  The Kepler Mission, combined with ground based radial velocity (RV) follow-up
and dynamical analyses of transit timing variations, has revolutionized the
observational constraints on sub-Neptune-size planet compositions. The results
of an extensive Kepler follow-up program including multiple Doppler
measurements for 22 planet-hosting stars more than doubles the population of
sub-Neptune-sized transiting planets that have RV mass constraints. This
unprecedentedly large and homogeneous sample of planets with both mass and
radius constraints opens the possibility of a statistical study of the
underlying population of planet compositions. We focus on the intriguing
transition between rocky exoplanets (comprised of iron and silicates) and
planets with voluminous layers of volatiles (H/He and astrophysical ices).
Applying a hierarchical Bayesian statistical approach to the sample of Kepler
transiting sub-Neptune planets with Keck RV follow-up, we constrain the
fraction of close-in planets (with orbital periods less than ~50 days) that are
sufficiently dense to be rocky, as a function of planet radius. We show that
the majority of 1.6 Earth-radius planets are too low density to be comprised of
Fe and silicates alone. At larger radii, the constraints on the fraction of
rocky planets are even more stringent. These insights into the size
demographics of rocky and volatile-rich planets offer empirical constraints to
planet formation theories, and guide the range of planet radii to be considered
in studies of the occurrence rate of "Earth-like" planets, $\eta_{Earth}$.
