Top left: additional underlying Rayleigh and Gaussian HBM tests for the full sample of warm Jupiters. Solid lines represent a truncated Gaussian hyperprior, while dashed lines represent a log-uniform hyperprior. Thin lines in the background show randomly sampled distributions from the σ_R, μ_G, and σ_G hyperparameter posteriors. Top right: KDE test for the full sample of warm Jupiters in our analysis. Bottom: additional HBM tests for host star metallicity. We find that these additional tests are in good agreement with the differences between the underlying eccentricity distribution of warm Jupiters residing in metal-rich ([Fe/H] ≥ 0) and metal-poor ([Fe/H] < 0) systems seen in Figure 7.