Comparison Between χ~2 and Bayesian Statistics with Considering the Redshift Dependence of Stretch and Color from JLA Data

In this work, we compare the impacts given by χ^2 statistics and Bayesian statistics. Bayesian statistics is a new statistical method proposed by [C. Ma, P. S. Corasaniti, and B. A. Bassett, arXiv:1603.08519[astro-ph.CO](2016)]recently, which gives a fully account for the standard-candle parameter dependence of the data covariance matrix. For this two statistical methods, we explore the possible redshift-dependence of stretch-luminosity parameter α and colorluminosity parameter β by using redshift tomography. By constraining the ΛCDM model, we check the consistency of cosmology-fit results given by the SN sample of each redshift bin. We also adopt the linear parametrization to explore the possible evolution of α and β and the deceleration parameter q(z) for CPL, JBP, BA and Wang models. We find that:(i) Using the full JLA data, at high redshift α has a trend of decreasing at more than 1.5σ confidence level(CL),and β has a significant trend of decreasing at more than 19σ CL.(ii) Compared with χ^2 statistics(constant α, β) and Bayesian statistics(constant α, β), Bayesian statistics(linear α and β) yields a larger best-fit value of fractional matter density ?m0 from JLA+CMB+GC data, which is much closer to slightly deviates from the best-fit result given by other cosmological observations.(iii) The figure of merit(FoM) given by JLA+CMB+GC data from Bayesian statistics is also larger than the FoM from χ^2 statistics, which indicates that former statistics has a better accuracy.(iv) q(z) given by both statistical methods favor an eternal cosmic acceleration at 1σ CL.