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Context. Stars form in dense, dusty clumps of molecular clouds, but little isknown about their origin, their evolution and their detailed physicalproperties. In particular, the relationship between the mass distribution ofthese clumps (also known as the "clump mass function", or CMF) and the stellarinitial mass function (IMF), is still poorly understood. Aims. In order tobetter 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 arerequired. Two such datasets obtained from the Herschel infrared GALactic PlaneSurvey (Hi-GAL) have been described in paper I. Robust statistical methods areneeded in order to infer the parameters describing the models used to fit theCMF, and to compare the competing models themselves. Methods. In this paper weapply Bayesian inference to the analysis of the CMF of the two regionsdiscussed in Paper I. First, we determine the Bayesian posterior probabilitydistribution for each of the fitted parameters. Then, we carry out aquantitative comparison of the models used to fit the CMF. Results. We havecompared the results from several methods implementing Bayesian inference, andwe have also analyzed the impact of the choice of priors and the influence ofvarious constraints on the statistical conclusions for the preferred values ofthe parameters. We find that both parameter estimation and model comparisondepend on the choice of parameter priors. Conclusions. Our results confirm ourearlier conclusion that the CMFs of the two Hi-GAL regions studied here havevery similar shapes but different mass scales. Furthermore, the lognormal modelappears to better describe the CMF measured in the two Hi-GAL regions studiedhere. However, this preliminary conclusion is dependent on the choice ofparameters priors.

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