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Modeling Globular Cluster Counts with Bayesian Latent Models

Rafael S. de Souza, Ana L. Chies-Santos

Abstract

We present a Bayesian latent model to describe the scaling relation between globular cluster populations and their host galaxies, updating the framework proposed in de Souza 2015. GC counts are drawn from a negative-binomial (NB) process linked to host stellar mass, augmented with a newly introduced Gaussian observation layer that enables efficient propagation of measurement errors. The revised formulation preserves the underlying NB process while improving computational tractability. The code snippets, implemented in Nimble and PyMC are released under the MIT license at https://github.com/COINtoolbox/Generalized-Linear-Models-Tutorial/blob/master/Count/readme.md

Modeling Globular Cluster Counts with Bayesian Latent Models

Abstract

We present a Bayesian latent model to describe the scaling relation between globular cluster populations and their host galaxies, updating the framework proposed in de Souza 2015. GC counts are drawn from a negative-binomial (NB) process linked to host stellar mass, augmented with a newly introduced Gaussian observation layer that enables efficient propagation of measurement errors. The revised formulation preserves the underlying NB process while improving computational tractability. The code snippets, implemented in Nimble and PyMC are released under the MIT license at https://github.com/COINtoolbox/Generalized-Linear-Models-Tutorial/blob/master/Count/readme.md
Paper Structure (4 sections, 1 equation, 1 figure)

This paper contains 4 sections, 1 equation, 1 figure.

Table of Contents

  1. Introduction
  2. Dataset
  3. Model
  4. Analysis and Discussion

Figures (1)

  • Figure 1: Negative–binomial regression with a latent errors-in-variables treatment for the relation between $N_{\rm GC}$ and $\log_{10}(M_{\star}/M_{\odot})$. Data points are elliptical galaxies from Harris2013. The solid blue curve shows the posterior median, and the orange band the 95% credible interval. Points include 1$\sigma$ uncertainties.