Langevin and Hamiltonian Based Sequential MCMC for Efficient Bayesian Filtering in High-Dimensional Spaces

The paper is available on and the corresponding Matlab codes here

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.

A Bayesian Perspective on Multiple Source Localization in Wireless Sensor Networks

The paper is available on and the corresponding Matlab codes here

Abstract In this paper we address the challenging problem of multiple source localization in Wireless Sensor Networks (WSN). We develop an efficient statistical algorithm, based on the novel application of Sequential Monte Carlo (SMC) sampler methodology, that is able to deal with an unknown number of sources given quantized data obtained at the fusion center from different sensors with imperfect wireless channels. We also derive the Posterior Cramér-Rao Bound (PCRB) of the source location estimate. The PCRB is used to analyze the accuracy of the proposed SMC sampler algorithm and the impact that quantization has on the accuracy of location estimates of the sources. Extensive experiments show that the benefits of the proposed scheme in terms of the accuracy of the estimation method that are required for model selection (i.e., the number of sources) and the estimation of the source characteristics compared to the classical importance sampling method.

Estimation and Calibration in Gaussian Process State Space Models: MCDC Tool

The corresponding Matlab codes with a reference manual are available on the following website.

Abstract This article presents a toolbox developed in MATLAB for the estimation, calibration and filtering of very flexible and general Gaussian Process specified state space models. State-space models are widely used in many areas of science, engineering and economics to model time series and dynamical systems. We develop a toolbox for a complete Bayesian approach to inference and learning (i.e., state estimation and system identification) on nonlinear nonparametric state-space models. The methodology developed to perform the statistical estimation and filtering involves two modes of operations: the first is for a Monte Carlo solution involving a Sequential Monte Carlo filter combined with an unbiased particle estimator of the marginal likelihood; the second involves a version of the Particle Markov chain Monte Carlo algorithm based on the Particle Gibbs sampler modified for the Gaussian Process State Space Model.