  Progenitors of short gamma-ray bursts are thought to be neutron stars
coalescing with their companion black hole or neutron star, which are one of
the main gravitational wave sources. We have devised a Bayesian framework for
combining gamma-ray burst and gravitational wave information that allows us to
probe short gamma-ray burst luminosities. We show that combined short gamma-ray
burst and gravitational wave observations not only improve progenitor distance
and inclination angle estimates, they also allow the isotropic luminosities of
short gamma-ray bursts to be determined without the need for host galaxy or
light-curve information. We characterise our approach by simulating 1000 joint
short gamma-ray burst and gravitational wave detections by Advanced LIGO and
Advanced Virgo. We show that ${\sim}90\%$ of the simulations have uncertainties
on short gamma-ray burst isotropic luminosity estimates that are within a
factor of 2 of the ideal scenario, where the distance is known exactly.
Therefore, isotropic luminosities can be confidently determined for short
gamma-ray bursts observed jointly with gravitational wave detected by Advanced
LIGO and Advanced Virgo. Planned enhancements to Advanced LIGO will extend its
range and likely produce several joint detections of short gamma-ray bursts and
gravitational waves. Third-generation gravitational wave detectors will allow
for isotropic luminosity estimates for the majority of the short gamma-ray
burst population within a redshift of $z{\sim}1$.
