Corner plots of MCMC posteriors corresponding to the KOI populations APRV/BPRV (left/right), from which samples were drawn for Figure 2. The sampled parameters are the zero-point (z) and mean molecular weight (μ). The dashed lines correspond to a 1σ error. The posterior of μ associated with the APRV population implies a small, but detectable refraction effect consistent with an optically thin atmosphere lighter than Earth’s but heavier than the expected H/He dominated atmosphere. The posterior of μ associated with the BPRV population implies that when it comes to refraction effects, a much heavier atmosphere is essentially indiscernible from the lack of an atmosphere.