  With the advance in computational resources, Bayesian inference is
increasingly becoming the standard tool of practise in GW astronomy. However,
algorithms such as Markov Chain Monte Carlo (MCMC) require a large number of
iterations to guarantee convergence to the target density. Each chain demands a
large number of evaluations of the likelihood function, and in the case of a
Hessian MCMC, calculations of the Fisher information matrix for use as a
proposal distribution. As each iteration requires the generation of at least
one gravitational waveform, we very quickly reach a point of exclusion for
current Bayesian algorithms, especially for low mass systems where the length
of the waveforms is large and the waveform generation time is on the order of
seconds. This suddenly demands a timescale of many weeks for a single MCMC. As
each likelihood and Fisher information matrix calculation requires the
evaluation of noise-weighted scalar products, we demonstrate that by using the
linearity of integration, and the fact that more than 90% of the generation
time is spent at frequencies less that one third of the maximum, we can
construct composite integrals that speed up the MCMCs for comparable mass
binaries by a factor of between 3.5 and 5.5, depending on the waveform length.
This method is both source and detector type independent, and can be applied to
any waveform that displays significant frequency evolution, such as stellar
mass binaries with Advanced LIGO/Virgo, as well as supermassive black holes
with eLISA
