Delay-differential-equation models of reverberant-energy decay in systems of coupled rooms were recently introduced as a semi-empirical correction to standard statistical-acoustics models in order to better account for the delay of energy transfer between subrooms of a coupled system [Summers, J. Acoust. Soc. Am. 132, EL129―EL134, 2012]. Here, a Bayesian approach to parameter estimation for these models is developed and evaluated on simulated and measured data. Using these data, the ability to invert for delays from measured decay curves is assessed and an interpretation of the physical meaning of those inferred delays is presented. Finally, the theoretical and mathematical relationships between higher-degree-of-freedom models resulting from the introduction of delay and those resulting from the introduction of additional decay rates to the standard sum-of-decaying-exponential model are considered, and the resulting implications for parameter estimation and model selection are described.