In this article we consider Bayesian estimation of static parameters for a
class of partially observed McKean-Vlasov diffusion processes with
discrete-time observations over a fixed time interval. This problem features
several obstacles to its solution, which include that the posterior density is
numerically intractable in continuous-time, even if the transition
probabilities are available and even when one uses a time-discretization, the
posterior still cannot be used by adopting well-known computational methods
such as Markov chain Monte Carlo (MCMC). In this paper we provide a solution to
this problem by using new MCMC algorithms which can solve the afore-mentioned
issues. This MCMC algorithm is extended to use multilevel Monte Carlo (MLMC)
methods. We prove convergence bounds on our parameter estimators and show that
the MLMC-based MCMC algorithm reduces the computational cost to achieve a mean
square error versus ordinary MCMC by an order of magnitude. We numerically
illustrate our results on two models.

Cet article explore les excursions dans le temps et leurs implications.

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