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We describe several new techniques which accelerate Bayesian searches forcontinuous gravitational-wave emission from supermassive black-hole binariesusing pulsar timing arrays. These techniques mitigate the problematic increaseof search-dimensionality with the size of the pulsar array which arises fromhaving to include an extra parameter per pulsar as the array is expanded. Thisextra parameter corresponds to searching over the phase of thegravitational-wave as it propagates past each pulsar so that we can coherentlyinclude the pulsar-term in our search strategies. Our techniques make theanalysis tractable with powerful evidence-evaluation packages like MultiNest.We find good agreement of our techniques with the parameter-estimation andBayes factor evaluation performed with full signal templates, and conclude thatthese techniques make excellent first-cut tools for detection andcharacterisation of continuous gravitational-wave signals with pulsar timingarrays. Crucially, at low to moderate signal-to-noise ratios the factor bywhich the analysis is sped up can be > 100, permitting rigorous programs ofsystematic injection and recovery of signals to establish robust detectioncriteria within a Bayesian formalism.

Accelerated Bayesian model-selection and parameter-estimation in continuous gravitational-wave searches with pulsar-timing arrays