Examples of the use of Markovian fields in explanatory modeling.

Summary Markov fields have undergone significant development in applied research, mainly because they are suitable for the study of spatial phenomena such as image analysis. But outside this framework, Markovian models have been little exploited. This work deals with their use in explanatory modeling, in an economic context for example. The different tools related to model fitting are detailed in the first chapter. The possibilities of Markovian fields in explanatory modeling are then explored through two studies for which real data are available. The first study deals with the modeling of a field, not structured a priori, of binary variables influenced by explanatory variables. A search and adjustment module adapted to the model is developed, then applied to data provided by the Renault company, data representative of the quality control of an assembly line. The second study concerns the modeling of multivariate series with integer values by self-poissonian fields. This modelization is an alternative to the arma modelization for data with non-Gaussian characteristics. Prediction methods adapted to this Poissonian model are proposed, and their performances are compared on simulations. An application, realized for the Ministry of Transport and dealing with the modeling of a bivariate set of road safety indicators, is then presented in detail.