A Dust spectral energy distribution model with hierarchical Bayesian
  inference. I. Formalism & benchmarking
  This article presents a new dust SED model, named HerBIE, aimed at
eliminating the noise-induced correlations and large scatter obtained when
performing least-squares fits. The originality of this code is to apply the
hierarchical Bayesian approach to full dust models, including realistic optical
properties, stochastic heating and the mixing of physical conditions in the
observed regions. We test the performances of our model by applying it to
synthetic observations. We explore the impact on the recovered parameters of
several effects: signal-to-noise ratio, SED shape, sample size, the presence of
intrinsic correlations, the wavelength coverage and the use of different SED
model components. We show that this method is very efficient: the recovered
parameters are consistently distributed around their true values. We do not
find any clear bias, even for the most degenerate parameters, or with extreme
signal-to-noise ratios.
