tokens: redshift of the drag epoch, z d , can be calculated aswhere . Note that z d is well approximated analytically (Eisenstein Hu 1998 ) aswhere We use a fixed value of the baryon density from the Planck result (Planck Collaboration et al. 2016 ). 6 6 We have tested to marginalize over with a Gaussian prior derived from the Planck measurement and find that the result is largely unchanged. The baryon density can also be accurately determined in a CMB-independent way, e.g., using the primordial deuterium abundance in the Big Bang Nucleosynthesis (BBN) theory (Riemer-Sørensen Sem Jenssen 2017 ). Note that the quantities and can be estimated from anisotropic BAO measurements, while the quantity,is determined by isotropic BAO measurements. As shown above, the BAO distance measurements, or , are two-variable functions of and H 0 (once is known) in a flat ΛCDM cosmology, and therefore the Hubble constant can be, in principle, determined from the BAO distances with marginalized over. In what follows, we use isotropic or anisotropic BAO distance measurements to determine the Hubble constant with marginalized over, i.e., our parameter space is simply (assuming a flatness of the Universe)The sound horizon at the drag redshift r d is calculated using Equation ( 3 ). 7 7 Except for 6dF, the value of r d is rescaled by a factor , where value is calculated from CAMB (Lewis et al. 2000 , available at http://camb.info/ ) in the same fiducial cosmology (Bennett et al. 2014 ). We perform a Monte Carlo Markov Chain (MCMC) global fitting for parameter estimation using a modified version of CosmoMC (Lewis Bridle 2002 ). 8 8 http://cosmologist.info/cosmomc/ The BAO data sets used in this work include 1. the isotropic BAO measurements using the 6dFRS (6dF; Beutler et al. 2011 ) and SDSS main galaxy sample (MGS) (Ross et al. 2015 ) at effective redshifts and , respectively; 2. the BOSS DR12 anisotropic BAO measurements at three effective redshifts (BOSS 3 z bin) in Alam et al. ( 2017 ) or at nine effective redshifts (BOSS 9 z bin) in Wang et al. ( 2017 ) and Zhao et al. ( 2017b ); 3. the eBOSS DR14 isotropic BAO measurement at (Ata et al. 2017 ); and 4. a combination of 6dF + MGS + BOSS 3 z bin + eBOSS DR14 (All 3 z bin), or a combination of 6dF + MGS + BOSS 9 z bin + eBOSS DR14 (All 9 z bin). To check the consistency of the H 0 values determined from different data sets within the ΛCDM model, we compute the tension, T , based on the KL divergence (Kunz et al. 2006 ; Paykari Jaffe 2013 ; Amara Refregier 2014 ; Seehars et al. 2014 , 2016 ; Verde et al. 2014 ; Grandis et al. 2016 ; Raveri et al. 2016 ), which quantifies the distance between two probability density functions (PDFs), p 1, and p 2 . If both p 1 and p 2 are assumed to be Gaussian, the relative entropy in bits between the two PDFs can be evaluated aswhere is the best-fit parameter vector, is the corresponding covariance matrix, and d denotes the dimensions of the parameter space (e.g., d = 2 in our case where
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