On the accuracy and precision of correlation functions and field-level
inference in cosmology
inference in cosmology
File(s)
Accepted version
Author(s)
Leclercq, Florent
Heavens, Alan
Type
Journal Article
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 lognormal (LN) fields and their two-point correlation function. Although a simplified analytic model, the LN 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.
Date Issued
2021-09-01
Date Acceptance
2021-07-12
Citation
Monthly Notices of the Royal Astronomical Society, 2021, 506 (1), pp.L85-L90
ISSN
0035-8711
Publisher
Royal Astronomical Society
Start Page
L85
End Page
L90
Journal / Book Title
Monthly Notices of the Royal Astronomical Society
Volume
506
Issue
1
Copyright Statement
© 2021 The Author(s) Published by Oxford University Press on behalf of Royal Astronomical Society. This is a pre-copy-editing, author-produced version of an article accepted for publication in Monthly Notices of the Royal Astronomical Society following peer review. The definitive publisher-authenticated version [insert complete citation information here] is available online at: https://academic.oup.com/mnrasl/article/506/1/L85/6324582
Identifier
http://arxiv.org/abs/2103.04158v1
Subjects
astro-ph.CO
astro-ph.CO
astro-ph.IM
stat.AP
Notes
6 pages, 4 figures. Our code and data are publicly available at https://github.com/florent-leclercq/correlations_vs_field
Publication Status
Published
Date Publish Online
2021-07-20