Statistical Recovery of 21 cm Visibilities and Their Power Spectra with Gaussian-constrained Realizations and Gibbs Sampling

Radio interferometers designed to probe the 21 cm signal from Cosmic Dawn and the Epoch of Reionization must contend with systematic effects that make it difficult to achieve sufficient dynamic range to separate the 21 cm signal from foreground emission and other effects. For instance, the instrument's chromatic response modulates the otherwise spectrally smooth foregrounds, making them difficult to model, while a significant fraction of the data must be excised due to the presence of radio-frequency interference, leaving gaps in the data. Errors in modeling the (modulated and gappy) foregrounds can easily generate spurious contamination of what should otherwise be 21 cm signal-dominated modes. Various approaches have been developed to mitigate these issues by, for example, using nonparametric reconstruction of the foregrounds, in-painting the gaps, and weighting the data to reduce the level of contamination. We present a Bayesian statistical method that combines these approaches, using the coupled techniques of Gaussian-constrained realizations and Gibbs sampling. This provides a way of drawing samples from the joint posterior distribution of the 21 cm signal modes and their power spectrum in the presence of gappy data and an uncertain foreground model in a computationally scalable manner. The data are weighted by an inverse covariance matrix that is estimated as part of the inference, along with a foreground model that can then be marginalized over. We demonstrate the application of this technique on a simulated Hydrogen Epoch of Reionization Array-like delay spectrum analysis, comparing three different approaches for accounting for the foreground components.