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