Uniform priors are not as uninformative as you might think

Characterising the Variability of the Black Hole at the Centre of our Galaxy using Multi-Output Gaussian Processes

Multi-Output Gaussian Process (MOGP) regression extends univariate Gaussian Process regression to cases where multiple response variables should be modelled together. For example, these may be response variables that co-vary because they share an underlying origin. This makes MOGP regression perfectly suited for modelling the multi-band data collected by astronomical facilities such as the Atacama Large Millimeter/submillimeter Array (ALMA). In this instance, the multiple outputs correspond to the brightness of emissions from a celestial source as detected at different electromagnetic (EM) frequencies. Here, the celestial source is Sagittarius A* (Sgr A*), the supermassive black hole (SMBH) at the Galactic centre of the Milky Way, and we assume that its changing brightness over time, known as its light curve, is a stochastic process. Using a Bayesian hierarchical model, we demonstrate how MOGPs can be used to infer the relationship between the brightnesses observed at different frequency bands, known as the spectral index. We compare the results of different modelling decisions, such as the choice of cross-covariance structure, and despite light curves being notoriously sparse and unevenly sampled, we obtain a reasonable estimate of the spectral index. Astronomers are interested in the spectral index because it offers clues to the mechanism behind the EM emission.