MCMC fitting of the intrinsic uncertainty and measurement uncertainty in our ﹩{M}_{K{\rm{s}}}﹩ estimates. Binaries were excluded iteratively. The intrinsic uncertainty σ_int indicates the epistemic uncertainty in ﹩{M}_{K{\rm{s}}}﹩ estimates, whereas the measurement uncertainty σ_s quantifies the aleatoric uncertainty induced by spectral noise. The MCMC results show an intrinsic uncertainty of σ_int = 0.25 mag and a typical measurement uncertainty of σ_s = 0.10 mag at S/N = 100.