Scaling up for astronomical big data: Hierarchical inferences based on neural posterior estimates

Gravitational lenses, in which massive galaxies warp the spacetime around themselves causing multiple, distorted images of galaxies in the background, are remarkably useful objects for cosmologists. Lenses with time-varying images can be used to measure distance, and hence infer the expansion history of the Universe, while tiny perturbations of the "Einstein Rings" are caused by the population of sub-galactic Dark Matter clumps, and hence contain clues as to the nature of Dark Matter itself. We know of several hundred lens systems, and we expect to discover thousands more in Rubin Observatory's 10-year Legacy Survey of Space and Time (LSST), due to begin in 2024: each one must be modeled carefully in order to achieve parameter inferences that have the required accuracy, and we aim to use as many systems as we can to maximize the available precision. In this sense, gravitational lenses are interesting pathfinders for inference from astronomical Big Data more generally. We will show how we are using various deep learning techniques to enable accurate inferences from large samples of gravitational lenses, including hierarchical inference of global (and cosmological) hyper-parameters from neural network estimated posterior densities.