  Inferring the astrophysical parameters of coalescing compact binaries is a
key science goal of the upcoming advanced LIGO-Virgo gravitational-wave
detector network and, more generally, gravitational-wave astronomy. However,
current parameter estimation approaches for such scenarios can lead to
computationally intractable problems in practice. Therefore there is a pressing
need for new, fast and accurate Bayesian inference techniques. In this letter
we demonstrate that a reduced order modeling approach enables rapid parameter
estimation studies. By implementing a reduced order quadrature scheme within
the LIGO Algorithm Library, we show that Bayesian inference on the
9-dimensional parameter space of non-spinning binary neutron star inspirals can
be sped up by a factor of 30 for the early advanced detectors' configurations.
This speed-up will increase to about $150$ as the detectors improve their
low-frequency limit to 10Hz, reducing to hours analyses which would otherwise
take months to complete. Although these results focus on gravitational
detectors, the techniques are broadly applicable to any experiment where fast
Bayesian analysis is desirable.
