Robust Inference by Particle Filtering

Particle filters (PFs) are recursive Monte Carlo methods for online tracking and forecasting in state-space systems. They are very general and, hence, can be used with a broad class of models, including ones that are nonlinear and/or non-Gaussian. PFs suffer from a number of drawbacks including their computational complexity and sensitivity to the choice of the state space model (i.e., its compatibility with the observed data). Indeed, modelling errors and sharp changes in the dynamics of the state or the observation processes
that are not accounted for usually lead to a degradation of the performance of the PFs. In this paper we draw from recent results on online assessment of convergence of PFs to propose a simple scheme to (a) detect changes in a sate-space model from a series of observations that are described by the model and (b) re-estimate the model to make it compatible with the observed data. The detection stage is fully general, as it relies on a model-invariant statistic, while re-estimation can be done in several manners. Here, we discuss possible schemes and illustrate the theory with a simple example for a conditionally-linear Gaussian model.