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Searching for gravitational waves in pulsar timing array data iscomputationally intensive. The data is unevenly sampled, and the noise isheteroscedastic, necessitating the use of a time-domain likelihood functionwith attendant expensive matrix operations. The computational cost isexacerbated when searching for individual supermassive black hole binaries,which have a large parameter space due to the additional pulsar distance, phaseoffset and noise model parameters needed for each pulsar. We introduce a newformulation of the likelihood function which can be used to make the Bayesiananalysis significantly faster. We divide the parameters into projection andshape parameters. We then accelerate the exploration of the projectionparameters by more than four orders of magnitude by precomputing the expensiveinner products for each set of shape parameters. The projection parametersinclude nuisance parameters such as the gravitational wave phase offset at eachpulsar. In the new scheme, these troublesome nuisance parameters areefficiently marginalized over using multiple-try Markov chain Monte Carlosampling as part of a Metropolis-within-Gibbs scheme. The acceleration providedby our method will become increasingly important as pulsar timing datasetsrapidly grow. Our method also makes sophisticated analyses more tractable, suchas searches for multiple binaries, or binaries with non-negligibleeccentricities.

Fast Bayesian analysis of individual binaries in pulsar timing array data