  We present a Bayesian inference method to characterise the dust emission
properties using the well-known dust-HI correlation in the diffuse interstellar
medium at Planck frequencies $\nu \ge 217$ GHz. We use the Galactic HI map from
the Galactic All-Sky Survey (GASS) as a template to trace the Galactic dust
emission. We jointly infer the pixel-dependent dust emissivity and the zero
level present in the Planck intensity maps. We use the Hamiltonian Monte Carlo
technique to sample the high dimensional parameter space ($D \sim 10^3$). We
demonstrate that the methodology leads to unbiased recovery of dust emissivity
per pixel and the zero level when applied to realistic Planck sky simulations
over a 6300 deg$^2$ area around the Southern Galactic pole. As an application
on data, we analyse the Planck intensity map at 353 GHz to jointly infer the
pixel-dependent dust emissivity at Nside=32 resolution (1.8\deg\ pixel size)
and the global offset. We find that the spatially varying dust emissivity has a
mean of 0.031 MJysr$^{-1} (10^{20} \mathrm{cm^{-2}})^{-1}$ and $1\sigma$
standard deviation of 0.007 MJysr$^{-1} (10^{20} \mathrm{cm^{-2}})^{-1}$. The
mean dust emissivity increases monotonically with increasing mean HI column
density. We find that the inferred global offset is consistent with the
expected level of Cosmic Infrared Background (CIB) monopole added to the Planck
data at 353 GHz. This method is useful in studying the line-of-sight variations
of dust spectral energy distribution in the multi-phase interstellar medium.
