The Iterated Auxiliary Particle Filter

Pieralberto Guarniero, Adam Johansen and Anthony Lee

Journal of the American Statistical Association, 2017, vol. 112, issue 520, 1636-1647

Abstract: 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 ψ${\bm \psi }$ and has an associated ψ${\bm \psi }$-auxiliary particle filter that provides unbiased estimates of L. We identify a sequence ψ*${\bm \psi }^{*}$ that is optimal in the sense that the ψ*${\bm \psi }^{*}$-auxiliary particle filter’s estimate of L has zero variance. In practical applications, ψ*${\bm \psi }^{*}$ is unknown so the ψ*${\bm \psi }^{*}$-auxiliary particle filter cannot straightforwardly be implemented. We use an iterative scheme to approximate ψ*${\bm \psi }^{*}$ 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.

Date: 2017
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Citations: View citations in EconPapers (8)

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DOI: 10.1080/01621459.2016.1222291

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