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

François Septier (1, 2) , Gareth W. Peters (3)

1 CRIStAL - Centre de Recherche en Informatique, Signal et Automatique de Lille - UMR 9189
2 Institut TELECOM/TELECOM Lille1
3 UCL - University College of London [London]

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 highdimensional applications. Simulation results show that the proposed algorithms achieve significantly better performance compared to existing algorithms.

Domains: Signal and Image processing; Applications [stat.AP]; Computation [stat.CO]; Methodology [stat.ME]

François Septier, Gareth W. Peters. Langevin and Hamiltonian based Sequential MCMC for Efficient Bayesian Filtering in High-dimensional Spaces. IEEE Journal of Selected Topics in Signal Processing, 2016, ⟨10.1109/JSTSP.2015.2497211⟩. ⟨hal-01238978⟩