Practical filtering with sequential parameter learning

Summary. The 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 by using two examples: a benchmark auto‐regressive model with observation error and a high dimensional dynamic spatiotemporal model. We show that the method provides accurate inference in the presence of outliers, model misspecification and high dimensionality.