We consider a Markovian inference and modeling approach applied to land-use dynamics within the context of parcels of land on the edge of the forest corridor linking the two national parks of Ranomafana and Andringitra. Preservation of the forest on the east coast of Madagascar is crucial, so it is important to develop tools for inferring the dynamics of plots deforestation, of their use and of their possible return to the state forest. Our studies rely on two sets of field data established by IRD. The usual first step in such studies, which is to build the empirical transition matrix, is similar to a Markovian modeling of the dynamics. In this context, we consider the maximum likelihood approach and the Bayesian approach. This latter approach allows us to integrate information not present in the data but accredited by specialists, this approach uses Monte Carlo Markov Chain (MCMC) approximation techniques. We study the asymptotic properties of the models deduced from these two approaches, including the convergence time to the quasi-stationary distribution in the first case and to the stationary distribution in the second. We test various hypotheses on the models. The Markovian approach is no longer valid on the second larger data set where he had to use a semi-Markov models: the distributions of the sojourn times on given states are not necessarily geometric and may depend on the next state. Again we use maximum likelihood and Bayesian approaches. We study the asymptoticbehavior of each of these models. In terms of applications, we have determined the time scales of these dynamics.
