  Extreme mass ratio inspirals (EMRIs) are thought to be one of the most
exciting gravitational wave sources to be detected with LISA. Due to their
complicated nature and weak amplitudes the detection and parameter estimation
of such sources is a challenging task. In this paper we present a statistical
methodology based on Bayesian inference in which the estimation of parameters
is carried out by advanced Markov chain Monte Carlo (MCMC) algorithms such as
parallel tempering MCMC. We analysed high and medium mass EMRI systems that
fall well inside the low frequency range of LISA. In the context of the Mock
LISA Data Challenges, our investigation and results are also the first instance
in which a fully Markovian algorithm is applied for EMRI searches. Results show
that our algorithm worked well in recovering EMRI signals from different
(simulated) LISA data sets having single and multiple EMRI sources and holds
great promise for posterior computation under more realistic conditions. The
search and estimation methods presented in this paper are general in their
nature, and can be applied in any other scenario such as AdLIGO, AdVIRGO and
Einstein Telescope with their respective response functions.
