Statistics Seminar, "Maximum likelihood for state-space models using an ABC sequential Monte Carlo filter", Umberto Picchini, Lund
State-space models (SSMs) are an important class of partially observed models, involving a latent (unobserved) component. Inference for SSMs has generated a very large amount of literature in the past four decades, both for state and parameter inference. Here we consider maximum likelihood estimation for the parameters of general nonlinear/non-Gaussian SSMs. However, as we illustrate, this is coupled with the problem of performing inference for the latent state of the SSM. We consider a stochastic approximation expectation-maximization (SAEM) algorithm to maximize the parameters likelihood function with the novelty of using approximate Bayesian computation (ABC) within SAEM. The task is to provide each iteration of SAEM with a filtered state of the system, and this is achieved using an ABC sampler for the hidden state, based on particle filters methodology. It is shown that the resulting SAEM-ABC algorithm can be calibrated to return accurate inference, and in some situations it can outperform a version of SAEM using the "bootstrap filter". We show how the
simple bust still widely used bootstrap filter can produce poor sampled paths, especially when few particles are employed. Instead a simple modification using ABC assigns high weights only to very "important" particles, allowing better paths to be selected, this in turn producing less biased parameter estimation.
[joint work with Adeline Samson, Universite Grenoble Alpes, published on "Computational Statistics"]