Results from M = 100 independent simulation realizations followed by Bayesian analysis, shown for H₂O, on LP 890-9 c, after 20 transits. Top: the cumulative median of ﹩{\mathrm{log}}_{10}B﹩ stabilizes by M ≈ 80 realizations while the 95% confidence interval narrows. Bottom: the 95% MoE on ﹩{\mathrm{log}}_{10}B﹩ decreases approximately as M^−1/2 and stabilizes by M ≈ 90. At that point the convergence criterion is met, yielding a statistically stable estimate of ﹩{\mathrm{log}}_{10}B﹩.