Dust SEDs in the era of Herschel and Planck: a Hierarchical Bayesian
  fitting technique
  We present a hierarchical Bayesian method for fitting infrared spectral
energy distributions (SEDs) of dust emission to observed fluxes. Under the
standard assumption of optically thin single temperature (T) sources the dust
SED as represented by a power--law modified black body is subject to a strong
degeneracy between T and the spectral index beta. The traditional
non-hierarchical approaches, typically based on chi-square minimization, are
severely limited by this degeneracy, as it produces an artificial
anti-correlation between T and beta even with modest levels of observational
noise. The hierarchical Bayesian method rigorously and self-consistently treats
measurement uncertainties, including calibration and noise, resulting in more
precise SED fits. As a result, the Bayesian fits do not produce any spurious
anti-correlations between the SED parameters due to measurement uncertainty. We
demonstrate that the Bayesian method is substantially more accurate than the
chi-square fit in recovering the SED parameters, as well as the correlations
between them. As an illustration, we apply our method to Herschel and sub
millimeter ground-based observations of the star-forming Bok globule CB244.
This source is a small, nearby molecular cloud containing a single low-mass
protostar and a starless core. We find that T and beta are weakly positively
correlated -- in contradiction with the chi-square fits, which indicate a
T-beta anti-correlation from the same data-set. Additionally, in comparison to
the chi-square fits the Bayesian SED parameter estimates exhibit a reduced
range in values.
