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