Methods of Error Estimation for Delay Power Spectra in $21\,\textrm{cm}$ Cosmology

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.