I will describe two separate methods to statistically infer the properties of dark matter substructure using, in turn, (astrometric) weak and strong gravitational lensing observations. In the first part of the talk, I will describe how the motion of dark matter subhalos in the Milky Way induces a correlated pattern of motions in background celestial objects, known as astrometric weak lensing. These measurements can be used to statistically infer the underlying distribution of subhalos, and I will show how this can be practically achieved using data from future astrometric surveys and/or radio telescopes such as the Roman Space Telescope and SKA. Next, I will describe a novel method to disentangle the collective imprint of dark matter substructure on extended arcs in galaxy-galaxy strong lensing systems using machine learning-based inference techniques. These methods use neural networks in order to directly estimate the likelihood ratios associated with population-level parameters characterizing substructure within lensing systems. I will show how this can provide an efficient and principled way to mine the large sample of strong lenses that will be imaged by future surveys like Euclid and the Vera Rubin Observatory to look for signatures of dark matter substructure.
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