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A seamless multilevel ensemble transform particle filter

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Title: A seamless multilevel ensemble transform particle filter
Authors: Gregory, ACA
Cotter, CJ
Item Type: Journal Article
Abstract: This paper presents a seamless algorithm for the application of the multilevel Monte Carlo (MLMC) method to the ensemble transform particle filter (ETPF). The algorithm uses a combi- nation of optimal coupling transformations between coarse and fine ensembles in difference estimators within a multilevel framework, to minimise estimator variance. It differs from that of Gregory et al. (2016) in that strong coupling between the coarse and fine ensembles is seamlessly maintained during all stages of the assimilation algorithm, instead of using independent transformations to equal weights followed by recoupling with an assignment problem. This modification is found to lead to an increased rate in variance decay between coarse and fine ensembles with level in the hierarchy, a key component of MLMC. This offers the potential for greater computational cost reductions. This is shown, alongside evidence of asymptotic consistency, in numerical examples.
Issue Date: 28-Nov-2017
Date of Acceptance: 20-Jun-2017
URI: http://hdl.handle.net/10044/1/49527
DOI: https://dx.doi.org/10.1137/16M1102021
ISSN: 1095-7197
Publisher: Society for Industrial and Applied Mathematics
Start Page: A2684
End Page: A2701
Journal / Book Title: SIAM Journal on Scientific Computing
Volume: 39
Issue: 6
Copyright Statement: © 2017 SIAM. Published by SIAM under the terms of the Creative Commons 4.0 license
Sponsor/Funder: Engineering & Physical Science Research Council (E
Funder's Grant Number: FG4500853166-RG.MATH.103301
Keywords: math.NA
0102 Applied Mathematics
0103 Numerical And Computational Mathematics
0802 Computation Theory And Mathematics
Numerical & Computational Mathematics
Publication Status: Published
Open Access location: https://arxiv.org/abs/1611.00266
Appears in Collections:Applied Mathematics and Mathematical Physics
Faculty of Natural Sciences