Improving Bayesian posterior correlation analysis on Type Ia supernova luminosity evolution
Much of the cosmological utility thus far extracted from Type Ia supernovae (SNe Ia) relies on the assumption that SN~Ia peak luminosities do not evolve significantly with the age (local or global) of their stellar environments. Two recent studies have provided conflicting results in evaluating the validity of this assumption, with one finding no correlation between Hubble residuals (HR) and stellar environment age, while the other claims a significant correlation. In this Letter we perform an independent reanalysis that rectifies issues with the statistical methods employed by both of the aforementioned studies. Our analysis follows a principled approach that properly accounts for regression dilution and critically (and unlike both prior studies) utilises the Bayesian-model-produced SN environment age estimates (posterior samples) instead of point estimates. Moreover, the posterior is used as an informative prior in the regression. We find the Pearson correlation between the HR and local (global) age to be in excess of $4\sigma$ ($3\sigma$). Assuming there exists a linear relationship between HR and local (global) age, we find a corresponding slope of $-0.035 \pm 0.007\,\mathrm{mag\,Gyr}^{-1}$ ($-0.036 \pm 0.007\,\mathrm{mag\,Gyr}^{-1}$). We encourage further usage of our approach to examine possible cosmological implications of the HR and age correlation.