@article{GregoryCotterReich2016,
  author    = {Gregory, A. and Cotter, C. J. and Reich, Sebastian},
  title     = {MULTILEVEL ENSEMBLE TRANSFORM PARTICLE FILTERING},
  series = {SIAM journal on scientific computing},
  volume    = {38},
  journal   = {SIAM journal on scientific computing},
  publisher = {Society for Industrial and Applied Mathematics},
  address   = {Philadelphia},
  issn      = {1064-8275},
  doi       = {10.1137/15M1038232},
  pages     = {A1317 -- A1338},
  year      = {2016},
  abstract  = {This paper extends the multilevel Monte Carlo variance reduction technique to nonlinear filtering. In particular, multilevel Monte Carlo is applied to a certain variant of the particle filter, the ensemble transform particle filter (EPTF). A key aspect is the use of optimal transport methods to re-establish correlation between coarse and fine ensembles after resampling; this controls the variance of the estimator. Numerical examples present a proof of concept of the effectiveness of the proposed method, demonstrating significant computational cost reductions (relative to the single-level ETPF counterpart) in the propagation of ensembles.},
  language  = {en}
}
@article{Reich2013,
  author    = {Reich, Sebastian},
  title     = {A nonparametric ensemble transform method for bayesian inference},
  series = {SIAM journal on scientific computing},
  volume    = {35},
  journal   = {SIAM journal on scientific computing},
  number    = {4},
  publisher = {Society for Industrial and Applied Mathematics},
  address   = {Philadelphia},
  issn      = {1064-8275},
  doi       = {10.1137/130907367},
  pages     = {A2013 -- A2024},
  year      = {2013},
  abstract  = {Many applications, such as intermittent data assimilation, lead to a recursive application of Bayesian inference within a Monte Carlo context. Popular data assimilation algorithms include sequential Monte Carlo methods and ensemble Kalman filters (EnKFs). These methods differ in the way Bayesian inference is implemented. Sequential Monte Carlo methods rely on importance sampling combined with a resampling step, while EnKFs utilize a linear transformation of Monte Carlo samples based on the classic Kalman filter. While EnKFs have proven to be quite robust even for small ensemble sizes, they are not consistent since their derivation relies on a linear regression ansatz. In this paper, we propose another transform method, which does not rely on any a priori assumptions on the underlying prior and posterior distributions. The new method is based on solving an optimal transportation problem for discrete random variables.},
  language  = {en}
}