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.
