Bayesian inversion is performed on real observations to predict the diagenetic classes of a carbonate reservoir where the proportions of carbonate rock and depositional properties are known. The complete solution is the posterior model. The model is first developed in a 1D setting where the likelihood model is generalized Dirichlet distributed and the prior model is a Markov chain. The 1D model is used to justify the general assumptions on which the model is based. Thereafter the model is expanded to a 3D setting where the likelihood model remains the same and the prior model is a profile Markov random field where each profile is a Markov chain. Lateral continuity is incorporated into the model by adapting the transition matrices to fit a given associated limiting distribution, two algorithms for the adjustment are presented. The result is a good statistical formulation of the problem in 3D. Results from a study on real observations from a 2D reservoir show that simulations reproduce characteristics of the real data and it is also possible to incorporate conditioning on well observations into the model.