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Physica D Nonlinear Phenomena
Article . 2017 . Peer-reviewed
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https://dx.doi.org/10.48550/ar...
Article . 2015
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A Hierarchical Bayes Ensemble Kalman Filter

A hierarchical Bayes ensemble Kalman filter
Authors: Michael Tsyrulnikov; Alexander Rakitko;

A Hierarchical Bayes Ensemble Kalman Filter

Abstract

A new ensemble filter that allows for the uncertainty in the prior distribution is proposed and tested. The filter relies on the conditional Gaussian distribution of the state given the model-error and predictability-error covariance matrices. The latter are treated as random matrices and updated in a hierarchical Bayes scheme along with the state. The (hyper)prior distribution of the covariance matrices is assumed to be inverse Wishart. The new Hierarchical Bayes Ensemble Filter (HBEF) assimilates ensemble members as generalized observations and allows ordinary observations to influence the covariances. The actual probability distribution of the ensemble members is allowed to be different from the true one. An approximation that leads to a practicable analysis algorithm is proposed. The new filter is studied in numerical experiments with a doubly stochastic one-variable model of "truth". The model permits the assessment of the variance of the truth and the true filtering error variance at each time instance. The HBEF is shown to outperform the EnKF and the HEnKF by Myrseth and Omre (2010) in a wide range of filtering regimes in terms of performance of its primary and secondary filter.

Keywords

inverse Wishart distribution, Data smoothing in stochastic control theory, random matrix, FOS: Physical sciences, conditionally Gaussian model, Filtering in stochastic control theory, Physics - Atmospheric and Oceanic Physics, observations, secondary filter, Physics - Data Analysis, Statistics and Probability, Atmospheric and Oceanic Physics (physics.ao-ph), data assimilation, Data Analysis, Statistics and Probability (physics.data-an)

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selected citations
These citations are derived from selected sources.
This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Citations provided by BIP!
popularity
This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.
BIP!Popularity provided by BIP!
influence
This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Influence provided by BIP!
impulse
This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.
BIP!Impulse provided by BIP!
10
Top 10%
Average
Top 10%
Green
bronze