# Explicit Bayesian treatment of unknown foreground contaminations in galaxy surveys

## TL;DR

This paper introduces a robust Bayesian likelihood method that effectively marginalizes over unknown foreground contaminations in galaxy surveys, leading to unbiased estimates of the matter power spectrum and density fields, crucial for future large-scale structure analyses.

## Contribution

The paper presents a novel likelihood approach that accounts for unknown foreground effects, improving the accuracy of galaxy clustering inferences compared to standard methods.

## Key findings

- Unbiased matter power spectrum estimates across all Fourier modes.
- Effective correction of foreground contamination effects in density field inference.
- Outperforms standard Poissonian likelihood in contaminated data scenarios.

## Abstract

The treatment of unknown foreground contaminations will be one of the major challenges for galaxy clustering analyses of coming decadal surveys. These data contaminations introduce erroneous large-scale effects in recovered power spectra and inferred dark matter density fields. In this work, we present an effective solution to this problem in the form of a robust likelihood designed to account for effects due to unknown foreground and target contaminations. Conceptually, this robust likelihood marginalizes over the unknown large-scale contamination amplitudes. We showcase the effectiveness of this novel likelihood via an application to a mock SDSS-III data set subject to dust extinction contamination. In order to illustrate the performance of our proposed likelihood, we infer the underlying dark-matter density field and reconstruct the matter power spectrum, being maximally agnostic about the foregrounds. The results are compared to those of an analysis with a standard Poissonian likelihood, as typically used in modern large-scale structure analyses. While the standard Poissonian analysis yields excessive power for large-scale modes and introduces an overall bias in the power spectrum, our likelihood provides unbiased estimates of the matter power spectrum over the entire range of Fourier modes considered in this work. Further, we demonstrate that our approach accurately accounts for and corrects the effects of unknown foreground contaminations when inferring three-dimensional density fields. Robust likelihood approaches, as presented in this work, will be crucial to control unknown systematic error and maximize the outcome of the decadal surveys.