  Supermassive black hole binaries are the most promising source of
gravitational-waves in the frequency band accessible to pulsar timing arrays.
Most of these binaries will be too distant to detect individually, but together
they will form an approximately stochastic background that can be detected by
measuring the correlation pattern induced between pairs of pulsars. A small
number of nearby and especially massive systems may stand out from this
background and be detected individually. Analyses have previously been
developed to search for stochastic signals and isolated signals separately.
Here we present BayesHopper, an algorithm capable of jointly searching for both
signal components simultaneously using trans-dimensional Bayesian inference.
Our implementation uses the Reversible Jump Markov Chain Monte Carlo method for
sampling the relevant parameter space with changing dimensionality. We have
tested BayesHopper on various simulated datasets. We find that it gives results
consistent with fixed-dimensional methods when tested on data with a stochastic
background or data with a single binary. For the full problem of analyzing a
dataset with both a background and multiple black hole binaries, we find two
kinds of interactions between the binary and background components. First, the
background effectively increases the noise level, thus making individual binary
signals less significant. Second, weak binary signals can be absorbed by the
background model due to the natural parsimony of Bayesian inference. Because of
its flexible model structure, we anticipate that BayesHopper will outperform
existing approaches when applied to realistic data sets produced from
population synthesis models.
