Bayesian angular power spectrum analysis of interferometric data

Abstract

We present a Bayesian angular power spectrum and signal map inference engine which can be adapted to interferometric observations of anisotropies in the cosmic microwave background (CMB), 21cm emission line mapping of galactic brightness fluctuations, or 21cm 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 plogn 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. © 2012. The American Astronomical Society. All rights reserved.