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[abridged] The interstellar medium is now widely recognized to displayfeatures ascribable to magnetized turbulence. With the public release of Planckdata and the current balloon-borne and ground-based experiments, the growingamount of data tracing the polarized thermal emission from Galactic dust in thesubmillimetre provides choice diagnostics to constrain the properties of thismagnetized turbulence. We aim to constrain these properties in a statisticalway, focusing in particular on the power spectral index of the turbulentcomponent of the interstellar magnetic field in a diffuse molecular cloud, thePolaris Flare. We present an analysis framework which is based on simulatingpolarized thermal dust emission maps using model dust density (proportional togas density) and magnetic field cubes, integrated along the line of sight, andcomparing these statistically to actual data. The model fields are derived fromfBm processes, which allow a precise control of their one- and two-pointstatistics. We explore the nine-dimensional parameter space of these modelsthrough a MCMC analysis, which yields best-fitting parameters and associateduncertainties. We find that the power spectrum of the turbulent component ofthe magnetic field in the Polaris Flare molecular cloud scales with wavenumberas a power law with a spectral index $2.8\pm 0.2$. It complements a uniformfield whose norm in the POS is approximately twice the norm of the fluctuationsof the turbulent component. The density field is well represented by alog-normally distributed field with a mean gas density $40\,\mathrm{cm}^{-3}$and a power spectrum with as spectral index $1.7^{+0.4}_{-0.3}$. The agreementbetween the Planck data and the simulated maps for these best-fittingparameters is quantified by a $\chi^2$ value that is only slightly larger thanunity.

On the statistics of the polarized submillimetre emission maps from thermal dust in the turbulent, magnetized, diffuse ISM