  One of the greatest data analysis challenges for the Laser Interferometer
Space Antenna (LISA) is the need to account for a large number of gravitational
wave signals from compact binary systems expected to be present in the data. We
introduce the basis of a Bayesian method that we believe can address this
challenge, and demonstrate its effectiveness on a simplified problem involving
one hundred synthetic sinusoidal signals in noise. We use a reversible jump
Markov chain Monte Carlo technique to infer simultaneously the number of
signals present, the parameters of each identified signal, and the noise level.
Our approach therefore tackles the detection and parameter estimation problems
simultaneously, without the need to evaluate formal model selection criteria,
such as the Akaike Information Criterion or explicit Bayes factors. The method
does not require a stopping criterion to determine the number of signals, and
produces results which compare very favorably with classical spectral
techniques.
