A von Mises Markov random field model for the analysis of spatial circular data

A von Mises Markov random field model is introduced for the analysis of spatial series of angles. Because the likelihood function of the model is unknown up to a normalizing constant, two inferential procedures are proposed for parameter estimation. The first one is based on the maximization of a pseudo-likelihood function and provides a computationally convenient, consistent, although inefficient estimator. The second one is based on the maximization of a Monte Carlo Markov Chain approximation of the likelihood and is more efficient than the pseudo-likelihood estimator, although computationally more expensive. The model is illustrated on a spatial series of sea currents directions