Bayesian inference of the properties of compact binary sources detected by
gravitational wave detectors is a computationally challenging task. For the
twin advanced LIGO detectors operating at design sensitivity, it is estimated
to take several weeks to months of wall clock time to reconstruct a single
binary neutron star source using current approaches. In this context, we
present a new, computationally efficient way of rapidly reconstructing the
source properties using a combination of numerical linear algebra and meshfree
interpolation techniques. For a canonical binary neutron star system, we show
that the method proposed in this Letter is ~ 4000 times faster than traditional
algorithms, at a negligible loss of accuracy of O(10^{-5}) across the sample
space. This implies that the properties of such sources can be accurately
measured within a few minutes of their detection in upcoming science runs,
which will have significant ramifications for their prompt electromagnetic
follow-up. The blueprint of this idea can be applied to Bayesian inference in
other domains
