Context. High resolution observations have permitted the resolution of solar prominences/filaments into sets of threads/fibrils. However, the values of the physical parameters of these threads and their structuring remain poorly constrained. Aims: We use prominence seismology techniques to analyse transverse oscillations in threads by comparing magnetohydrodynamic (MHD) models and observations. Methods: We applied Bayesian methods to obtain two different types of information. We first inferred the marginal posterior distribution of physical parameters such as the magnetic field strength or length of the thread, when a totally filled tube, partially filled tube, and three damping models are considered as certain; the three damping models are resonant absorption in the Alfvén continuum, resonant absorption in the slow continuum, and Cowling's diffusion. Then, we compared the relative plausibility between alternative MHD models by computing the Bayes factors. Results: Well-constrained probability density distributions can be obtained for the magnetic field strength, length of the thread, density contrast, and parameters associated with the damping models. In a comparison of the damping models of resonant absorption in the Alfvén continuum, resonant absorption in the slow continuum, and Cowling's diffusion due to partial ionisation of prominence plasma, the resonant absorption in the Alfvén continuum is the most plausible mechanism to explain the existing observations. Relations between periods of fundamental and first overtone kink modes with values around 1 are better explained by expressions of the period ratio in the long thread approximation, while the rest of the values are more probable in the short thread limit for the period ratio. Conclusions: Our results show that Bayesian analysis offers valuable methods to perform parameter inference and a model comparison in the context of prominence seismology.