Differentiable Stochastic Halo Occupation Distribution

TL;DR

This paper introduces a differentiable approach to infer parameters of Halo Occupation Distribution models using gradient-based sampling, significantly improving efficiency in cosmological simulations.

Contribution

It develops a novel differentiable stochastic sampling method for HOD parameter inference, enabling faster convergence compared to traditional MCMC methods.

Findings

Achieved near-identical posteriors to standard MCMC

Increased convergence efficiency by approximately 8 times

Demonstrated applicability to cosmological simulation data

Abstract

In this work, we demonstrate how differentiable stochastic sampling techniques developed in the context of deep Reinforcement Learning can be used to perform efficient parameter inference over stochastic, simulation-based, forward models. As a particular example, we focus on the problem of estimating parameters of Halo Occupancy Distribution (HOD) models which are used to connect galaxies with their dark matter halos. Using a combination of continuous relaxation and gradient parameterization techniques, we can obtain well-defined gradients with respect to HOD parameters through discrete galaxy catalogs realizations. Having access to these gradients allows us to leverage efficient sampling schemes, such as Hamiltonian Monte-Carlo, and greatly speed up parameter inference. We demonstrate our technique on a mock galaxy catalog generated from the Bolshoi simulation using the Zheng et al. 2007 HOD model and find near identical posteriors as standard Markov Chain Monte Carlo techniques with an increase of ~8x in convergence efficiency. Our differentiable HOD model also has broad applications in full forward model approaches to cosmic structure and cosmological analysis.