  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 Alfv\'en continuum, phase-mixing of Alfv\'en 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.
