Methods of Error Estimation for Delay Power Spectra in $21\,\textrm{cm}$ Cosmology
Creators: name: Tan, Jianrong
name: Liu, Adrian
name: Kern, Nicholas S.
name: Abdurashidova, Zara
name: Aguirre, James E.
name: Alexander, Paul
name: Ali, Zaki S.
name: Balfour, Yanga
name: Beardsley, Adam P.
name: Bernardi, Gianni
name: Billings, Tashalee S.
name: Bowman, Judd D.
name: Bradley, Richard F.
name: Bull, Philip
name: Burba, Jacob
name: Carey, Steven
name: Carilli, Christopher L.
name: Cheng, Carina
name: DeBoer, David R.
name: Dexter, Matt
name: Acedo, Eloy de Lera
name: Dillon, Joshua S.
name: Ely, John
name: Ewall-Wice, Aaron
name: Fagnoni, Nicolas
name: Fritz, Randall
name: Furlanetto, Steve R.
name: Gale-Sides, Kingsley
name: Glendenning, Brian
name: Gorthi, Deepthi
name: Greig, Bradley
name: Grobbelaar, Jasper
name: Halday, Ziyaad
name: Hazelton, Bryna J.
name: Hewitt, Jacqueline N.
name: Hickish, Jack
name: Jacobs, Daniel C.
name: Julius, Austin
name: Kerrigan, Joshua
name: Kittiwisit, Piyanat
name: Kohn, Saul A.
name: Kolopanis, Matthew
name: Lanman, Adam
name: La Plante, Paul
name: Lekalake, Telalo
name: MacMahon, David
name: Malan, Lourence
name: Malgas, Cresshim
name: Maree, Matthys
name: Martinot, Zachary E.
name: Matsetela, Eunice
name: Mesinger, Andrei
name: Molewa, Mathakane
name: Morales, Miguel F.
name: Mosiane, Tshegofalang
name: Murray, Steven G.
name: Neben, Abraham R.
name: Nikolic, Bojan
name: Nunhokee, Chuneeta D.
name: Parsons, Aaron R.
name: Patra, Nipanjana
name: Pieterse, Samantha
name: Pober, Jonathan C.
name: Razavi-Ghods, Nima
name: Ringuette, Jon
name: Robnett, James
name: Rosie, Kathryn
name: Sims, Peter
name: Singh, Saurabh
name: Smith, Craig
name: Syce, Angelo
name: Thyagarajan, Nithyanandan
name: Williams, Peter K. G.
name: Zheng, Haoxuan
Publisher: name: arXiv
Year: 2021
Subjects: subject: Instrumentation and Methods for Astrophysics (astro-ph.IM)
subject: Cosmology and Nongalactic Astrophysics (astro-ph.CO)
subject: FOS: Physical sciences
subject: FOS: Physical sciences

description: Precise measurements of the 21 cm power spectrum are crucial for understanding the physical processes of hydrogen reionization. Currently, this probe is being pursued by low-frequency radio interferometer arrays. As these experiments come closer to making a first detection of the signal, error estimation will play an increasingly important role in setting robust measurements. Using the delay power spectrum approach, we have produced a critical examination of different ways that one can estimate error bars on the power spectrum. We do this through a synthesis of analytic work, simulations of toy models, and tests on small amounts of real data. We find that, although computed independently, the different error bar methodologies are in good agreement with each other in the noise-dominated regime of the power spectrum. For our preferred methodology, the predicted probability distribution function is consistent with the empirical noise power distributions from both simulated and real data. This diagnosis is mainly in support of the forthcoming HERA upper limit, and also is expected to be more generally applicable.
description: 35 Pages, 9 Figures, 4 Tables. Replaced with accepted ApJ version; some clarifying text added in response to referee comments with no changes to results