The iterated auxiliary particle filter
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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 psi and has an associated psi-auxiliary particle filter that provides unbiased estimates of L. We identify a sequence psi* that is optimal in the sense that the psi*-auxiliary particle filter's estimate of L has zero variance. In practical applications, psi* is unknown so the psi*-auxiliary particle filter cannot straightforwardly be implemented. We use an iterative scheme to approximate 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.Keywords
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This publication has 25 references indexed in Scilit:
- Stability of noisy Metropolis–HastingsStatistics and Computing, 2015
- Efficient implementation of Markov chain Monte Carlo when using an unbiased likelihood estimatorBiometrika, 2015
- Variance bounding and geometric ergodicity of Markov chain Monte Carlo kernels for approximate Bayesian computationBiometrika, 2014
- A note on auxiliary particle filtersStatistics & Probability Letters, 2008
- Estimation of Population Growth or Decline in Genetically Monitored PopulationsGenetics, 2003
- On sequential Monte Carlo sampling methods for Bayesian filteringStatistics and Computing, 2000
- Exponential Family State Space Models Based on a Conjugate Latent ProcessJournal of the Royal Statistical Society Series B: Statistical Methodology, 1999
- Stochastic Volatility: Likelihood Inference and Comparison with ARCH ModelsReview of Economic Studies, 1998
- Novel approach to nonlinear/non-Gaussian Bayesian state estimationIEE Proceedings F Radar and Signal Processing, 1993
- New fast method for generating discrete random numbers with arbitrary frequency distributionsElectronics Letters, 1974