Novel methods of Bayesian predictive model comparison developed for count modeling of star cluster populations

There exists a tight scaling relation between a galaxy's stellar mass (M_*) and the number of globular clusters (N_GC) -- a class of old, massive, and dense star cluster -- that it hosts. However, in the astronomy literature, this relationship is often modeled as linear instead of with count models. In this work, we test the utility of Poisson and negative binomial models for describing the scaling relation. We introduce the use of zero-inflated versions of these models, which allow for larger zero populations (e.g., galaxies without GCs). To determine the value of these models, we evaluate them with a variety of predictive model comparison methods, including predictive intervals and the leave-one-out cross-validation criterion. We also develop a novel posterior predictive comparison method.

We find that the NB model is consistent with our data, but the naive Poisson is not. Moreover, we find that zero inflation of the models is not necessary to describe the large population of low-mass galaxies that lack GCs, suggesting that a single formation and evolutionary process acts over all galaxy masses. Under the NB model, there does not appear to be anything unique about the lack of GCs in many low-mass galaxies; they are simply the low-mass extension of the larger N GC‑M * scaling relation.