Particle-based likelihood inference in partially observed diffusion processes using generalised Poisson estimators

TL;DR

This paper introduces a novel particle-based method using unbiased transition density estimators to improve EM inference in partially observed diffusion processes, addressing degeneracy issues and validated through simulations.

Contribution

It presents a new unbiased estimator for diffusion transition densities integrated into a particle smoother within the EM framework, enhancing inference accuracy.

Findings

The method effectively estimates transition densities without bias.

It avoids particle degeneracy in smoothing.

Validated on simulated diffusion data.

Abstract

This paper concerns the use of the expectation-maximisation (EM) algorithm for inference in partially observed diffusion processes. In this context, a well known problem is that all except a few diffusion processes lack closed-form expressions of the transition densities. Thus, in order to estimate efficiently the EM intermediate quantity we construct, using novel techniques for unbiased estimation of diffusion transition densities, a random weight fixed-lag auxiliary particle smoother, which avoids the well known problem of particle trajectory degeneracy in the smoothing mode. The estimator is justified theoretically and demonstrated on a simulated example.