Statistical inference for structured populations alimented by fragmentation-transport

Statistics and Modeling for Complex Data

We investigate inference in simple models that decribe the evolution (in size or age) a a population of bactria across scales. The size of the system evolves according to a transport-fragmentation equation: each individual grows with a given transport rate, and splits into two offsprings, according to a binary fragmentation process with unknown division rate that depends on its size. Macroscopically, the system is well approximated by a PDE and statstical inference transfers into a nonlinear inverse problem. Microscopically, a more accurate description is given by a stochastic piecewise deterministic Markov process, which allows for other methods of inference, introducing however stochastic dependences. We will discuss and present some very simple results on the inference of the parameters of the system across scales. Real data analysis is conducted on E. Coli experiments. This is a joint (ongoing) work with M. Doumic (INRIA and Paris 6), N. Krell (Rennes 1) and L. Robert (ENS).