Why and When to Expect Gaussian Error Distributions in Epoch of Reionization 21-cm Power Spectrum Measurements

Abstract

We explore error distributions in Epoch of Reionization 21-cm power spectrum estimators using a combination of mathematical analysis and numerical simulations. We provide closed form solutions for the error distributions of individual bins in 3d-power spectra for two estimators currently in use in the field, which we designate as ``straight-square" and ``cross-multiply" estimators. We then demonstrate when the corresponding spherically binned power spectra should (and should not) have Gaussian error distributions, which requires appealing to nonstandard statements of the central limit theorem. This has important implications for how upper limits are reported, as well as how cosmological inferences are performed based on power spectrum measurements. Specifically, assuming a Gaussian error distribution can over or underestimate the upper limit depending on the type of estimator, and produces overly compact likelihood functions for the power spectrum.

Revisions from peer review

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Cited by in corpus (3)

• Evidence of Ultra-faint Radio Frequency Interference in Deep 21~cm Epoch of Reionization Power Spectra with the Murchison Widefield Array
• Forecasts and Statistical Insights for Line Intensity Mapping Cross-Correlations: A Case Study with 21cm x [CII]
• Towards $21$-cm intensity mapping at $z=2.28$ with uGMRT using the tapered gridded estimator III: Foreground removal