A Flexible Markov Mesh Model for Facies Modelling

In this presentation we consider the problem of estimating a prior model for spatial discrete variables from a training image. To be able to combine the estimated prior model with a likelihood for observed data, we argue that one needs to use a prior formulation where an explicit formula is available for the prior distribution. Moreover, we argue that to avoid overfitting it is essential to limit the number of parameters in the prior. We propose to formulate a prior within the class of Markov mesh models, for which formulas for the point mass function are available. We define a flexible prior model within the class of Markov mesh models, where we are able to limit the number of model parameters even with a reasonably large sequential neighbourhood by restricting interactions of very high orders to be zero. To fit the Markov mesh prior to a training image we adopt a Bayesian approach, in which we consider the training image as observed data. We fit the model parameters to the training image by simulating from the resulting posterior distribution, and for this we use Gibbs sampler algorithm. We demonstrate the qualities of our approach in simulation examples.