  We use a well-motivated galaxy formation framework to predict stellar masses,
star formation rates (SFR), and ultraviolet (UV) luminosities of galaxy
populations at redshifts $z\in 5-16$, taking into account stochasticity of SFR
in a controlled manner. We demonstrate that the model can match observational
estimates of UV luminosity functions (LFs) at $5<z<10$ with a modest level of
SFR stochasticity, resulting in the scatter of absolute UV luminosity at a
given halo mass of $\sigma_{M_{\rm UV}}\approx 0.75$. To match the observed UV
LFs at $z\approx 11-13$ and $z\approx 16$ the SFR stochasticity should increase
so that $\sigma_{M_{\rm UV}}\approx 1-1.3$ and $\approx 2$, respectively. Model
galaxies at $z\approx 11-13$ have stellar masses and SFRs in good agreement
with existing measurements. The median fraction of the baryon budget that was
converted into stars, $f_\star$, is only $f_\star\approx 0.005-0.05$, but a
small fraction of galaxies at $z=16$ have $f_\star>1$ indicating that SFR
stochasticity cannot be higher. We discuss several testable consequences of the
increased SFR stochasticity at $z>10$. The increase of SFR stochasticity with
increasing $z$, for example, prevents steepening of UV LF and even results in
some flattening of UV LF at $z\gtrsim 13$. The median stellar ages of model
galaxies at $z\approx 11-16$ are predicted to decrease from $\approx 20-30$ Myr
for $M_{\rm UV}\gtrsim -21$ galaxies to $\approx 5-10$ Myr for brighter ones.
Likewise, the scatter in median stellar age is predicted to decrease with
increasing luminosity. The scatter in the ratio of star formation rates
averaged over 10 and 100 Myr should increase with redshift. Fluctuations of
ionizing flux should increase at $z>10$ resulting in the increasing scatter in
the line fluxes and their ratios for the lines sensitive to ionization
parameter.
