The Square Kilometre Array is in the business of deep radio-galaxy surveys, giving astronomers Big Data from which they want to extract the maximum amount of information. Pathfinders like MeerKAT will play a crucial role in forecasting for these surveys. But quoted survey detection sensitivities are deliberately conservative (5 sigma, say) in order to avoid biases that appear in the noise regime. Modelling these biases mitigates them, typically allowing us to push the data 1-2 orders of magnitude deeper. That means more physics right now, as well as better predictions for successor telescopes like SKA.

Current deconvolution methods for analysing radio interferometric data produce from the raw telescope data a single image of the sky that one must assume is its true representation, when in fact it is just one realisation of an infinite ensemble of images compatible with the noise in those raw data. With several advantages, but at the expense of even Bigger Data, it is possible to pose the problem in the raw ('visibility') domain, and it is this that is the focus of the project.

As well as the brightest (detected) galaxies in a radio data set, the telescope is sensitive to very many faint sources buried within the (usually gaussian, stationary and uncorrelated) measurement noise. Simply counting the numbers of sources of different fluxes at these faint levels is not only of fundamental importance, but also a hot topic vital for studying models of galaxy evolution and, in the past, cosmology.

In the visibility domain, fluctuations from these sources contribute a noise-variance term that can be modelled alongside the thermal-noise contribution from the telescope itself (including possible systematic effects) and even fluctuations from astronomical foregrounds such as the cosmic microwave background. The inverse problem of inferring the distribution of the source counts from the data, in the presence of nuisance parameters, is then perfectly cast in a bayesian framework.

We will provide simulated visibility data in which are buried different populations of radio sources in the presence of systematic artefacts. The aim is to select the source-count model (via the Bayesian evidence or some other means) used for each simulation, infer the correct parameters used for the model, and quantify how such inferences are corrupted by telescope systematic effects in each case.

Although we have identified a robust (but computationally challenging) approach, we are excited to have participants who can bring to bear original and unexpected lines of attack to solve this problem. There will be ample opportunity to practise bayesian inference - including MCMC and friends - at first hand, leaning on our combined expertise

About the dataset

• Blind, simulated MeerKAT/KAT7 visibility data (64/7 antennas), with several frequency channels and a few thousand time samples;

• Each data point (a 'visibility') represents a single measurement of the voltage cross-correlation from a pair of antennas at a given point in time and frequency;
• There will be a range of data sets of increasing complexity, incorporating more complicated source count models, telescope systematic effects, and astronomical foregrounds;
• The data sets can be tailored to the hardware at hand;
• The key variables are the few parameters describing the counts of  the sources themselves. There will be more and more several nuisance  parameters describing physical aspects of the telescope - a key challenge is to identify what is feasible in a real-world scenario