2014/06/12 by Pete Bunch, Bunch, Pete, Simon Godsill +1
Computer Science · Mathematics · #Algorithm #Applied mathematics #Auxiliary particle filter #Bayesian Methods and Mixture Models #Bayesian probability #Computation (stat.CO) #Computer science #Context (archaeology) #Ensemble Kalman filter #Extended Kalman filter #FOS: Computer and information sciences #Filter (signal processing) #Flow (mathematics) #Gaussian #Gaussian Processes and Bayesian Inference #Geometry #Importance sampling #Kalman filter #Mathematical optimization #Mathematics #Monte Carlo method #Particle (ecology) #Particle filter #Physics #Posterior probability #Sampling (signal processing) #Statistical Methods and Bayesian Inference #Statistical physics #Statistics #stat.CO
paper · pdf · doi:10.48550/arxiv.1406.3183
published in arXiv (Cornell University) (Cornell University)
openalex publication_date 2014/06/12 · arxiv created 2014/11/27 · arxiv updated 2014/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
Recently developed particle flow algorithms provide an alternative to\nimportance sampling for drawing particles from a posterior distribution, and a\nnumber of particle filters based on this principle have been proposed. Samples\nare drawn from the prior and then moved according to some dynamics over an\ninterval of pseudo-time such that their final values are distributed according\nto the desired posterior. In practice, implementing a particle flow sampler\nrequires multiple layers of approximation, with the result that the final\nsamples do not in general have the correct posterior distribution. In this\npaper we consider using an approximate Gaussian flow for sampling with a class\nof nonlinear Gaussian models. We use the particle flow within an importance\nsampler, correcting for the discrepancy between the target and actual densities\nwith importance weights. We present a suitable numerical integration procedure\nfor use with this flow and an accompanying step-size control algorithm. In a\nfiltering context, we use the particle flow to sample from the optimal\nimportance density, rather than the filtering density itself, avoiding the need\nto make analytical or numerical approximations of the predictive density.\nSimulations using particle flow importance sampling within a particle filter\ndemonstrate significant improvement over standard approximations of the optimal\nimportance density, and the algorithm falls within the standard sequential\nMonte Carlo framework.\n