The Iterated Auxiliary Particle Filter

Pieralberto Guarniero, Adam M. Johansen, Anthony Lee*

*Corresponding author for this work

Research output: Contribution to journalArticle (Academic Journal)peer-review

52 Citations (Scopus)
375 Downloads (Pure)


We present an offline, iterated particle filter to facilitate statistical inference in general state space hidden Markov models. Given a model and a sequence of observations, the associated marginal likelihood L is central to likelihood-based inference for unknown statistical parameters. We define a class of “twisted” models: each member is specified by a sequence of positive functions (Formula presented.) and has an associated (Formula presented.)-auxiliary particle filter that provides unbiased estimates of L. We identify a sequence (Formula presented.) that is optimal in the sense that the (Formula presented.)-auxiliary particle filter’s estimate of L has zero variance. In practical applications, (Formula presented.) is unknown so the (Formula presented.)-auxiliary particle filter cannot straightforwardly be implemented. We use an iterative scheme to approximate (Formula presented.) and demonstrate empirically that the resulting iterated auxiliary particle filter significantly outperforms the bootstrap particle filter in challenging settings. Applications include parameter estimation using a particle Markov chain Monte Carlo algorithm.

Original languageEnglish
Pages (from-to)1636-1647
Number of pages12
JournalJournal of the American Statistical Association
Issue number520
Early online date18 Jul 2017
Publication statusPublished - Oct 2017


  • Hidden Markov models
  • Look-ahead methods
  • Particle Markov chain Monte Carlo
  • Sequential Monte Carlo
  • Smoothing
  • State-space models


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