  In this paper, we describe a procedure for modelling strong lensing galaxy
clusters with parametric methods, and to rank models quantitatively using the
Bayesian evidence. We use a publicly available Markov chain Monte-Carlo (MCMC)
sampler ('Bayesys'), allowing us to avoid local minima in the likelihood
functions. To illustrate the power of the MCMC technique, we simulate three
clusters of galaxies, each composed of a cluster-scale halo and a set of
perturbing galaxy-scale subhalos. We ray-trace three light beams through each
model to produce a catalogue of multiple images, and then use the MCMC sampler
to recover the model parameters in the three different lensing configurations.
We find that, for typical Hubble Space Telescope (HST)-quality imaging data,
the total mass in the Einstein radius is recovered with ~1-5% error according
to the considered lensing configuration. However, we find that the mass of the
galaxies is strongly degenerated with the cluster mass when no multiple images
appear in the cluster centre. The mass of the galaxies is generally recovered
with a 20% error, largely due to the poorly constrained cut-off radius.
Finally, we describe how to rank models quantitatively using the Bayesian
evidence. We confirm the ability of strong lensing to constrain the mass
profile in the central region of galaxy clusters in this way. Ultimately, such
a method applied to strong lensing clusters with a very large number of
multiple images may provide unique geometrical constraints on cosmology. The
implementation of the MCMC sampler used in this paper has been done within the
framework of the Lenstool software package, which is publicly available.
