  The spatial variation of physical quantities, such as the mass density,
across solar atmospheric waveguides governs the timescales and spatial scales
for wave damping and energy dissipation. The direct measurement of the spatial
distribution of density, however, is difficult and indirect seismology
inversion methods have been suggested as an alternative. We applied Bayesian
inference, model comparison, and model-averaging techniques to the inference of
the cross-field density structuring in solar magnetic waveguides using
information on periods and damping times for resonantly damped
magnetohydrodynamic (MHD) transverse kink oscillations. Three commonly employed
alternative profiles were used to model the variation of the mass density
across the waveguide boundary. Parameter inference enabled us to obtain
information on physical quantities such as the Alfv\'en travel time, the
density contrast, and the transverse inhomogeneity length scale. The inference
results from alternative density models were compared and their differences
quantified. Then, the relative plausibility of the considered models was
assessed by performing model comparison. Our results indicate that the evidence
in favor of any of the three models is minimal, unless the oscillations are
strongly damped. In such a circumstance, the application of model-averaging
techniques enables the computation of an evidence-weighted inference that takes
into account the plausibility of each model in the calculation of a combined
inversion for the unknown physical parameters.
