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A sequential particle filter method for static models. (English) Zbl 1036.62062
Summary: 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 \(\pi(\theta\mid y_1,\dots, y_N)\) \((n<N)\) is the only posterior distribution of interest but the preliminary exploration of partial posteriors \(\pi (\theta\mid y_1,\dots, y_n)\) 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.

MSC:
62L12 Sequential estimation
62G09 Nonparametric statistical resampling methods
65C05 Monte Carlo methods
62J12 Generalized linear models (logistic models)
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