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. In order 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 in order 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 Bayesian 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 the results from several methods implementing Bayesian inference, and
we have also analyzed the impact of the choice of priors and the influence of
various constraints on the statistical conclusions for the preferred values of
the 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
parameters priors.
