dc.contributor.author Crisan, Dan dc.contributor.author Moral, Pierre Del dc.contributor.author Jasra, Ajay dc.contributor.author Ruzayqat, Hamza Mahmoud dc.date.accessioned 2021-01-28T07:24:11Z dc.date.available 2021-01-28T07:24:11Z dc.date.issued 2021-01-27 dc.identifier.uri http://hdl.handle.net/10754/667074 dc.description.abstract In this article we consider the estimation of the log-normalization constant associated to a class of continuous-time filtering models. In particular, we consider ensemble Kalman-Bucy filter based estimates based upon several nonlinear Kalman-Bucy diffusions. Based upon new conditional bias results for the mean of the afore-mentioned methods, we analyze the empirical log-scale normalization constants in terms of their $\mathbb{L}_n-$errors and conditional bias. Depending on the type of nonlinear Kalman-Bucy diffusion, we show that these are of order $(\sqrt{t/N}) + t/N$ or $1/\sqrt{N}$ ($\mathbb{L}_n-$errors) and of order $[t+\sqrt{t}]/N$ or $1/N$ (conditional bias), where $t$ is the time horizon and $N$ is the ensemble size. Finally, we use these results for online static parameter estimation for above filtering models and implement the methodology for both linear and nonlinear models. dc.description.sponsorship AJ & HR were supported by KAUST baseline funding. DC has been partially supported by EU project STUOD - DLV-856408. dc.publisher arXiv dc.relation.url https://arxiv.org/pdf/2101.11460 dc.rights Archived with thanks to arXiv dc.subject Kalman-Bucy filter dc.subject Riccati equations dc.subject normalizing constant dc.subject nonlinear Markov processes dc.subject parameter estimation dc.title Log-Normalization Constant Estimation using the Ensemble Kalman-Bucy Filter with Application to High-Dimensional Models dc.type Preprint dc.contributor.department Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division dc.eprint.version Pre-print dc.contributor.institution Department of Mathematics, Imperial College London, London, SW7 2AZ, UK dc.contributor.institution Center INRIA Bordeaux Sud-Ouest & Institut de Mathematiques de Bordeaux, Bordeaux, 33405, FR dc.identifier.arxivid 2101.11460 kaust.person Jasra, Ajay kaust.person Ruzayqat, Hamza Mahmoud refterms.dateFOA 2021-01-27T00:00:00Z kaust.acknowledged.supportUnit KAUST baseline funding
﻿

Name:
enkbf_nc.pdf
Size:
17.92Mb
Format:
PDF
Description:
Preprint