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Among the class of nonlinear particle filtering methods, the Ensemble Kalman Filter (EnKF) has gained recent attention for its use in solving inverse problems. We review the original method and discuss recent developments in particular in…
Many real-world systems modeled using differential equations involve unknown or uncertain parameters. Standard approaches to address parameter estimation inverse problems in this setting typically focus on estimating constants; yet some…
The accuracy of Earth system models is compromised by unknown and/or unresolved dynamics, making the quantification of systematic model errors essential. While a model parameter estimation, which allows parameters to change…
In computational inverse problems, it is common that a detailed and accurate forward model is approximated by a computationally less challenging substitute. The model reduction may be necessary to meet constraints in computing time when…
We propose an affine-mapping based variational Ensemble Kalman filter for sequential Bayesian filtering problems with generic observation models. Specifically, the proposed method is formulated as to construct an affine mapping from the…
Fitting a simplifying model with several parameters to real data of complex objects is a highly nontrivial task, but enables the possibility to get insights into the objects physics. Here, we present a method to infer the parameters of the…
Filters, especially wide range of Kalman Filters have shown their impacts on predicting variables of stochastic models with higher accuracy then traditional statistic methods. Updating mean and covariance each time makes Bayesian inferences…
The Ensemble Kalman Filter (EnKF) has achieved great successes in data assimilation in atmospheric and oceanic sciences, but its failure in convergence to the right filtering distribution precludes its use for uncertainty quantification. We…
The Ensemble Kalman Filter (EnKF), as a fundamental data assimilation approach, has been widely used in many fields of the sciences and engineering. When the state variable is of high dimensional accompanied with high resolution…
Undirected graphical models are widely used in statistics, physics and machine vision. However Bayesian parameter estimation for undirected models is extremely challenging, since evaluation of the posterior typically involves the…
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…
Nonlinear stochastic differential equation models with unobservable variables are now widely used in the analysis of PK/PD data. The unobservable variables are often estimated with extended Kalman filter (EKF), and the unknown…
We consider the problem of conditioning a geological process-based computer simulation, which produces basin models by simulating transport and deposition of sediments, to data. Emphasising uncertainty quantification, we frame this as a…
In a recent methodological paper, we showed how to learn chaotic dynamics along with the state trajectory from sequentially acquired observations, using local ensemble Kalman filters. Here, we more systematically investigate the possibility…
The Ensemble Kalman Filter (EnKF) is a popular sequential data assimilation method that has been increasingly used for parameter estimation and forecast prediction in epidemiological studies. The observation function plays a critical role…
We study parameter estimation for non-global parameters in a low-dimensional chaotic model using the local ensemble transform Kalman filter (LETKF). By modifying existing techniques for using observational data to estimate global…
Data assimilation plays a key role in large-scale atmospheric weather forecasting, where the state of the physical system is estimated from model outputs and observations, and is then used as initial condition to produce accurate future…
Approximate Bayesian computation (ABC) is the most popular approach to inferring parameters in the case where the data model is specified in the form of a simulator. It is not possible to directly implement standard Monte Carlo methods for…
In this study, two classes of methods including statistical and variational data assimilation algorithms will be described. In statistical methods, the model state is updated sequentially based on the previous estimate. Variational methods,…
The Ensemble Kalman Filters (EnKF) employ a Monte-Carlo approach to represent covariance information, and are affected by sampling errors in operational settings where the number of model realizations is much smaller than the model state…