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We present Young Supernova Experiment $grizy$ photometry of SN 2021hpr, thethird Type Ia supernova sibling to explode in the Cepheid calibrator galaxy,NGC 3147. Siblings are useful for improving SN-host distance estimates, andinvestigating the contributions towards the SN Ia intrinsic scatter(post-standardisation residual scatter in distance estimates). We thus developa principled Bayesian framework for analyzing SN Ia siblings. At its core isthe cosmology-independent relative intrinsic scatter parameter, $\sigma_{Rel}$:the dispersion of siblings distance estimates relative to one another within agalaxy. It quantifies the contribution towards the total intrinsic scatter,$\sigma_0$, from within-galaxy variations about the siblings' commonproperties. It also affects the combined-distance uncertainty. We presentanalytic formulae for computing a $\sigma_{Rel}$-posterior from individualsiblings distances (estimated using any SN-model). Applying a newly trainedBayeSN 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 aninformative prior: $\sigma_{Rel}\sim U(0,\sigma_0)$. Simultaneously fitting thetrio's light curves improves constraints on distance, and each sibling'sindividual dust parameters, compared to individual fits. Higher correlationalso tightens dust parameter constraints. Therefore,$\sigma_{Rel}$-marginalization yields robust estimates of siblings distancesfor 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.

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