Bayesian Analysis

Sampling Latent States for High-Dimensional Non-Linear State Space Models with the Embedded HMM Method

Alexander Y. Shestopaloff and Radford M. Neal

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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.

Article information

Source
Bayesian Anal. (2017), 26 pages.

Dates
First available in Project Euclid: 21 October 2017

Permanent link to this document
https://projecteuclid.org/euclid.ba/1508551720

Digital Object Identifier
doi:10.1214/17-BA1077

Subjects
Primary: 65C40: Computational Markov chains
Secondary: 65C05: Monte Carlo methods

Keywords
MCMC non-linear state space

Rights
Creative Commons Attribution 4.0 International License.

Citation

Shestopaloff, Alexander Y.; Neal, Radford M. Sampling Latent States for High-Dimensional Non-Linear State Space Models with the Embedded HMM Method. Bayesian Anal., advance publication, 21 October 2017. doi:10.1214/17-BA1077. https://projecteuclid.org/euclid.ba/1508551720


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