Bayesian inference of cosmic density fields from non-linear, scale-dependent, and stochastic biased tracers

TL;DR

This paper introduces a Bayesian method using a non-Poisson likelihood and Hamiltonian Monte Carlo to accurately reconstruct dark matter density fields from galaxy data, accounting for complex biasing.

Contribution

The authors develop a novel Bayesian reconstruction algorithm with a non-Poisson likelihood and scale-dependent bias modeling, implemented via Hamiltonian Monte Carlo.

Findings

Accurately reconstructs dark matter fields up to k~1 h/Mpc.

Outperforms Poisson likelihood in power spectrum accuracy.

Effective for emission line galaxy data with complex bias.

Abstract

We present a Bayesian reconstruction algorithm to generate unbiased samples of the underlying dark matter field from halo catalogues. Our new contribution consists of implementing a non-Poisson likelihood including a deterministic non-linear and scale-dependent bias. In particular we present the Hamiltonian equations of motions for the negative binomial (NB) probability distribution function. This permits us to efficiently sample the posterior distribution function of density fields given a sample of galaxies using the Hamiltonian Monte Carlo technique implemented in the Argo code. We have tested our algorithm with the Bolshoi $N$-body simulation at redshift $z = 0$, inferring the underlying dark matter density field from sub-samples of the halo catalogue with biases smaller and larger than one. Our method shows that we can draw closely unbiased samples (compatible within 1-$\sigma$) from the posterior distribution up to scales of about $k$~1 h/Mpc in terms of power-spectra and cell-to-cell correlations. We find that a Poisson likelihood yields reconstructions with power spectra deviating more than 10% at $k$=0.2 h/Mpc. Our reconstruction algorithm is especially suited for emission line galaxy data for which a complex non-linear stochastic biasing treatment beyond Poissonity becomes indispensable.