Sampling latent states for high-dimensional non-linear state space models with the embedded HMM method

TL;DR

This paper introduces a novel pool state selection scheme for the embedded HMM MCMC method, enabling efficient high-dimensional state space sampling with linear time complexity per iteration, and addresses multimodal posteriors.

Contribution

The paper presents a new local pool state selection scheme that extends embedded HMM methods to high-dimensional models, matching performance of advanced samplers.

Findings

Efficient high-dimensional sampling with linear time complexity.

Performance comparable to Particle Gibbs with Backward Sampling.

Effective handling of multimodal posteriors using mirroring technique.

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 applied to models with a one-dimensional state space. 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. We also consider a model with a multimodal posterior, and show how a technique we term "mirroring" can be used to efficiently move between the modes.