Comparison Between $\chi^2$ and Bayesian Statistics with Considering the Redshift Dependence of Stretch and Color from JLA Data

Ze Zhao

Fig. 3 (Color online) The 1D marginalized probability distributions of $\alpha_0$, $\alpha_1$, $\beta_0$, $\beta_1$ and the evolution of $\alpha(z)$, $\beta(z)$ given by $\chi^2$ statistics (blue dashed line) and Bayesian statistics (red solid line). Note that, we consider linear parametrization: $\alpha{(z)}=\alpha_0+\alpha_1z$ and $\beta{(z)}=\beta_0+\beta_1z$ for $\Lambda$CDM based on the full JLA sample.