Bayesian power-spectrum inference for Large Scale Structure data

TL;DR

The paper introduces ARES, a Bayesian Gibbs sampling algorithm for joint estimation of the large-scale structure and power-spectrum from cosmological data, accounting for observational masks and uncertainties.

Contribution

It presents a novel, efficient Bayesian method for reconstructing the 3D power-spectrum and density field simultaneously, with full uncertainty quantification.

Findings

Successfully reconstructs power-spectrum from mock data with complex masks

Provides joint posterior samples for density and power-spectrum

Demonstrates robustness to observational effects

Abstract

We describe an exact, flexible, and computationally efficient algorithm for a joint estimation of the large-scale structure and its power-spectrum, building on a Gibbs sampling framework and present its implementation ARES (Algorithm for REconstruction and Sampling). ARES is designed to reconstruct the 3D power-spectrum together with the underlying dark matter density field in a Bayesian framework, under the reasonable assumption that the long wavelength Fourier components are Gaussian distributed. As a result ARES does not only provide a single estimate but samples from the joint posterior of the power-spectrum and density field conditional on a set of observations. This enables us to calculate any desired statistical summary, in particular we are able to provide joint uncertainty estimates. We apply our method to mock catalogs, with highly structured observational masks and selection functions, in order to demonstrate its ability to reconstruct the power-spectrum from real data sets, while fully accounting for any mask induced mode coupling.