Contex te :

Agricultural landscape simulators are used to study the impact of landscape elements on spatial processes in agro-ecology, such as spore dispersal, gene flow between species or suface runoff. They allow for studying the processes at a large spatial scale and thus account for the long-range interactions. Our Unit is developing a simulator of agricultural landscapes, approximated by polygonal tessellations.The simulator is based on the Gibbs model of tessellations, defined by an energy function depending on tessellation summary statistics.  The model parameters are currently estimated by  Monte Carlo Maximum Likelihood method. This approach is efficient when the number of statistics included in the model remains low. When the parametric dimension of the model increases, the convergence issues of the optimization algorithm appear. Yet, in order to simulate landscape-like tessellations we need to test high-dimensional sets of summary statistics, likely to be correlated. Thus we are looking for the estimation method that would be robust enough in this context.

Missions :

The goal of the internship is to test alternative estimation approaches.  In particular, we would like to
compare MCML method with inference based on the ABC Shadow algorithm. This algorithm allow the approximate sampling of the posterior distribution, hence hypothesis tests, confindence intervals and model choice procedures can be proposed in order to analyze landscape modelling.

Compétences :

We are looking for a student in Applied Mathematics or Statistics with strong computer skills and knowledge of R language, motivated by applications in environmental sciences. First experiences in stochastic modelling and  MCMC algorithms will be an asset.