The SAMI Galaxy Survey: Bayesian Inference for Gas Disk Kinematics using
  a Hierarchical Gaussian Mixture Model
  We present a novel Bayesian method, referred to as Blobby3D, to infer gas
kinematics that mitigates the effects of beam smearing for observations using
Integral Field Spectroscopy (IFS). The method is robust for regularly rotating
galaxies despite substructure in the gas distribution. Modelling the gas
substructure within the disk is achieved by using a hierarchical Gaussian
mixture model. To account for beam smearing effects, we construct a modelled
cube that is then convolved per wavelength slice by the seeing, before
calculating the likelihood function. We show that our method can model complex
gas substructure including clumps and spiral arms. We also show that kinematic
asymmetries can be observed after beam smearing for regularly rotating galaxies
with asymmetries only introduced in the spatial distribution of the gas. We
present findings for our method applied to a sample of 20 star-forming galaxies
from the SAMI Galaxy Survey. We estimate the global H$\alpha$ gas velocity
dispersion for our sample to be in the range $\bar{\sigma}_v \sim $[7, 30] km
s$^{-1}$. The relative difference between our approach and estimates using the
single Gaussian component fits per spaxel is $\Delta \bar{\sigma}_v /
\bar{\sigma}_v = - 0.29 \pm 0.18$ for the H$\alpha$ flux-weighted mean velocity
dispersion.
