Forecasted number of galaxies required to constrain ${\overline{x}}_{\mathrm{H}\mathrm{I}}$ to a higher significance with the NIRSpec prism (top) and G140M grating (bottom) modes using our approach. Dotted lines show normalized $p(D_b|x_{\mathrm{H}\mathrm{I}})$ distributions from our simulations at x_HI = [0.5,0.7,0.9]. Solid lines and shaded regions show the recovered median D_b and 68% credible interval from sampling N galaxies each with D_b drawn from these distributions, assuming a median uncertainty on D_b of 0.7 and 0.3 dex for the prism and G140M observations respectively (corresponding to S/N ≈ 20 and 5 per pixel respectively).