Bayesian method for the analysis of the dust emission in the
  Far-Infrared and Submillimeter
  We present a method, based on Bayesian statistics, to fit the dust emission
parameters in the far-infrared and submillimeter wavelengths. The method
estimates the dust temperature and spectral emissivity index, plus their
relationship, taking into account properly the statistical and systematic
uncertainties. We test it on three sets of simulated sources detectable by the
Herschel Space Observatory in the PACS and SPIRE spectral bands (70-500
micron), spanning over a wide range of dust temperatures. The simulated
observations are a one-component Interstellar Medium, and two two-component
sources, both warm (HII regions) and cold (cold clumps). We first define a
procedure to identify the better model, then we recover the parameters of the
model and measure their physical correlations by means of a Monte Carlo Markov
Chain algorithm adopting multi-variate Gaussian priors. In this process we
assess the reliability of the model recovery, and of parameters estimation. We
conclude that the model and parameters are properly recovered only under
certain circumstances, and that false models may be derived in some case. We
applied the method to a set of 91 starless cold clumps in an inter-arm region
of the Galactic Plane with low star formation activity, observed by Herschel in
the Hi-GAL survey. Our results are consistent with a temperature independent
spectral index.
