Measuring the HI mass function below the detection threshold.

We present a Bayesian Stacking technique to directly measure the HI mass function (HIMF) and its evolution with redshift using galaxies formally below the nominal detection threshold. We generate galaxy samples over several sky areas given an assumed HIMF described by a Schechter function and simulate the HI emission lines with different levels of background noise to test the technique. We use Multinest to constrain the parameters of the HIMF in a broad redshift bin, demonstrating that the HIMF can be accurately reconstructed, using the simulated spectral cube far below the HI mass limit determined by the $5\sigma$ flux-density limit, i.e. down to $M_{\rm HI} = 10^{7.5}$ M$_{\odot}$ over the redshift range $0 0.1$) redshifts.