Although neural interactions are usually characterized only by their coupling strength and directionality, there is often a need to go beyond this by establishing the functional mechanisms of the interaction. We introduce the use of dynamical Bayesian inference for estimation of the coupling functions of neural oscillations in the presence of noise. By grouping the partial functional contributions, the coupling is decomposed into its functional components and its most important characteristics-strength and form-are quantified. The method is applied to characterize the δ-to-α phase-to-phase neural coupling functions from electroencephalographic (EEG) data of the human resting state, and the differences that arise when the eyes are either open (EO) or closed (EC) are evaluated. The δ-to-α phase-to-phase coupling functions were reconstructed, quantified, compared, and followed as they evolved in time. Using phase-shuffled surrogates to test for significance, we show how the strength of the direct coupling, and the similarity and variability of the coupling functions, characterize the EO and EC states for different regions of the brain. We confirm an earlier observation that the direct coupling is stronger during EC, and we show for the first time that the coupling function is significantly less variable. Given the current understanding of the effects of e.g., aging and dementia on δ-waves, as well as the effect of cognitive and emotional tasks on α-waves, one may expect that new insights into the neural mechanisms underlying certain diseases will be obtained from studies of coupling functions. In principle, any pair of coupled oscillations could be studied in the same way as those shown here.