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tokens: that the age and metallicity distributions are Gaussian, with , σ T = 2 Gyr (e.g., Kalirai 2012 ), , and σ Fe/H = 0.5 (e.g., Xue et al. 2008 ). We model the resulting weighted CMD with a kernel density estimate (KDE), using a kernel bandwidth of 0.025. The resulting pdf’s for M F814W , for six different colors, are shown in Figure 11 . Figure 11. Normalized pdf’s for absolute magnitude for six different choices of m F606W − m F814W color. These pdf’s are derived from the KDE constructed from the VandenBerg et al. ( 2006 ) isochrones, weighted by a Salpeter IMF and the approximate age and metallicity distributions of the halo. Using the pdf for absolute magnitude as a function of color in conjunction with the halo density profile (Deason et al. 2011 ), we derive the pdf for the log distance distribution to our sample:where is the probability of log D given the Deason et al. ( 2011 ) density profile, and is the probability of object n having absolute magnitude M F814W (log D ) given its color m F606W, n − m F814W, n . 6 6 In the COSMOS field, in the area where we used additional catalogs for selection, we used the Subaru B and V photometric measurements from Capak et al. ( 2007 ) and converted these to STMAG F606W as directed by Sirianni et al. ( 2005 ). We used the F814W magnitudes as published in the Leauthaud et al. ( 2007 ) catalog. We then estimate the mean distance to each field . Each of the four fields has an average distance . Figure 12 shows the cumulative logarithmic distance pdf’s of our samples across the four fields, and average distances to each field are listed in Table 5 . We note that no kinematic information is incorporated into our distance estimate and that information from 3D kinematics will improve our distance estimates in subsequent work. Figure 12. Cumulative distance distributions for the four HALO7D fields. Distance distributions are computed as given by Equation ( 13 ), using colors and assuming an MW stellar density profile (Deason et al. 2011 ). All fields have . Figure 13 shows the LOS dispersions of the four HALO7D fields plotted as a function of mean galactocentric radius (where we have converted heliocentric distance to galactocentric radius ). Points indicate the median of the σ LOS posterior samples, and error bars indicate the 16th and 84th posterior percentiles. We compare our results to the velocity dispersion profiles measured in other studies. The figure also shows measured velocity dispersion profiles from SDSS BHB stars (Xue et al. 2008 ; black dashed line), BHB and blue straggler (BS) stars from the Hypervelocity Star Survey (Brown et al. 2010 ; gray dot-dashed line), and the SEGUE K -giant survey (Xue et al. 2016 ; connected black circles). The measured LOS velocity dispersions in the HALO7D fields using MSTO stars are consistent with other studies that have measured the LOS velocity dispersion profile over our distance range. Figure 13. LOS velocity dispersions of the four HALO7D fields, plotted