The Overlooked Potential of Generalized Linear Models in Astronomy-III: Bayesian Negative Binomial Regression and Globular Cluster Populations

Abstract

In this paper, the third in a series illustrating the power of generalized linear models (GLMs) for the astronomical community, we elucidate the potential of the class of GLMs which handles count data. The size of a galaxy's globular cluster population $N_{\mathrm{GC}}$ is a prolonged puzzle in the astronomical literature. It falls in the category of count data analysis, yet it is usually modelled as if it were a continuous response variable. We have developed a Bayesian negative binomial regression model to study the connection between $N_{\mathrm{GC}}$ and the following galaxy properties: central black hole mass, dynamical bulge mass, bulge velocity dispersion, and absolute visual magnitude. The methodology introduced herein naturally accounts for heteroscedasticity, intrinsic scatter, errors in measurements in both axes (either discrete or continuous), and allows modelling the population of globular clusters on their natural scale as a non-negative integer variable. Prediction intervals of 99% around the trend for expected $N_{\mathrm{GC}}$comfortably envelope the data, notably including the Milky Way, which has hitherto been considered a problematic outlier. Finally, we demonstrate how random intercept models can incorporate information of each particular galaxy morphological type. Bayesian variable selection methodology allows for automatically identifying galaxy types with different productions of GCs, suggesting that on average S0 galaxies have a GC population 35% smaller than other types with similar brightness.

14 pages, 12 figures. Accepted for publication in MNRAS

References in corpus (6)

• Bayesian inference of cosmic density fields from non-linear, scale-dependent, and stochastic biased tracers
• The Overlooked Potential of Generalized Linear Models in Astronomy - I: Binomial Regression
• Relation Between Globular Clusters and Supermassive Black Holes in Ellipticals as a Manifestation of the Black Hole Fundamental Plane
• Variable Selection for Modeling the Absolute Magnitude at Maximum of Type Ia Supernovae
• Do cluster properties affect the quenching rate?
• Dark halo microphysics and massive black hole scaling relations in galaxies

Cited by in corpus (21)

• Black Hole Mass Scaling Relations for Spiral Galaxies. I. $M_{\mathrm{BH}}$-$M_{\ast ,\mathrm{sph}}$
• On the realistic validation of photometric redshifts, or why Teddy will never be Happy
• Are star formation rates of galaxies bimodal?
• Clearing the hurdle: The mass of globular cluster systems as a function of host galaxy mass
• Astrophysical S-factors, thermonuclear rates, and electron screening potential for the ${}^3$He(d,p)${}^4$He Big Bang reaction via a hierarchical Bayesian model
• Is the cluster environment quenching the Seyfert activity in elliptical and spiral galaxies?
• 21st Century Statistical and Computational Challenges in Astrophysics
• On the Significance of Rare Objects at High Redshift: The Impact of Cosmic Variance
• The relation between globular cluster systems and supermassive black holes in spiral galaxies. The case study of NGC 4258
• Spatial field reconstruction with INLA: Application to IFU galaxy data
• A case study of hurdle and generalized additive models in astronomy: the escape of ionizing radiation
• Multiplicity of stars with planets in the solar neighbourhood
• The HERBAL model: A hierarchical errors-in-variables Bayesian lognormal hurdle model for galactic globular cluster populations
• Discovery of Two Ultra-Diffuse Galaxies with Unusually Bright Globular Cluster Luminosity Functions via a Mark-Dependently Thinned Point Process (MATHPOP)
• Fallopian tube anatomy predicts pregnancy and pregnancy outcomes after tubal reversal surgery
• Probing the origins. I. Generalised Additive Model inference of birth radii for Milky Way stars in the solar vicinity
• The Rest-Frame Golenetskii Correlation via a Hierarchical Bayesian Analysis
• Simulation-based marginal likelihood for cluster strong lensing cosmology
• Modeling Globular Cluster Counts with Bayesian Latent Models
• UV bright red-sequence galaxies: a comparative study between UV upturn and UV weak systems
• Finding High-Redshift Galaxies with JWST