Langevin and Hamiltonian Based Sequential MCMC for Efficient Bayesian Filtering in High-Dimensional Spaces
IEEE Journal of Selected Topics in Signal Processing, Special issue on Stochastic Simulation and Optimisation in Signal Processing (2015)
32 Pages Posted: 6 Jun 2017
Date Written: 2015
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.
Keywords: Bayesian inference, ﬁltering, Sequential Monte Carlo, Markov Chain Monte Carlo, state-space model, high-dimensional
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