UNBIASED ESTIMATION OF THE VANILLA AND DETERMINISTIC ENSEMBLE KALMAN-BUCY FILTERS

IF 1.5 4区工程技术 Q2 ENGINEERING, MULTIDISCIPLINARY

International Journal for Uncertainty Quantification Pub Date : 2023-01-01 DOI:10.1615/int.j.uncertaintyquantification.2023045369

Miguel Angel Alvarez Ballesteros, Neil K. Chada, Ajay Jasra

{"title":"UNBIASED ESTIMATION OF THE VANILLA AND DETERMINISTIC ENSEMBLE KALMAN-BUCY FILTERS","authors":"Miguel Angel Alvarez Ballesteros, Neil K. Chada, Ajay Jasra","doi":"10.1615/int.j.uncertaintyquantification.2023045369","DOIUrl":null,"url":null,"abstract":"In this paper, we consider the development of unbiased estimators for the ensemble Kalman-Bucy filter (EnKBF). The EnKBF is a continuous-time filtering methodology, which can be viewed as a continuous-time analog of the famous discrete-time ensemble Kalman filter. Our unbiased estimators will be motivated from recent work (Rhee and Glynn, Oper. Res., 63:1026-1053, 2015) which introduces randomization as a means to produce unbiased and finite variance estimators. The randomization enters through both the level of discretization and through the number of samples at each level. Our unbiased estimator will be specific to models that are linear and Gaussian. This is due to the fact that the EnKBF itself is consistent, in the large particle limit N &#8594; &#8734;, with the Kalman-Bucy filter, which allows us one derive theoretical insights. Specifically, we introduce two unbiased EnKBF estimators that will be applied to two particular variants of the EnKBF, which are the deterministic and vanilla EnKBF. Numerical experiments are conducted on a linear Ornstein-Uhlenbeck process, which includes a high-dimensional example. Our unbiased estimators will be compared to the multilevel. We also provide a proof of the multilevel deterministic EnKBF, which provides a guideline for some of the unbiased methods.","PeriodicalId":48814,"journal":{"name":"International Journal for Uncertainty Quantification","volume":"40 1","pages":"0"},"PeriodicalIF":1.5000,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"1","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"International Journal for Uncertainty Quantification","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1615/int.j.uncertaintyquantification.2023045369","RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"ENGINEERING, MULTIDISCIPLINARY","Score":null,"Total":0}

引用次数: 1

Abstract

In this paper, we consider the development of unbiased estimators for the ensemble Kalman-Bucy filter (EnKBF). The EnKBF is a continuous-time filtering methodology, which can be viewed as a continuous-time analog of the famous discrete-time ensemble Kalman filter. Our unbiased estimators will be motivated from recent work (Rhee and Glynn, Oper. Res., 63:1026-1053, 2015) which introduces randomization as a means to produce unbiased and finite variance estimators. The randomization enters through both the level of discretization and through the number of samples at each level. Our unbiased estimator will be specific to models that are linear and Gaussian. This is due to the fact that the EnKBF itself is consistent, in the large particle limit N → ∞, with the Kalman-Bucy filter, which allows us one derive theoretical insights. Specifically, we introduce two unbiased EnKBF estimators that will be applied to two particular variants of the EnKBF, which are the deterministic and vanilla EnKBF. Numerical experiments are conducted on a linear Ornstein-Uhlenbeck process, which includes a high-dimensional example. Our unbiased estimators will be compared to the multilevel. We also provide a proof of the multilevel deterministic EnKBF, which provides a guideline for some of the unbiased methods.

查看原文本刊更多论文

香草和确定性集合卡尔曼-布希滤波器的无偏估计

本文研究了集成卡尔曼-布西滤波器(EnKBF)无偏估计量的发展。EnKBF是一种连续时间滤波方法，可以看作是著名的离散时间集合卡尔曼滤波的连续时间模拟。我们的无偏估计将从最近的工作中得到激励(Rhee和Glynn, Oper。Res.， 63:1026- 1053,2015)，其中引入了随机化作为产生无偏和有限方差估计量的手段。随机化通过离散化水平和每个水平上的样本数量进入。我们的无偏估计量将特定于线性和高斯模型。这是因为在大粒子极限N →∞，通过卡尔曼-布西滤波器，我们可以获得理论见解。具体来说，我们引入了两个无偏的EnKBF估计器，它们将应用于EnKBF的两个特定变体，即确定性和香草EnKBF。对一个包含高维算例的线性Ornstein-Uhlenbeck过程进行了数值实验。我们的无偏估计量将与多水平估计量进行比较。我们还提供了多层确定性EnKBF的证明，这为一些无偏方法提供了指导。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

求助全文

约1分钟内获得全文求助全文

来源期刊

International Journal for Uncertainty Quantification ENGINEERING, MULTIDISCIPLINARY-MATHEMATICS, INTERDISCIPLINARY APPLICATIONS

CiteScore

3.60

自引率

5.90%

发文量

期刊介绍： The International Journal for Uncertainty Quantification disseminates information of permanent interest in the areas of analysis, modeling, design and control of complex systems in the presence of uncertainty. The journal seeks to emphasize methods that cross stochastic analysis, statistical modeling and scientific computing. Systems of interest are governed by differential equations possibly with multiscale features. Topics of particular interest include representation of uncertainty, propagation of uncertainty across scales, resolving the curse of dimensionality, long-time integration for stochastic PDEs, data-driven approaches for constructing stochastic models, validation, verification and uncertainty quantification for predictive computational science, and visualization of uncertainty in high-dimensional spaces. Bayesian computation and machine learning techniques are also of interest for example in the context of stochastic multiscale systems, for model selection/classification, and decision making. Reports addressing the dynamic coupling of modern experiments and modeling approaches towards predictive science are particularly encouraged. Applications of uncertainty quantification in all areas of physical and biological sciences are appropriate.