Sensitivity of the Hydrogen Epoch of Reionization Array and its
  Build-out Stages to One-point Statistics from Redshifted 21 cm Observations
  We present a baseline sensitivity analysis of the Hydrogen Epoch of
Reionization Array (HERA) and its build-out stages to one-point statistics
(variance, skewness, and kurtosis) of redshifted 21 cm intensity fluctuation
from the Epoch of Reionization (EoR) based on realistic mock observations. By
developing a full-sky 21 cm lightcone model, taking into account the proper
field of view and frequency bandwidth, utilising a realistic measurement
scheme, and assuming perfect foreground removal, we show that HERA will be able
to recover statistics of the sky model with high sensitivity by averaging over
measurements from multiple fields. All build-out stages will be able to detect
variance, while skewness and kurtosis should be detectable for HERA128 and
larger. We identify sample variance as the limiting constraint of the variance
measurement while skewness and kurtosis measurements will be primarily limited
by thermal noise. The sensitivity can be improved by performing frequency
binning and windowing. In addition, we find that strong sample variance
fluctuation in the kurtosis measured from an individual field of observation
indicates the present of outlying cold or hot regions in the underlying
fluctuations, a feature that can potentially be used as an EoR bubble
indicator. This manuscript is altered from the originally published paper to
reflect corrections in the erratum.
