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      The practical irrelevance of the collapse of the ensemble Kalman filter and other particle filters

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          Abstract

          A particle filter "collapses", i.e.~only one of its particles is significant, if the variance of its weights is large. The ensemble Kalman filter (EnKF) can be interpreted as a particle filter and, therefore, can also collapse. We point out that EnKF collapses in the same way as any other particle filter, i.e., using EnKF as a proposal density does not solve the degeneracy problem in particle filtering. We investigate the practical implications of the collapse of EnKF and show that the mean square error (MSE) of a localized EnKF can be small even when it collapses. We explain these seemingly contradicting results. The collapse of EnKF results from a global assessment of the EnKF approximation of the posterior distribution which may not be relevant in problems where error and forecast scores are assessed locally rather than globally. Thus, the collapse of EnKF may have no significant practical consequences and may even be happening on a regular basis in geophysical applications. However, the collapse is avoided if the weight calculation was local, which suggests that a major obstacle to the practical application particle filters may be the determination of localized weights akin to the particle filter interpretation of the localized EnKF.

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          1512.03720

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