Recovered posteriors for an example mock prism spectrum with S/N = 50 per pixel. All input parameters (shown as red crosshairs) are recovered well within 2σ. Our constraint on ${\overline{x}}_{\mathrm{H}\mathrm{I}}$ is driven by the prior $p(D_b|{\overline{x}}_{\mathrm{H}\mathrm{I}})$ (Figure 2). As expected from the prior, given our recovered D_b ≈ 5 cMpc, the most likely ${\overline{x}}_{\mathrm{H}\mathrm{I}}\approx 0.7$, which drives our constraint here. This demonstrates how accurately recovering ${\overline{x}}_{\mathrm{H}\mathrm{I}}$ from prism spectra requires ≳10 galaxies per redshift bin to estimate distribution of D_b (see discussion in Section 6.3).