  One of the main bottlenecks in gravitational wave (GW) astronomy is the high
cost of performing parameter estimation and GW searches on the fly. We propose
a novel technique based on Reduced Order Quadratures (ROQs), an application and
data-specific quadrature rule, to perform fast and accurate likelihood
evaluations. These are the dominant cost in Markov chain Monte Carlo (MCMC)
algorithms, which are widely employed in parameter estimation studies, and so
ROQs offer a new way to accelerate GW parameter estimation. We illustrate our
approach using a four dimensional GW burst model embedded in noise. We build an
ROQ for this model, and perform four dimensional MCMC searches with both the
standard and ROQs quadrature rules, showing that, for this model, the ROQ
approach is around 25 times faster than the standard approach with essentially
no loss of accuracy. The speed-up from using ROQs is expected to increase for
more complex GW signal models and therefore has significant potential to
accelerate parameter estimation of GW sources such as compact binary
coalescences.
