Left column: the variation of the free parameters while fitting Equation (3) as a function of g assuming flat priors. While the horizontal lines correspond to the g interval on which the fit was performed, the vertical lines correspond to the 16th–84th interval of the posterior distribution. The BHB stellar parameters are relatively constant within 15 < g < 19 which motivated the use of Gaussian priors throughout this work, see Section 3.1 for discussion. Right column: now with Gaussian priors on the BHB component and within 14.5 < r < 21.5. The decrease in the BHB fraction as a function of magnitude is expected due to the intrinsic density profile of the MW halo.