tokens: bias models that distinguish between centrals and satellites in upcoming work. 2.5 Incompleteness factor <italic>f</italic><sub>ic</sub> The final parameter in our extended HOD model is the incompleteness factor (e.g. Leauthaud et al. 2016 ; Rodríguez-Torres et al. 2016 ; Guo, Yang Lu 2018 ). The inclusion of incompleteness is partially motivated by detection of incompleteness in the BOSS CMASS and LOWZ galaxy samples compared with theoretical stellar mass functions, but it is also needed to marginalize over uncertainties in the galaxy number densities since we do not model its full redshift dependence. We define f ic as a modification to in equation ( 1 ): where 0 f ic ≤ 1. Our implementation simply uniformly downsamples the mock galaxies by f ic to produce the desired galaxy number density. To summarize, our extended HOD model contains the five baseline parameters: M cut , M 1 , σ, α, and κ; six extended parameters: s, s p , s v , α c , A , and A e ; and one incompleteness factor f ic , for a total of 12 parameters. 3 DATA AND SIMULATIONS 3.1 BOSS CMASS galaxy sample The Baryon Oscillation Spectroscopic Survey (BOSS; Bolton et al. 2012 ; Dawson et al. 2013 ) is part of the SDSS-III programme (Eisenstein et al. 2011 ). BOSS Data Release 12 (DR12) provides redshifts for 1.5 million galaxies in an effective area of 9329 deg 2 divided into two samples: LOWZ and CMASS. The LOWZ galaxies are selected to be the brightest and reddest of the low-redshift galaxy population at z 0.4, whereas the CMASS sample is designed to isolate galaxies of approximately constant mass at higher redshift ( z > 0.4), most of them being also luminous red galaxies (LRGs; Reid et al. 2016 ; Rodríguez-Torres et al. 2016 ). The survey footprint is divided into chunks that are covered in overlapping plates of radius . Each plate can house up to 1000 fibres, but due to the finite size of the fibre housing, no two fibres can be placed closer than 62 arcsec, referred to as the fibre collision scale (Guo, Zehavi Zheng 2012 ). For this paper, we limit our measurements to the galaxy sample in the redshift range 0.46 z 0.6 in DR12. We choose this moderate redshift range for completeness and to minimize the systematics due to redshift evolution. Applying this redshift range to both the North and South Galactic Caps gives a total of approximately 600 000 galaxies in our sample. We showcase the number density variation over redshift in Fig. 1 . The average galaxy number density is given by n data = (3.01 ± 0.03) × 10 −4 h 3 Mpc −3 . Figure 1. The CMASS DR12 galaxy comoving number density distribution across our redshift range. The red dashed line corresponds to the North Galactic Cap, whereas the blue dotted line corresponds to the South Galactic Cap. The green solid line shows the combined number density. The two vertical lines mark z = 0.46 and z = 0.6, respectively. Fig. 2 shows the redshift-space 2PCF of the same BOSS sample and its corresponding correlation matrix,
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