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September 2018 Sampling Latent States for High-Dimensional Non-Linear State Space Models with the Embedded HMM Method
Alexander Y. Shestopaloff, Radford M. Neal
Bayesian Anal. 13(3): 797-822 (September 2018). DOI: 10.1214/17-BA1077

Abstract

We propose a new scheme for selecting pool states for the embedded Hidden Markov Model (HMM) Markov Chain Monte Carlo (MCMC) method. This new scheme allows the embedded HMM method to be used for efficient sampling in state space models where the state can be high-dimensional. Previously, embedded HMM methods were only applicable to low-dimensional state-space models. We demonstrate that using our proposed pool state selection scheme, an embedded HMM sampler can have similar performance to a well-tuned sampler that uses a combination of Particle Gibbs with Backward Sampling (PGBS) and Metropolis updates. The scaling to higher dimensions is made possible by selecting pool states locally near the current value of the state sequence. The proposed pool state selection scheme also allows each iteration of the embedded HMM sampler to take time linear in the number of the pool states, as opposed to quadratic as in the original embedded HMM sampler.

Citation

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Alexander Y. Shestopaloff. Radford M. Neal. "Sampling Latent States for High-Dimensional Non-Linear State Space Models with the Embedded HMM Method." Bayesian Anal. 13 (3) 797 - 822, September 2018. https://doi.org/10.1214/17-BA1077

Information

Published: September 2018
First available in Project Euclid: 21 October 2017

zbMATH: 06989968
MathSciNet: MR3807867
Digital Object Identifier: 10.1214/17-BA1077

Subjects:
Primary: 65C40
Secondary: 65C05

Keywords: MCMC , non-linear , state space

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Vol.13 • No. 3 • September 2018
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