Parameter estimation for partially observed McKean–Vlasov diffusions

Abstract In this article, we consider likelihood-based estimation of static parameters for a class of partially observed McKean–Vlasov (MV) diffusion process with discrete-time observations over a fixed time interval. In particular, using the framework of (Awadelkarim, Jasra, Ruzayqat 2024 SIAM J. Control Optim. 62, 2664–2694 (doi:10.1137/23M160298X)) we develop a new randomized multilevel Monte Carlo method for estimating the parameters, based upon Markovian stochastic approximation (MSA) methodology. New Markov chain Monte Carlo (MCMC) algorithms for the partially observed MV model are introduced facilitating the application of (Awadelkarim, Jasra, Ruzayqat 2024 SIAM J. Control Optim. 62, 2664–2694 (doi:10.1137/23M160298X)). We prove, under assumptions, that the expectation of our estimator is biased, but with expected small and controllable bias. Our approach is implemented on several examples.