  We perform a Bayesian parameter inference in the context of resonantly damped
transverse coronal loop oscillations. The forward problem is solved in terms of
parametric results for kink waves in one-dimensional flux tubes in the thin
tube and thin boundary approximations. For the inverse problem, we adopt a
Bayesian approach to infer the most probable values of the relevant parameters,
for given observed periods and damping times, and to extract their confidence
levels. The posterior probability distribution functions are obtained by means
of Markov Chain Monte Carlo simulations, incorporating observed uncertainties
in a consistent manner. We find well localized solutions in the posterior
probability distribution functions for two of the three parameters of interest,
namely the Alfven travel time and the transverse inhomogeneity length-scale.
The obtained estimates for the Alfven travel time are consistent with previous
inversion results, but the method enables us to additionally constrain the
transverse inhomogeneity length-scale and to estimate real error bars for each
parameter. When observational estimates for the density contrast are used, the
method enables us to fully constrain the three parameters of interest. These
results can serve to improve our current estimates of unknown physical
parameters in coronal loops and to test the assumed theoretical model.
