Corner plot showing 1D and 2D marginalized posterior distributions for the four hyperparameters used to describe the carbonate–silicate weathering feedback population-level trend for rocky HZ exoplanets. The median inferred population trend is displayed in the upper right inset (solid purple line) with shading to denote 1σ and 3σ credible intervals. Using the importance sampling HBAR method, we are able to retrieve statistically robust constraints on the parameters characterizing the silicate weathering population trend in CO₂ abundance with stellar irradiation.