  One of the key questions in understanding the formation and evolution of
galaxies is how starbursts affect the assembly of stellar populations in
galaxies over time. We define a burst indicator ($\eta$), which compares a
galaxy's star formation rates on short ($\sim10$ Myr) and long ($\sim100$ Myr)
timescales. To estimate $\eta$, we apply the detailed time-luminosity
relationship for H$\alpha$ and near-ultraviolet emission to simulated star
formation histories (SFHs) from semi-analytic models and the Mufasa
hydrodynamical cosmological simulations. The average of $\eta$ is not a good
indicator of star formation stochasticity (burstiness); indeed, we show that
this average should be close to zero unless the population has an average SFH
which is rising or falling rapidly. Instead, the width of the $\eta$
distribution characterizes the burstiness of a galaxy population's recent star
formation. We find this width to be robust to variations in stellar initial
mass function and metallicity. We apply realistic noise and selection effects
to the models to generate mock HST and JWST galaxy catalogs and compare these
catalogs with 3D-HST observations of 956 galaxies at $0.65<z<1.5$ detected in
H$\alpha$. Measurements of $\eta$ are unaffected by dust measurement errors
under the assumption that $E(B-V)_\mathrm{stars}=0.44\,E(B-V)_\mathrm{gas}$
(i.e., $Q_\mathrm{sg}=0.44$). However, setting
$Q_\mathrm{sg}=0.8^{+0.1}_{-0.2}$ removes an unexpected dependence of the
average value of $\eta$ upon dust attenuation and stellar mass in the 3D-HST
sample while also resolving disagreements in the distribution of star formation
rates. However, even varying the dust law cannot resolve all discrepancies
between the simulated and the observed galaxies.

Astrophysics of Galaxies