# Toward a robust inference method for the galaxy bispectrum: likelihood function and model selection

## TL;DR

This paper evaluates how methodological choices affect bispectrum-based inferences of galaxy bias and shot noise, proposing an optimal model and demonstrating its effectiveness with simulation data for upcoming galaxy surveys.

## Contribution

It introduces a robust inference framework for the galaxy bispectrum, including likelihood function selection and model comparison, tailored for future large-scale structure analyses.

## Key findings

- A three-parameter bias model with Poisson shot noise fits data up to k_max ≈ 0.08 h/Mpc.
- Local Eulerian and Lagrangian bias models are disfavored by the data.
- Model-selection techniques help identify the best theoretical description of the bispectrum.

## Abstract

The forthcoming generation of galaxy redshift surveys will sample the large-scale structure of the Universe over unprecedented volumes with high-density tracers. This advancement will make robust measurements of three-point clustering statistics possible. In preparation for this improvement, we investigate how several methodological choices can influence inferences based on the bispectrum about galaxy bias and shot noise. We first measure the real-space bispectrum of dark-matter haloes extracted from 298 N-body simulations covering a volume of approximately $1000 h^{-3} \mathrm{Gpc}^3$. We then fit a series of theoretical models based on tree-level perturbation theory to the numerical data. To achieve this, we estimate the covariance matrix of the measurement errors by using 10,000 mock catalogues generated with the Pinocchio code. We study how the model constraints are influenced by the binning strategy for the bispectrum configurations and by the form of the likelihood function. We also use Bayesian model-selection techniques to single out the optimal theoretical description of our data. We find that a three-parameter bias model combined with Poissonian shot noise is necessary to model the halo bispectrum up to scales of $k_\mathrm{max}\lesssim 0.08 h \mathrm{Mpc}^{-1}$, although fitting formulae that relate the bias parameters can be helpful to reduce the freedom of the model without compromising accuracy. Our data clearly disfavour local Eulerian and local Lagrangian bias models and do not require corrections to Poissonian shot noise. We anticipate that model-selection diagnostics will be particularly useful to extend the analysis to smaller scales as, in this case, the number of model parameters will grow significantly large.