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

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