Relative intrinsic scatter in hierarchical Type Ia supernova siblings analyses: Application to SNe 2021hpr, 1997bq & 2008fv in NGC 3147

We present Young Supernova Experiment $grizy$ photometry of SN 2021hpr, the third Type Ia supernova sibling to explode in the Cepheid calibrator galaxy, NGC 3147. Siblings are useful for improving SN-host distance estimates, and investigating the contributions towards the SN Ia intrinsic scatter (post-standardisation residual scatter in distance estimates). We thus develop a principled Bayesian framework for analyzing SN Ia siblings. At its core is the cosmology-independent relative intrinsic scatter parameter, $\sigma_{Rel}$: the dispersion of siblings distance estimates relative to one another within a galaxy. It quantifies the contribution towards the total intrinsic scatter, $\sigma_0$, from within-galaxy variations about the siblings' common properties. It also affects the combined-distance uncertainty. We present analytic formulae for computing a $\sigma_{Rel}$-posterior from individual siblings distances (estimated using any SN-model). Applying a newly trained BayeSN model, we fit the light curves of each sibling in NGC 3147 individually, to yield consistent distance estimates. However, the wide $\sigma_{Rel}$-posterior means $\sigma_{Rel}\approx\sigma_0$ is not ruled out. We thus combine the distances by marginalizing over $\sigma_{Rel}$ with an informative prior: $\sigma_{Rel}\sim U(0,\sigma_0)$. Simultaneously fitting the trio's light curves improves constraints on distance, and each sibling's individual dust parameters, compared to individual fits. Higher correlation also tightens dust parameter constraints. Therefore, $\sigma_{Rel}$-marginalization yields robust estimates of siblings distances for cosmology, and dust parameters for siblings-host correlation studies. Incorporating NGC 3147's Cepheid-distance yields $H_0=78.4\pm 6.5\,$km/s/Mpc. Our work motivates analyses of homogeneous siblings samples, to constrain $\sigma_{Rel}$, and its SN-model dependence.