Bayesian analysis of spatially distorted cosmic signals from Poissonian data

TL;DR

This paper presents a Bayesian method for reconstructing cosmic matter density fields from galaxy counts, accounting for shot noise, velocity distortions, and measurement uncertainties, with improved results demonstrated on a 1D toy model.

Contribution

It introduces a Bayesian maximum a posteriori approach to reconstruct log-normal density fields with velocity distortions, addressing multiple real-world observational challenges.

Findings

Significant improvement over simple data inversion in toy tests

Effective handling of redshift space distortions and measurement uncertainties

Versatile application to various observational scenarios

Abstract

Reconstructing the matter density field from galaxy counts is a problem frequently addressed in current literature. Two main sources of error are shot noise from galaxy counts and insufficient knowledge of the correct galaxy position caused by peculiar velocities and redshift measurement uncertainty. Here we address the reconstruction problem of a Poissonian sampled log-normal density field with velocity distortions in a Bayesian way via a maximum a posteriory method. We test our algorithm on a 1D toy case and find significant improvement compared to simple data inversion. In particular, we address the following problems: photometric redshifts, mapping of extended sources in coded mask systems, real space reconstruction from redshift space galaxy distribution and combined analysis of data with different point spread functions.