Methods of Error Estimation for 21cm Power Spectra

Precise measurements of 21 cm power spectra are crucial for us to understand the physical process of hydrogen reionization. Currently, this is pursued by low-frequency radio interferometer arrays, such as the MWA, LOFAR, PAPER and HERA. With large amounts of data available in the near future, error estimation plays an important role in data processing and analysis. Based on the HERA-style delay power spectrum approach, we have produced a critical examination on different possible ways that one can put error bars on power spectra through a synthesis of analytic work, simulations of toy models, and tests on small amounts of real data. We find that, although computed independently, different error bar methodologies agree well with each other in the noise-dominated region. For our preferred methodology, the predicted probability distribution function is consistent with noise power distributions from data simulations and real data. We favour the analytic method using the covariance matrices of quadratic estimator formalism, in which we construct a foreground and systematics dependent error bar that includes the signal-noise coupling term in the variance of power spectra. This diagnosis is mainly in support of the forthcoming HERA upper limit, and also is expected to be more generally applicable.