1. On the accuracy and precision of correlation functions and field-level inference in cosmology
- Author
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Florent Leclercq and Alan Heavens
- Subjects
FOS: Computer and information sciences ,Accuracy and precision ,Cosmology and Nongalactic Astrophysics (astro-ph.CO) ,Field (physics) ,FOS: Physical sciences ,Inference ,Astrophysics ,Astronomy & Astrophysics ,Statistics - Applications ,Cosmology ,LIKELIHOOD ,Correlation ,DATA-COMPRESSION ,Data assimilation ,0201 Astronomical and Space Sciences ,Bayesian hierarchical modeling ,Applications (stat.AP) ,Statistical physics ,cosmological parameters ,stat.AP ,Instrumentation and Methods for Astrophysics (astro-ph.IM) ,Physics ,methods: statistical ,Science & Technology ,Astronomy and Astrophysics ,STATISTICS ,Correlation function (statistical mechanics) ,Space and Planetary Science ,Physical Sciences ,astro-ph.CO ,large-scale structure of Universe ,Astrophysics - Instrumentation and Methods for Astrophysics ,Astrophysics - Cosmology and Nongalactic Astrophysics ,astro-ph.IM - 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., Comment: 6+8 pages, 4+5 figures. Matches MNRAS Letters published version. Appendices provide supplementary information, including calculations of Fisher matrices. Our code and data are publicly available at https://github.com/florent-leclercq/correlations_vs_field
- Published
- 2021
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