I will talk about using statistics and machine learning methods, such as Gaussian processes and deep learning, to extract new insights from archival data. First, I will discuss our work on using galaxies similar to the Milky Way to probe properties of the Milky Way that are otherwise not accessible: namely, its UV-to-IR spectral energy distribution and how frequently its supermassive black hole is actively accreting material. Second, I will present state-of-the-art results using a novel neural network architecture, called a deep capsule network, to estimate photometric redshifts of galaxies directly from their images. I will discuss a use case for finding faint satellite galaxies to help identify a probe for dark matter halo assembly history. Finally, I will highlight some recent work on recalibrating photometric redshift probability distribution functions that could prove critical for optimizing cosmological results from upcoming surveys.