Just 25 years ago the first planets outside of our Solar System were discovered. Since then, astronomers have found thousands of these exoplanets orbiting other stars. Such a large sample enables our first glimpse into the Galactic diversity of planetary systems and provides observational constraints on our understanding of how these planets came to be. In particular, exoplanet astronomers aim to illuminate the compositions of these planets, to identify which are terrestrial like Earth, which are primarily gaseous like Jupiter, and which are wholly unlike any in our Solar System. These insights are based on the masses and radii of the planets, which unfortunately have significant measurement uncertainties. Furthermore, these compositions have likely changed over time, complicating the constraints that these current-day measurements provide for our physical theories of how these planets formed. In this talk I will present my work on building hierarchical Bayesian models that account for these various sources of uncertainty in our inferences about the population distribution of exoplanet compositions, and will show first results on the birth compositions of these planets.