On the accuracy and precision of correlation functions and field-level inference in cosmology

TL;DR

This study compares correlation function methods and full-field inference in cosmology, showing that field-level analysis provides significantly higher accuracy and precision, especially in non-Gaussian scenarios, with simulation-based inference reducing biases.

Contribution

It demonstrates the advantages of field-level inference over correlation functions in cosmology, highlighting the importance of data assimilation techniques and simulation-based methods.

Findings

Field-level analysis outperforms correlation functions in accuracy and precision.

Likelihood assumptions can introduce biases in correlation function analysis.

Simulation-based inference reduces biases and improves results.

Abstract

We present a comparative study of the accuracy and precision of correlation function methods and full-field inference in cosmological data analysis. To do so, we examine a Bayesian hierarchical model that predicts log-normal fields and their two-point correlation function. Although a simplified analytic model, the log-normal model produces fields that share many of the essential characteristics of the present-day non-Gaussian cosmological density fields. We use three different statistical techniques: (i) a standard likelihood-based analysis of the two-point correlation function; (ii) a likelihood-free (simulation-based) analysis of the two-point correlation function; (iii) a field-level analysis, made possible by the more sophisticated data assimilation technique. We find that (a) standard assumptions made to write down a likelihood for correlation functions can cause significant biases, a problem that is alleviated with simulation-based inference; and (b) analysing the entire field offers considerable advantages over correlation functions, through higher accuracy, higher precision, or both. The gains depend on the degree of non-Gaussianity, but in all cases, including for weak non-Gaussianity, the advantage of analysing the full field is substantial.