Inference of Coefficients for Use in Phase Correction I

TL;DR

This paper introduces a Bayesian method using a simple atmospheric model and MCMC to accurately estimate phase correction coefficients from water-vapour radiometer data, demonstrated with simulations and real observations.

Contribution

It presents a novel Bayesian approach with priors and MCMC for deriving phase correction coefficients, improving stability and accuracy in interferometric observations.

Findings

Method is stable over an hour-long test observation.

Performance approaches optimal accuracy in practical application.

Priors help resolve degeneracies in coefficient estimation.

Abstract

We present a Bayesian approach to calculating the coefficients that convert the outputs of ALMA 183 GHz water-vapour radiometers into estimates of path fluctuations which can then be used to correct the observed interferometric visibilities. The key features of the approach are a simple, thin-layer, three-parameter model of the atmosphere; using the absolute measurements from the radiometers to constrain the model; priors to incorporate physical constraints and ancillary information; and a Markov Chain Monte Carlo characterisation of the posterior distribution including full distributions for the phase correction coefficients. The outcomes of the procedure are therefore estimates of the coefficients and their confidence intervals. We illustrate the technique with simulations showing some degeneracies that can arise and the importance of priors in tackling them. We then apply the technique to an hour-long test observation at the Sub-Millimetre Array and find that the technique is stable and that, in this case, its performance is close to optimal. The modelling is described in detail in the appendices and all of the implementation source code is made publicly available under the GPL.