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Modern astronomy has been rapidly increasing our ability to see deeper intothe universe, acquiring enormous samples of cosmic populations. Gainingastrophysical insights from these datasets requires a wide range ofsophisticated statistical and machine learning methods. Long-standing problemsin cosmology include characterization of galaxy clustering and estimation ofgalaxy distances from photometric colors. Bayesian inference, central tolinking astronomical data to nonlinear astrophysical models, addresses problemsin solar physics, properties of star clusters, and exoplanet systems.Likelihood-free methods are growing in importance. Detection of faint signalsin complicated noise is needed to find periodic behaviors in stars and detectexplosive gravitational wave events. Open issues concern treatment ofheteroscedastic measurement errors and understanding probability distributionscharacterizing astrophysical systems. The field of astrostatistics needsincreased collaboration with statisticians in the design and analysis stages ofresearch projects, and to jointly develop new statistical methodologies.Together, they will draw more astrophysical insights into astronomicalpopulations and the cosmos itself.

21st Century Statistical and Computational Challenges in Astrophysics