A fast estimator for the bispectrum and beyond - a practical method for measuring non-Gaussianity in 21-cm maps

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Title: A fast estimator for the bispectrum and beyond - a practical method for measuring non-Gaussianity in 21-cm maps
Authors: Watkinson, CA
Majumdar, S
Pritchard, JR
Mondal, R
Item Type: Journal Article
Abstract: In this paper, we establish the accuracy and robustness of a fast estimator for the bispectrum – the ‘FFT-bispectrum estimator’. The implementation of the estimator presented here offers speed and simplicity benefits over a direct-measurement approach. We also generalize the derivation so it may be easily be applied to any order polyspectra, such as the trispectrum, with the cost of only a handful of Fast-Fourier Transforms (FFTs). All lower order statistics can also be calculated simultaneously for little extra cost. To test the estimator, we make use of a non-linear density field, and for a more strongly non-Gaussian test case, we use a toy-model of reionization in which ionized bubbles at a given redshift are all of equal size and are randomly distributed. Our tests find that the FFT-estimator remains accurate over a wide range of k, and so should be extremely useful for analysis of 21-cm observations. The speed of the FFT-bispectrum estimator makes it suitable for sampling applications, such as Bayesian inference. The algorithm we describe should prove valuable in the analysis of simulations and observations, and whilst, we apply it within the field of cosmology, this estimator is useful in any field that deals with non-Gaussian data.
Issue Date: 22-Aug-2017
Date of Acceptance: 15-Aug-2017
ISSN: 0035-8711
Publisher: Oxford University Press (OUP)
Start Page: 2436
End Page: 2446
Journal / Book Title: Monthly Notices of the Royal Astronomical Society
Volume: 472
Issue: 2
Copyright Statement: © 2017 The Authors Published by Oxford University Press on behalf of the Royal Astronomical Society
Sponsor/Funder: Commission of the European Communities
Funder's Grant Number: 638743
Keywords: Science & Technology
Physical Sciences
Astronomy & Astrophysics
methods: statistical
intergalactic medium
dark ages
first stars
cosmology: theory
0201 Astronomical And Space Sciences
Publication Status: Published
Appears in Collections:Physics
Faculty of Natural Sciences

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