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We present a new catalogue of Damped Lyman-$\alpha$ absorbers from SDSSDR16Q, as well as new estimates of their statistical properties. Our estimatesare computed with the Gaussian process models presented in Garnett et al.(2017); Ho et al. (2020) with an improved model for marginalising uncertaintyin the mean optical depth of each quasar. We compute the column densitydistribution function (CDDF) at $2 < z < 5$, the line density ($\textrm{d} N/\textrm{d} X$), and the neutral hydrogen density ($\Omega_{\textrm{DLA}}$). OurGaussian process model provides a posterior probability distribution of thenumber of DLAs per spectrum, thus allowing unbiased probabilistic predictionsof the statistics of DLA populations even with the noisiest data. We measure anon-zero column density distribution function for $N_{\textrm{HI}} < 3 \times10^{22} \,\textrm{cm}^{-2}$ with $95\%$ confidence limits, and $N_{\textrm{HI}}\lesssim 10^{22} \,\textrm{cm}^{-2}$ for spectra with signal-to-noise ratios $>4$. Our results for DLA line density and total hydrogen density are consistentwith previous measurements. Despite a small bias due to the poorly measuredblue edges of the spectra, we demonstrate that our new model can measure theDLA population statistics when the DLA is in the Lyman-$\beta$ forest region.We verify our results are not sensitive to the signal-to-noise ratios andredshifts of the background quasars although a residual correlation remains fordetections from $z_{\textrm{QSO}} < 2.5$, indicating some residual systematicswhen applying our models on very short spectra, where the SDSS spectralobserving window only covers part of the Lyman-$\alpha$ forest.

Damped Lyman-alpha Absorbers from Sloan Digital Sky Survey DR16Q with Gaussian processes