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We present MArk-dependently THinned POint Process (Mathpop), a novel method to infer the globular cluster (GC) counts in ultra-diffuse galaxies (UDGs) and low-surface brightness galaxies (LSBGs). Many known UDGs have a surprisingly high ratio of GC number to surface brightness. However, standard methods to infer GC counts in UDGs face various challenges, such as photometric measurement uncertainties, GC membership uncertainties, and assumptions about the GC luminosity functions (GCLFs). Mathpop tackles these challenges using the mark-dependent thinned point process, enabling joint inference of the spatial and magnitude distributions of GCs. In doing so, Mathpop allows us to infer and quantify the uncertainties in both GC counts and GCLFs with minimal assumptions. As a precursor to Mathpop, we also address the data uncertainties coming from the selection process of GC candidates: we obtain probabilistic GC candidates instead of the traditional binary classification based on the color–magnitude diagram. We apply Mathpop to 40 LSBGs in the Perseus cluster using GC catalogs from a Hubble Space Telescope imaging program. We then compare our results to those from an independent study using the standard method. We further calibrate and validate our approach through extensive simulations. Our approach reveals two LSBGs having GCLF turnover points much brighter than the canonical value with Bayes’ factor being ∼4.5 and ∼2.5, respectively. An additional crude maximum-likelihood estimation and simulation study show that their GCLF TO points are approximately 0.9 mag and 1.1 mag brighter than the canonical value, with p-values of ∼10^−8 and ∼10^−5, respectively. 

CDG-1 is a tight grouping of four likely globular clusters in the Perseus cluster, and a candidate dark galaxy with little or no diffuse light. Here we provide new constraints on the luminosity of any underlying stellar emission, using Hubble Space Telescope/UVIS F200LP imaging. No diffuse emission is detected, with a 2 σ upper limit of F200LP > 28.1 mag arcsec^−2 on the 5″ scale of CDG-1. This surface brightness limit corresponds to a 2 σ lower limit of >0.5 for the fraction of the total luminosity that is in the form of globular clusters. The most likely alternative, although improbable, is that CDG-1 is a chance grouping of four globular clusters in the halo of the Perseus galaxy IC 312.