Journal Article

The Iterated Auxiliary Particle Filter

Guarniero, Pieralberto, Johansen, Adam M., Lee, Anthony

2017

Overview

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.

• Publisher: Taylor & Francis,Taylor & Francis Ltd
• Subject: Algorithms / Bias / Computer simulation / Function words / Grammatical aspect / Heat recovery systems / Hidden Markov models / Inference / Iterative methods / Look-ahead methods / Markov analysis / Markov chain / Markov chains / Mathematical models / Monte Carlo method / Monte Carlo simulation / Parameter estimation / Particle Markov chain Monte Carlo / Regression analysis / Sequential Monte Carlo / Smoothing / State-space models / Statistical inference / Statistical methods / statistical models / Statistics / variance