  We demonstrate the use of automatic Bayesian inference for the analysis of
LISA data sets. In particular we describe a new automatic Reversible Jump
Markov Chain Monte Carlo method to evaluate the posterior probability density
functions of the a priori unknown number of parameters that describe the
gravitational wave signals present in the data. We apply the algorithm to a
simulated LISA data set containing overlapping signals from white dwarf binary
systems (DWD) and to a separate data set containing a signal from an extreme
mass ratio inspiral (EMRI). We demonstrate that the approach works well in both
cases and can be regarded as a viable approach to tackle LISA data analysis
challenges.
