A sequential particle filter method for static models

Particle filter methods are complex inference procedures, which combine importance sampling and Monte Carlo schemes in order to explore consistently a sequence of multiple distributions of interest. We show that such methods can also offer an efficient estimation tool in 'static' set-ups, in which case π(θ |y₁,..., y_N) (n < N) is the only posterior distribution of interest but the preliminary exploration of partial posteriors n(θ|y₁,...,y_n) makes it possible to save computing time. A complete algorithm is proposed for independent or Markov models. Our method is shown to challenge other common estimation procedures in terms of robustness and execution time, especially when the sample size is important. Two classes of examples, mixture models and discrete generalised linear models, are discussed and illustrated by numerical results.