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We use the BayeSN hierarchical probabilistic SED model to analyse theoptical-NIR ($BVriYJH$) light curves of 86 Type Ia supernovae (SNe Ia) from theCarnegie Supernova Project to investigate the SN Ia host galaxy dust lawdistribution and correlations between SN Ia Hubble residuals and host mass. OurBayesian analysis simultaneously constrains the mass step and dust $R_V$population distribution by leveraging optical-NIR colour information. Wedemonstrate how a simplistic analysis where individual $R_V$ values are firstestimated for each SN separately, and then the sample variance of these pointestimates is computed, overestimates the $R_V$ population variance$\sigma_R^2$. This bias is exacerbated when neglecting residual intrinsiccolour variation beyond that due to light curve shape. Instead, Bayesianshrinkage estimates of $\sigma_R$ are more accurate, with fully hierarchicalanalysis of the light curves being ideal. For the 75 SNe with low-to-moderatereddening (peak apparent $B-V\leq0.3$), we estimate an $R_V$ distribution withpopulation mean $\mu_R=2.59\pm0.14$, and standard deviation$\sigma_R=0.62\pm0.16$. Splitting this subsample at the median host galaxy mass($10^{10.57}~\mathrm{M}_\odot$) yields consistent estimated $R_V$ distributionsbetween low- and high-mass galaxies, with $\mu_R=2.79\pm0.18$,$\sigma_R=0.42\pm0.24$, and $\mu_R=2.35\pm0.27$, $\sigma_R=0.74\pm0.36$,respectively. When estimating distances from the full optical-NIR light curveswhile marginalising over various forms of the dust $R_V$ distribution, a massstep of $\gtrsim0.06$ mag persists in the Hubble residuals at the median hostmass.

Constraining the SN Ia Host Galaxy Dust Law Distribution and Mass Step: Hierarchical BayeSN Analysis of Optical and Near-Infrared Light Curves