  Several rapid parameter estimation methods have recently been advanced to
deal with the computational challenges of the problem of Bayesian inference of
the properties of compact binary sources detected in the upcoming science runs
of the terrestrial network of gravitational wave detectors. Some of these
methods are well-optimized to reconstruct gravitational wave signals in nearly
real-time necessary for multi-messenger astronomy. In this context, this work
presents a new, computationally efficient algorithm for fast evaluation of the
likelihood function using a combination of numerical linear algebra and
mesh-free interpolation methods. The proposed method can rapidly evaluate the
likelihood function at any arbitrary point of the sample space at a negligible
loss of accuracy and is an alternative to the grid-based parameter estimation
schemes. We obtain posterior samples over model parameters for a canonical
binary neutron star system by interfacing our fast likelihood evaluation method
with the nested sampling algorithm. The marginalized posterior distributions
obtained from these samples are statistically identical to those obtained by
brute force calculations. We find that such Bayesian posteriors can be
determined within a few minutes of detecting such transient compact binary
sources, thereby improving the chances of their prompt follow-up observations
with telescopes at different wavelengths. It may be possible to apply the
blueprint of the meshfree technique presented in this study to Bayesian
inference problems in other domains.
