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

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.