We present a method to assess the plausibility of alternative mechanisms to explain the damping of magnetohydrodynamic
(MHD) transverse waves in solar coronal loops. The considered mechanisms are resonant absorption of kink
waves in the Alfvén continuum, phase-mixing of Alfvén waves, and wave leakage. Our methods make use of Bayesian
inference and model comparison techniques. We first infer the values for the physical parameters that control the wave
damping, under the assumption of a particular mechanism, for typically observed damping time-scales. Then, the
computation of marginal likelihoods and Bayes factors enable us to quantify the relative plausibility between the alternative
mechanisms. We find that, in general, the evidence is not large enough to support a single particular damping
mechanism as the most plausible one. Resonant absorption and wave leakage offer the most probable explanations in
strong damping regimes, while phase mixing is the best candidate for weak/moderate damping. When applied to a
selection of 89 observed transverse loop oscillations, with their corresponding measurements of damping times scales
and taking into account data uncertainties, we find that only in a few cases positive evidence for a given damping
mechanism is available.