The Iterated Auxiliary Particle Filter

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.