The analysis of quickly damped transverse oscillations of solar coronal loops using magneto-hydrodynamic seismology allows us to infer physical parameters that are difficult to measure otherwise. Under the assumption that such damped oscillations are due to the resonant conversion of global modes into Alfvén oscillations of the tube surface, we carry out a global seismological analysis of a large set of coronal loops. A Bayesian hierarchical method is used to obtain distributions for coronal loop physical parameters by means of a global analysis of a large number of observations. The resulting distributions summarize global information and constitute data-favoured information that can be used for the inversion of individual events. The results strongly suggest that internal Alfvén travel times along the loop are longer than 100 s and shorter than 540 s with 95% probability. Likewise, the density contrast between the loop interior and the surrounding is larger than 2.3 and below 6.9 with 95% probability.