Résumé:
This thesis deals with the problem of loss of important information and features in spatial data modeling by building a causal spatial model that can capture the various main characteristics of these data. After a through discussion, a two-step strategy has been proposed : Örst, a 2D Markov Random Field (MRF) is generated where imposed causation allows to establish an analogy between this 2D MRF and a Markov chain representation ; secondly, based on the proposed 2D MRF, 2D MS-AR is deÖned according to some essential assumptions and useful symbols. Finally, estimation of model parameters is discussed, which opens the way for broad perspectives to exploit the proposed 2D MS-AR processes to e¢ ciently model several phenomena that present a structural discontinuity in the spatial dependence of the data.
