Approximate bayesian inference using the mean-field distribution

This chapter focuses on dynamical systems admitting a mean-field limit distribution when the population's size tends to infinity, such as the flocking models presented in Carrillo et al. It introduces a numerical scheme to simulate the mean-field distribution, which is a partial differential transport equation solution. These simulations are used to simplify the likelihood distributions associated with Bayesian inference problems arising when the population is only partially observed. Population models may be used to assess, from data, the interaction laws governing the individual dynamics. The chapter discusses the statistical inference problems related to the study of symmetric systems. It focuses on plant population model introduced by Schneideret al. that is taken as an example of systems leading to difficult inference problems when the size of the population is partially known. The chapter gives an illustration of simulations of the Schneider system under the mean-field approximation.