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Ensemble updating of binary state vectors by maximizing the expected number of unchanged components

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  • Margrethe Kvale Loe
  • Håkon Tjelmeland

Abstract

The main challenge in ensemble‐based filtering methods is the updating of a prior ensemble to a posterior ensemble. In the ensemble Kalman filter (EnKF), a linear‐Gaussian model is introduced to overcome this issue, and the prior ensemble is updated with a linear shift. In the current article, we consider how the underlying ideas of the EnKF can be applied when the state vector consists of binary variables. While the EnKF relies on Gaussian approximations, we instead introduce a first‐order Markov chain approximation. To update the prior ensemble we simulate samples from a distribution which maximizes the expected number of equal components in a prior and posterior state vector. The proposed approach is demonstrated in a simulation experiment where, compared with a more naive updating procedure, we find that it leads to an almost 50% reduction in the difference between true and estimated marginal filtering probabilities with respect to the Frobenius norm.

Suggested Citation

  • Margrethe Kvale Loe & Håkon Tjelmeland, 2021. "Ensemble updating of binary state vectors by maximizing the expected number of unchanged components," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 48(4), pages 1148-1185, December.
  • Handle: RePEc:bla:scjsta:v:48:y:2021:i:4:p:1148-1185
    DOI: 10.1111/sjos.12483
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    References listed on IDEAS

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    1. Cressie, Noel & Davidson, Jennifer L., 1998. "Image analysis with partially ordered markov models," Computational Statistics & Data Analysis, Elsevier, vol. 29(1), pages 1-26, November.
    2. Jon Sætrom & Henning Omre, 2013. "Uncertainty Quantification in the Ensemble Kalman Filter," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 40(4), pages 868-885, December.
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    Cited by:

    1. Margrethe Kvale Loe & Håkon Tjelmeland, 2022. "Ensemble updating of categorical state vectors," Computational Statistics, Springer, vol. 37(5), pages 2363-2397, November.

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