  As the quality of the available galaxy cluster data improves, the models
fitted to these data might be expected to become increasingly complex. Here we
present the Bayesian approach to the problem of cluster data modelling:
starting from simple, physically motivated parameterised functions to describe
the cluster's gas density, gravitational potential and temperature, we explore
the high-dimensional parameter spaces with a Markov-Chain Monte-Carlo sampler,
and compute the Bayesian evidence in order to make probabilistic statements
about the models tested. In this way sufficiently good data will enable the
models to be distinguished, enhancing our astrophysical understanding; in any
case the models may be marginalised over in the correct way when estimating
global, perhaps cosmological, parameters. In this work we apply this
methodology to two sets of simulated interferometric Sunyaev-Zel'dovich effect
and gravitational weak lensing data, corresponding to current and
next-generation telescopes. We calculate the expected precision on the
measurement of the cluster gas fraction from such experiments, and investigate
the effect of the primordial CMB fluctuations on their accuracy. We find that
data from instruments such as AMI, when combined with wide-field ground-based
weak lensing data, should allow both cluster model selection and estimation of
gas fractions to a precision of better than 30 percent for a given cluster.
