Paper detail

A New Method of Accelerated Bayesian Inference for Comparable Mass Binaries in both Ground and Space-Based Gravitational Wave Astronomy

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