On the shape of the mass-function of dense clumps in the Hi-GAL fields II: Using Bayesian inference to study the clump mass function

Context. Stars form in dense, dusty clumps of molecular clouds, but little is known about their origin, their evolution, and their detailed physical properties. In particular, the relationship between the mass distribution of these clumps (also known as the "clump mass function", or CMF) and the stellar initial mass function (IMF) is still poorly understood. Aims. To better understand how the CMF evolve toward the IMF and to discern the "true" shape of the CMF, large samples of bona-fide pre-and proto-stellar clumps are required. Two such datasets obtained from the Herschel infrared GALactic Plane Survey (Hi-GAL) have been described in Paper I. Robust statistical methods are needed to infer the parameters describing the models used to fit the CMF and to compare the competing models themselves. Methods. In this paper, we apply Bayesian inference to the analysis of the CMF of the two regions discussed in Paper I. First, we determine the posterior probability distribution for each of the fitted parameters. Then, we carry out a quantitative comparison of the models used to fit the CMF. Results. We have compared several methods of sampling posterior distributions and calculating global likelihoods, and we have also analyzed the impact of the choice of priors and the influence of various constraints on the statistical conclusions for the values of model parameters. We find that both parameter estimation and model comparison depend on the choice of parameter priors. Conclusions. Our results confirm our earlier conclusion that the CMFs of the two Hi-GAL regions studied here have very similar shapes but different mass scales. Furthermore, the lognormal model appears to better describe the CMF measured in the two Hi-GAL regions studied here. However, this preliminary conclusion is dependent on the choice of parameter priors.