Parameter Estimation for Partially Observed McKean-Vlasov Diffusions

TL;DR

This paper introduces a novel likelihood-based estimation method for parameters in partially observed McKean-Vlasov diffusions, utilizing a randomized multilevel Monte Carlo approach combined with Markovian stochastic approximation.

Contribution

It develops a new Monte Carlo estimation framework and MCMC algorithms tailored for POMV models, with theoretical bias analysis and practical implementation.

Findings

Estimator has small, controllable bias

Method successfully applied to multiple examples

New algorithms improve parameter inference for POMV models

Abstract

In this article we consider likelihood-based estimation of static parameters for a class of partially observed McKean-Vlasov (POMV) diffusion process with discrete-time observations over a fixed time interval. In particular, using the framework of [5] we develop a new randomized multilevel Monte Carlo method for estimating the parameters, based upon Markovian stochastic approximation methodology. New Markov chain Monte Carlo algorithms for the POMV model are introduced facilitating the application of [5]. 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.