Fully probabilistic quasar continua predictions near Lyman-{\alpha} with conditional neural spline flows.

Measurement of the red damping wing of neutral hydrogen in quasar spectra provides a probe of the epoch of reionization in the early Universe. Such quantification requires precise and unbiased estimates of the intrinsic continua near Lyman-$\alpha$ (Ly$\alpha$), a challenging task given the highly variable Ly$\alpha$ emission profiles of quasars. Here, we introduce a fully probabilistic approach to intrinsic continua prediction. We frame the problem as a conditional density estimation task and explicitly model the distribution over plausible blue-side continua ($1190\ \unicode{xC5} \leq \lambda_{\text{rest}} 7$ quasars and estimate the volume-averaged neutral fraction of hydrogen from each, finding $\bar{x}_\text{HI}=0.304 \pm 0.042$ for ULAS J1120+0641 ($z=7.09$) and $\bar{x}_\text{HI}=0.384 \pm 0.133$ for ULAS J1342+0928 ($z=7.54$).