Bayesian angular power spectrum analysis of interferometric data
  We present a Bayesian angular power spectrum and signal map inference engine
which can be adapted to interferometric observations of anisotropies inthe
cosmic microwave background, 21 cm emission line mapping of galactic brightness
fluctuations, or 21 cm absorption line mapping of neutral hydrogen in the dark
ages. The method uses Gibbs sampling to generate a sampled representation of
the angular power spectrum posterior and the posterior of signal maps given a
set of measured visibilities in the uv-plane. We use a mock interferometric CMB
observation to demonstrate the validity of this method in the flat-sky
approximation when adapted to take into account arbitrary coverage of the
uv-plane, mode-mode correlations due to observations on a finite patch, and
heteroschedastic visibility errors. The computational requirements scale as
O(n_p log n_p) where n_p measures the ratio of the size of the detector array
to the inter-detector spacing, meaning that Gibbs sampling is a promising
technique for meeting the data analysis requirements of future cosmology
missions.
