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

Understand

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.