Large-scale three-dimensional Gaussian process extinction mapping

Gaussian processes (GPs) are the ideal tool for modelling the Galactic interstellar medium, combining statistical flexibility with a good match to the underlying physics. In an earlier paper, we outlined how they can be employed to construct three-dimensional maps of dust extinction from stellar surveys. GPs scale poorly to large data sets though, which put the analysis of realistic catalogues out of reach. Here, we show how a novel combination of the expectation propagation method and certain sparse matrix approximations can be used to accelerate the dust mapping problem. We demonstrate, using simulated Gaia data, that the resultant algorithm is fast, accurate, and precise. Critically, it can be scaled up to map the Gaia catalogue.