Approximate Bayesian Computation in Large Scale Structure: constraining the galaxy-halo connection

TL;DR

This paper demonstrates that Approximate Bayesian Computation (ABC) can effectively infer galaxy-halo connection parameters in large scale structure, offering a likelihood-free alternative to traditional Gaussian-based methods.

Contribution

The study shows ABC's feasibility for LSS parameter inference using a forward model and compares its results with traditional MCMC, highlighting its reliability and potential advantages.

Findings

ABC constraints match true HOD parameters in mock data

ABC provides consistent results with Gaussian likelihood methods

ABC is a viable likelihood-free inference approach for LSS

Abstract

Standard approaches to Bayesian parameter inference in large scale structure assume a Gaussian functional form (chi-squared form) for the likelihood. This assumption, in detail, cannot be correct. Likelihood free inferences such as Approximate Bayesian Computation (ABC) relax these restrictions and make inference possible without making any assumptions on the likelihood. Instead ABC relies on a forward generative model of the data and a metric for measuring the distance between the model and data. In this work, we demonstrate that ABC is feasible for LSS parameter inference by using it to constrain parameters of the halo occupation distribution (HOD) model for populating dark matter halos with galaxies. Using specific implementation of ABC supplemented with Population Monte Carlo importance sampling, a generative forward model using HOD, and a distance metric based on galaxy number density, two-point correlation function, and galaxy group multiplicity function, we constrain the HOD parameters of mock observation generated from selected "true" HOD parameters. The parameter constraints we obtain from ABC are consistent with the "true" HOD parameters, demonstrating that ABC can be reliably used for parameter inference in LSS. Furthermore, we compare our ABC constraints to constraints we obtain using a pseudo-likelihood function of Gaussian form with MCMC and find consistent HOD parameter constraints. Ultimately our results suggest that ABC can and should be applied in parameter inference for LSS analyses.