  Kepler-78b is a transiting planet that is 1.2 times the radius of Earth and
orbits a young, active K dwarf every 8 hours. The mass of Kepler-78b has been
independently reported by two teams based on radial velocity measurements using
the HIRES and HARPS-N spectrographs. Due to the active nature of the host star,
a stellar activity model is required to distinguish and isolate the planetary
signal in radial velocity data. Whereas previous studies tested parametric
stellar activity models, we modeled this system using nonparametric Gaussian
process (GP) regression. We produced a GP regression of relevant Kepler
photometry. We then use the posterior parameter distribution for our
photometric fit as a prior for our simultaneous GP + Keplerian orbit models of
the radial velocity datasets. We tested three simple kernel functions for our
GP regressions. Based on a Bayesian likelihood analysis, we selected a
quasi-periodic kernel model with GP hyperparameters coupled between the two RV
datasets, giving a Doppler amplitude of 1.86 $\pm$ 0.25 m s$^{-1}$ and
supporting our belief that the correlated noise we are modeling is
astrophysical. The corresponding mass of 1.87 $^{+0.27}_{-0.26}$ M$_{\oplus}$
is consistent with that measured in previous studies, and more robust due to
our nonparametric signal estimation. Based on our mass and the radius
measurement from transit photometry, Kepler-78b has a bulk density of
6.0$^{+1.9}_{-1.4}$ g cm$^{-3}$. We estimate that Kepler-78b is 32$\pm$26% iron
using a two-component rock-iron model. This is consistent with an Earth-like
composition, with uncertainty spanning Moon-like to Mercury-like compositions.
