  We investigate the stochastic properties of typical red galaxy samples in a
controlled numerical environment. We use Halo Occupation Distribution (HOD)
modelling to create mock realizations of three separate bright red galaxy
samples consistent with datasets used for clustering and lensing analyses in
modern galaxy surveys. Second-order Hybrid Effective Field Theory (HEFT) is
used as a field-level forward model to describe the full statistical
distribution of these tracer samples, and their stochastic power spectra are
directly measured and compared to the Poisson shot-noise prediction. While all
of the galaxy samples we consider are hosted within haloes with sub-Poisson
stochasticity, we observe that the galaxy samples themselves possess
stochasticities that range from sub-Poisson to super-Poisson, in agreement with
predictions from the halo model. As an application of our methodology, we place
priors on the expected degree of non-Poisson stochasticity in cosmological
analyses using such samples. We expect these priors will be useful in reducing
the complexity of the full parameter space for future analyses using
second-order Lagrangian bias models. More generally, the techniques outlined
here present the first application of hybrid EFT methods to characterize models
of the galaxy--halo connection at the field level, revealing new connections
between once-disparate modelling frameworks.

Cosmology and Nongalactic Astrophysics