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

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

2010-08-17

arxiv.org/abs/1008.2886v1

Mathematics

Statistics Theory

Scientific paper

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.

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