The Iterated Auxiliary Particle Filter

• Published in: Journal of the American Statistical Association Vol. 112; no. 520; pp. 1636 - 1647
• Main Authors: Guarniero, Pieralberto, Johansen, Adam M., Lee, Anthony
• Format: Journal Article
• Language: English
• Published: Alexandria Taylor & Francis 01-12-2017; Taylor & Francis Group,LLC; Taylor & Francis Ltd
• Subjects: Algorithms; Computer simulation; Heat recovery systems; Hidden Markov models; Iterative methods; Look-ahead methods; Markov analysis; Markov chains; Mathematical models; Monte Carlo simulation; Parameter estimation; Particle Markov chain Monte Carlo; Regression analysis; Sequential Monte Carlo; Smoothing; State-space models; Statistical inference; Statistical methods; Statistics; Theory and Methods
• ISSN: 0162-1459; 1537-274X
• DOI: 10.1080/01621459.2016.1222291

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
and has an associated
-auxiliary particle filter that provides unbiased estimates of L. We identify a sequence
that is optimal in the sense that the
-auxiliary particle filter's estimate of L has zero variance. In practical applications,
is unknown so the
-auxiliary particle filter cannot straightforwardly be implemented. We use an iterative scheme to approximate
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.