Abstract
In this work, we compare the impacts given by 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 color-luminosity 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 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 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 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.
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