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Ensemble filters implement sequential Bayesian estimation by representing the probability distribution by an ensemble mean and covariance. Unbiased square root ensemble filters use deterministic algorithms to produce an analysis (posterior)…

Statistics Theory · Mathematics 2015-01-13 Evan Kwiatkowski , Jan Mandel

The Ensemble Kalman methodology in an inverse problems setting can be viewed as an iterative scheme, which is a weakly tamed discretization scheme for a certain stochastic differential equation (SDE). Assuming a suitable approximation…

Probability · Mathematics 2018-06-19 Dirk Blömker , Claudia Schillings , Philipp Wacker

In this work we employ importance sampling (IS) techniques to track a small over-threshold probability of a running maximum associated with the solution of a stochastic differential equation (SDE) within the framework of ensemble Kalman…

Numerical Analysis · Mathematics 2024-07-30 Nadhir Ben Rached , Erik von Schwerin , Gaukhar Shaimerdenova , Raul Tempone

The Ensemble Kalman Inversion (EKI) method is widely used for solving inverse problems, leveraging ensemble-based techniques to iteratively refine parameter estimates. Despite its versatility, the accuracy of EKI is constrained by the…

Numerical Analysis · Mathematics 2025-03-17 Ruben Harris , Claudia Schillings

Bayesian sampling is an important task in statistics and machine learning. Over the past decade, many ensemble-type sampling methods have been proposed. In contrast to the classical Markov chain Monte Carlo methods, these new methods deploy…

Numerical Analysis · Mathematics 2024-05-14 Shi Chen , Zhiyan Ding , Qin Li

Ensemble Kalman Inversion (EKI) methods are a family of iterative methods for solving weighted least-squares problems, especially those arising in scientific and engineering inverse problems in which unknown parameters or states are…

Numerical Analysis · Mathematics 2025-05-26 Elizabeth Qian , Christopher Beattie

This paper uses a probabilistic approach to analyze the converge of an ensemble Kalman filter solution to an exact Kalman filter solution in the simplest possible setting, the scalar case, as it allows us to build upon a rich literature of…

Optimization and Control · Mathematics 2020-03-31 Andrey A Popov , Adrian Sandu

Ensemble Kalman methods are widely used for state estimation in the geophysical sciences. Their success stems from the fact that they take an underlying (possibly noisy) dynamical system as a black box to provide a systematic,…

Optimization and Control · Mathematics 2024-10-10 Edoardo Calvello , Sebastian Reich , Andrew M. Stuart

Ensemble smoother (ES) has been widely used in various research fields to reduce the uncertainty of the system-of-interest. However, the commonly-adopted ES method that employs the Kalman formula, that is, ES$_\text{(K)}$, does not perform…

Optimization and Control · Mathematics 2021-02-03 Jiangjiang Zhang , Qiang Zheng , Laosheng Wu , Lingzao Zeng

The Expectation-Maximization (EM) algorithm is an iterative method to maximize the log-likelihood function for parameter estimation. Previous works on the convergence analysis of the EM algorithm have established results on the asymptotic…

Statistics Theory · Mathematics 2017-05-31 Chong Wu , Can Yang , Hongyu Zhao , Ji Zhu

Ensemble methods have become ubiquitous for the solution of Bayesian inference problems. State-of-the-art Langevin samplers such as the Ensemble Kalman Sampler (EKS), Affine Invariant Langevin Dynamics (ALDI) or its extension using weighted…

Numerical Analysis · Mathematics 2022-12-23 Martin Eigel , Robert Gruhlke , David Sommer

In this paper, we investigate a distributed estimation problem for multi-agent systems with state equality constraints (SEC). First, under a time-based consensus communication protocol, applying a modified projection operator and the…

Systems and Control · Computer Science 2019-03-12 Xingkang He , Chen Hu , Yiguang Hong , Ling Shi , Haitao Fang

The Expectation-Maximization (EM) algorithm is a widely used method for maximum likelihood estimation in models with latent variables. For estimating mixtures of Gaussians, its iteration can be viewed as a soft version of the k-means…

Machine Learning · Statistics 2017-06-06 Constantinos Daskalakis , Christos Tzamos , Manolis Zampetakis

For algorithms based on interacting particle systems that admit a mean-field description, convergence analysis is often more accessible at the mean-field level. In order to transfer convergence results obtained at the mean-field level to…

Probability · Mathematics 2025-11-03 Nicolai Jurek Gerber , Franca Hoffmann , Urbain Vaes

Ensemble methods, such as the ensemble Kalman filter (EnKF), the local ensemble transform Kalman filter (LETKF), and the ensemble Kalman smoother (EnKS) are widely used in sequential data assimilation, where state vectors are of huge…

Probability · Mathematics 2019-01-03 El houcine Bergou , Serge Gratton , Jan Mandel

The Ensemble Kalman filter assumes the observations to be Gaussian random variables with a pre-specified mean and variance. In practice, observations may also have detection limits, for instance when a gauge has a minimum or maximum value.…

Optimization and Control · Mathematics 2018-11-14 Abhishek Shah , Mohamad El Gharamti , Laurent Bertino

Ensemble Kalman inversion (EKI) is a technique for the numerical solution of inverse problems. A great advantage of the EKI's ensemble approach is that derivatives are not required in its implementation. But theoretically speaking, EKI's…

Numerical Analysis · Mathematics 2023-05-03 Xin T. Tong , Matthias Morzfeld

The iterative ensemble Kalman filter (IEnKF) is widely used in inverse problems to estimate system parameters from limited observations. However, the IEnKF, when applied to nonlinear systems, can be plagued by poor convergence. Here we…

Optimization and Control · Mathematics 2019-10-11 Jiacheng Wu , Jian-Xun Wang , Shawn C. Shadden

In this paper, we present an innovative particle system characterized by moderate interactions, designed to accurately approximate kinetic flocking models that incorporate singular interaction forces and local alignment mechanisms. We…

Analysis of PDEs · Mathematics 2024-04-23 Jinhuan Wang , Keyu Li , Hui Huang

The Ensemble Kalman Filter (EnKF) belongs to the class of iterative particle filtering methods and can be used for solving control--to--observable inverse problems. In this context, the EnKF is known as Ensemble Kalman Inversion (EKI). In…

Numerical Analysis · Mathematics 2022-02-17 Dieter Armbruster , Michael Herty , Giuseppe Visconti