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hal.structure.identifierDepartment of Mathematics [Imperial College London]
dc.contributor.authorCRISAN, Dan
hal.structure.identifierMéthodes avancées d’apprentissage statistique et de contrôle [ASTRAL]
dc.contributor.authorDEL MORAL, Pierre
hal.structure.identifierComputer, Electrical and Mathematical Sciences and Engineering Division [Thuwal]
dc.contributor.authorJASRA, Ajay
hal.structure.identifierComputer, Electrical and Mathematical Sciences and Engineering Division [Thuwal]
dc.contributor.authorRUZAYQAT, Hamza
dc.date.accessioned2024-04-04T02:39:23Z
dc.date.available2024-04-04T02:39:23Z
dc.date.issued2022-12
dc.identifier.issn0001-8678
dc.identifier.urihttps://oskar-bordeaux.fr/handle/20.500.12278/190967
dc.description.abstractEnAbstract 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 estimates based upon several nonlinear Kalman–Bucy diffusions. Using new conditional bias results for the mean of the aforementioned methods, we analyze the empirical log-scale normalization constants in terms of their $\mathbb{L}_n$ -errors and $\mathbb{L}_n$ -conditional bias. Depending on the type of nonlinear Kalman–Bucy diffusion, we show that these are bounded above by terms such as $\mathsf{C}(n)\left[t^{1/2}/N^{1/2} + t/N\right]$ or $\mathsf{C}(n)/N^{1/2}$ ( $\mathbb{L}_n$ -errors) and $\mathsf{C}(n)\left[t+t^{1/2}\right]/N$ or $\mathsf{C}(n)/N$ ( $\mathbb{L}_n$ -conditional bias), where t is the time horizon, N is the ensemble size, and $\mathsf{C}(n)$ is a constant that depends only on n , not on N or t . Finally, we use these results for online static parameter estimation for the above filtering models and implement the methodology for both linear and nonlinear models.
dc.language.isoen
dc.publisherApplied Probability Trust
dc.subject.enKalman-Bucy filter
dc.subject.enRiccati equations
dc.subject.ennonlinear Markov processes
dc.title.enLog-normalization constant estimation using the ensemble Kalman–Bucy filter with application to high-dimensional models
dc.typeArticle de revue
dc.identifier.doi10.1017/apr.2021.62
dc.subject.halMathématiques [math]/Probabilités [math.PR]
dc.identifier.arxiv2101.11460
bordeaux.journalAdvances in Applied Probability
bordeaux.page1139-1163
bordeaux.volume54
bordeaux.hal.laboratoriesInstitut de Mathématiques de Bordeaux (IMB) - UMR 5251*
bordeaux.issue4
bordeaux.institutionUniversité de Bordeaux
bordeaux.institutionBordeaux INP
bordeaux.institutionCNRS
bordeaux.peerReviewedoui
hal.identifierhal-03850299
hal.version1
hal.popularnon
hal.audienceInternationale
hal.origin.linkhttps://hal.archives-ouvertes.fr//hal-03850299v1
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