Bayesian Inference for Radio Observations

TL;DR

This paper introduces BIRO, a Bayesian inference method that jointly estimates sky and instrumental parameters directly from raw radio telescope data, improving uncertainty quantification and enabling super-resolution imaging.

Contribution

The paper presents a novel Bayesian formalism for radio data analysis that bypasses traditional imaging, jointly infers systematics and sky, and utilizes Bayesian evidence for source model selection.

Findings

Successfully estimated 103 parameters in simulated data

Achieved super-resolution imaging beyond the synthesized beam

Demonstrated accurate model selection using Bayesian evidence

Abstract

New telescopes like the Square Kilometre Array (SKA) will push into a new sensitivity regime and expose systematics, such as direction-dependent 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 image-making 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 'super-resolution' on scales much smaller than the synthesized beam.