codes for implementation of the method,
as well as for the explicit examples, accompany the tutorial.
