Langevin and Hamiltonian based Sequential MCMC for Efficient Bayesian Filtering in High-dimensional Spaces

Abstract

Nonlinear non-Gaussian state-space models arise in numerous applications in statistics and signal processing. In this context, one of the most successful and popular approximation techniques is the Sequential Monte Carlo (SMC) algorithm, also known as particle filtering. Nevertheless, this method tends to be inefficient when applied to high dimensional problems. In this paper, we focus on another class of sequential inference methods, namely the Sequential Markov Chain Monte Carlo (SMCMC) techniques, which represent a promising alternative to SMC methods. After providing a unifying framework for the class of SMCMC approaches, we propose novel efficient strategies based on the principle of Langevin diffusion and Hamiltonian dynamics in order to cope with the increasing number of high-dimensional applications. Simulation results show that the proposed algorithms achieve significantly better performance compared to existing algorithms.

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• Sharp failure rates for the bootstrap particle filter in high dimensions
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• Sequentially interacting Markov chain Monte Carlo methods
• Information-geometric Markov Chain Monte Carlo methods using Diffusions
• The Geometric Foundations of Hamiltonian Monte Carlo
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Cited by in corpus (5)

• Particle Filtering with Invertible Particle Flow
• Invertible Particle Flow-based Sequential MCMC with extension to Gaussian Mixture noise models
• Limit theorems for sequential MCMC methods
• Comprehensive review of models and methods for inferences in bio-chemical reaction networks
• The Application of Zig-Zag Sampler in Sequential Markov Chain Monte Carlo