Practical Filtering with Sequential Parameter Learning

Nicholas G. Polson, Jonathan R. Stroud, Peter Müller

University of Chicago, University of Pennsylvania, and MD Anderson Cancer Center

January 2008

This paper develops a simulation-based approach to sequential parameter learning and filtering in general state-space models. Our approach is based on approximating the target posterior by a mixture of fixed-lag smoothing distributions. Parameter inference exploits a sufficient statistic structure and the methodology can be easily implemented by modifying state space smoothing algorithms. We avoid reweighting particles and hence sample degeneracy problems that plague particle filters that use sequential importance sampling. The method is illustrated using two examples: a benchmark autoregressive model with observation error and a high-dimensional dynamic spatio-temporal model. We show that the method provides accurate inference in the presence of outliers, model misspecification and high dimensionality.

Keywords: Filtering, Markov Chain Monte Carlo, Particle Filtering, Sequential Parameter Learning, Spatio-Temporal Models, State-Space Models.

The manuscript is available in PDF format.