distribution, and encodes the prior information on the parameter values before fitting to the data. For example, the uncertainty in the position of the cluster centroid might be known from previous observations and from the pointing accuracy of the instrument. One might then wish to apply a Gaussian prior to the model cluster position based on the level of uncertainty. In this work the prior distributions for the model parameters are uniform distributions unless indicated otherwise, and comfortably encompass reasonable values based on previous work.

The normalisation of the posterior probability distribution is given by the evidence, which is equal to the probability of the data given the model. The evidence is a measure of the suitability of the model for fitting to the data and provides a quantitative measure of selecting between competing models. The evidence for the data, assuming a particular model, is calculated by marginalising the product of the likelihood and prior distributions over the model parameters. This is given by $$\label{equation:evidence}
  \rmn{Pr}(\bmath{d}|\mathcal{M}_\rmn{j}) = \int{\rmn{Pr}(\bmath{d}|\bmath{\theta},\mathcal{M}_\rmn{j})\rmn{Pr}(\bmath{\theta}|\mathcal{M}_\rmn{j})\rmn{d}\bmath{\theta}},$$ which follows from Equation\[equation:bayes\_theorem\] and the fact that the integrated posterior distribution is normalised to unity. When a model provides a good fit to the data, the likelihood peak will have a 