Frédéric Lavancier, Nantes University, France: Spatial birth-death-move processes: basic properties and inference
Overview
Abstract: Birth-death-move processes are Markov models for the spatio-temporal dynamics of a system of particles in motion where births and deaths can occur. Natural applications include epidemiology, individual-based modelling in ecology and spatio-temporal dynamics observed in bio-imaging. We present some of the basic probabilistic properties of these processes and we consider two inference problems: First, the non-parametric estimation of the birth and death intensity functions; Second, the parametric estimation of the full dynamics by maximum likelihood. We finally apply our statistical method to the analysis of a real dataset representing the spatio-temporel dynamics of biomolecules observed in a living cell.