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 parametrized 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 marginalized 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 cosmic microwave background (CMB) fluctuations on their accuracy. We find that data from instruments such as the Arcminute Microkelvin Imager (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 per cent for a given cluster.