(a) |$\Delta H/H_0$| posterior averaged over 100 SNIa realizations with 100 noise realizations each when peculiar velocities are ignored in the |$H_0$| inference. We find on average |$\langle \Delta H/H_0 \rangle = 0.006\pm 0.008$| (⁠|$0.4 \pm 0.5$| km s|$^{-1}$| Mpc|$^{-1}$|⁠) in the local Universe in the range |$0.023<z<0.046$| assuming |$\sigma _\mathrm{\mu } = 0.13$| mag, |$\sigma _z = 0.001$|⁠, and |$N_\mathrm{SN} \sim$| 200 SNe in each data set. The latter is determined by the number of available 2M++ realizations. (b) Contribution to |$H_0$| variation in the direction of known structures in the Universe. The Hydra–Centaurus and Shapley superclusters contribute the most to the increase in |$H_0$| when peculiar velocities are ignored, but the evidence is very weak.