Bayesian inference for radio observations
Abstract
New telescopes like the Square Kilometre Array (SKA) will push into a new sensitivity regime and expose systematics, such as directiondependent effects, that could previously be ignored. Current methods for handling such systematics rely on alternating best estimates of instrumental calibration and models of the underlying sky, which can lead to inadequate uncertainty estimates and biased results because any correlations between parameters are ignored. These deconvolution algorithms produce a single image that is assumed to be a true representation of the sky, when in fact it is just one realization of an infinite ensemble of images compatible with the noise in the data. In contrast, here we report a Bayesian formalism that simultaneously infers both systematics and science. Our technique, Bayesian Inference for Radio Observations (BIRO), determines all parameters directly from the raw data, bypassing imagemaking entirely, by sampling from the joint posterior probability distribution. This enables it to derive both correlations and accurate uncertainties, making use of the flexible software MEQTREES to model the sky and telescope simultaneously. We demonstrate BIRO with two simulated sets of Westerbork Synthesis Radio Telescope data sets. In the first, we perform joint estimates of 103 scientific (flux densities of sources) and instrumental (pointing errors, beamwidth and noise) parameters. In the second example, we perform source separation with BIRO. Using the Bayesian evidence, we can accurately select between a single point source, two point sources and an extended Gaussian source, allowing for `superresolution' on scales much smaller than the synthesized beam.
 Publication:

Monthly Notices of the Royal Astronomical Society
 Pub Date:
 June 2015
 DOI:
 10.1093/mnras/stv679
 arXiv:
 arXiv:1501.05304
 Bibcode:
 2015MNRAS.450.1308L
 Keywords:

 methods: data analysis;
 methods: statistical;
 techniques: interferometric;
 Astrophysics  Instrumentation and Methods for Astrophysics;
 Astrophysics  Cosmology and Nongalactic Astrophysics
 EPrint:
 Published in MNRAS. See https://vimeo.com/117391380 for a video of MultiNest converging to the correct source model