Bayesian hierarchical random-walk modelling for flux density and SEFD monitoring in broadband VLBI observations

Abstract

Broadband Very Long Baseline Interferometry (VLBI) observations spanning 3–14 GHz pose calibration challenges that traditional methods were not designed to handle. Frequency-dependent instrumental responses, radio frequency interference (RFI), and source variability all complicate the estimation of station sensitivity and source flux density. We present a Bayesian hierarchical random-walk model that jointly tracks source flux density and baseline System Equivalent Flux Density (SEFD) from scan-level signal-to-noise ratio (SNR) observations. The model captures temporal changes via random walks, frequency dependence through piecewise spectral indices and band-wise power-law SEFD scaling, and includes RFI and an elevation-dependent SEFD correction fitted from the scan-level data. We applied this model to 25 sessions on the Hobart–Katherine baseline, covering 81 sources over 3–13.5 GHz. Reliable system-temperature ( T _sys ) measurements were unavailable across these sessions, so the model uses scan-level SNR together with single-session catalogue anchors for each source, comprising an X-band flux-density value and a catalogue-derived S/X spectral index. It recovers flux density and baseline SEFD jointly across all 25 sessions and the fitted channels, each with full posterior uncertainty, and flags instrumental issues and a persistent 4 GHz RFI peak. Agreement with SKED measurements from sessions not used to construct the priors supports the recovered temporal evolution. The hierarchical approach shares information across sources and channels via partial pooling, reducing calibration uncertainty without relying on small reference source sets. This provides a diagnostic tool for detecting instrumental problems and could support SNR-based schedule optimisation, and may also apply to calibration at next-generation facilities such as SKA-Low and DSA-2000.