Bernstein-von Mises Theorem and Bayes Estimation in Interacting Particle Systems of Diffusions

Abstract

Consistency and asymptotic normality of the Bayes estimator of the drift coefficient of an interacting particles of diffusions are studied. For the Bayes estimator, observations are taken on a fixed time interval [0, T] and asymptotics are studied in the mean-field limit as the number of interacting particles increases. Interalia, the Bernstein-von Mises theorem concerning the convergence in the mean-field limit of the posterior distribution, for smooth prior distribution and loss function, to normal distribution is proved.