Recent studies on acoustically coupled volumes, worship spaces, and in concert hall acoustics, have prompted an increasing interest in analyzing sound energy decays consisting of more than one decay slope, so-called nonexponential decays. It has been considered very challenging to estimate parameters associated with double-slope decay characteristics, even more challenging when the coupled-volume systems contain more than two decay processes. To meet the need of characterizing energy decays of multiple decay processes, this paper reports investigations using both acoustical scale-models and numerical models of three coupled volumes. Characterization is based on Bayesian probabilistic inference. Acoustic scale models, and diffusion-equation based models are used to evaluate the estimation strategy, and to validate the results. The analysis method is then applied to geometric-acoustics models of concert halls with more complex geometries. The analysis method within Bayesian framework is capable of determining more than two decay slopes and estimating the corresponding decay parameters.