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

Ze Zhao

Fig. 1 (Color online) The 1$\sigma$ confidence regions of stretch-luminosity parameter $\alpha(z)$ obtained from $\chi^2$ statistics (a)—(c) and Bayesian statistics (d)—(f). for $\Lambda$CDM The results only consider the $\Lambda$CDM model, based on by using the full JLA samples at redshift zone [0,1]. And 3 bins, 4 bins, and 5 bins are shown in the upper, middle and lower panel. which are divided into 3 bins (upper panels), 4 bins (middle panels), and 5 bins (lower panels). in which the absolute B-band magnitude $M_B$ are marginalized. The gray zone represents the 1$\sigma$ region and the gray dashed line denotes the best-fit result given by the full JLA data.