@article{NueskenPavhotis2019,
  author    = {N{\"u}sken, Nikolas and Pavhotis, Grigorios A.},
  title     = {Constructing Sampling Schemes via Coupling},
  series = {SIAM ASA journal on uncertainty quantification / Society for Industrial and Applied Mathematics ; American Statistical Association},
  volume    = {7},
  journal   = {SIAM ASA journal on uncertainty quantification / Society for Industrial and Applied Mathematics ; American Statistical Association},
  number    = {1},
  publisher = {Society for Industrial and Applied Mathematics},
  address   = {Philadelphia},
  issn      = {2166-2525},
  doi       = {10.1137/18M119896X},
  pages     = {324 -- 382},
  year      = {2019},
  abstract  = {In this paper we develop a general framework for constructing and analyzing coupled Markov chain Monte Carlo samplers, allowing for both (possibly degenerate) diffusion and piecewise deterministic Markov processes. For many performance criteria of interest, including the asymptotic variance, the task of finding efficient couplings can be phrased in terms of problems related to optimal transport theory. We investigate general structural properties, proving a singularity theorem that has both geometric and probabilistic interpretations. Moreover, we show that those problems can often be solved approximately and support our findings with numerical experiments. For the particular objective of estimating the variance of a Bayesian posterior, our analysis suggests using novel techniques in the spirit of antithetic variates. Addressing the convergence to equilibrium of coupled processes we furthermore derive a modified Poincare inequality.},
  language  = {en}
}
@article{deWiljesPathirajaReich2020,
  author    = {de Wiljes, Jana and Pathiraja, Sahani Darschika and Reich, Sebastian},
  title     = {Ensemble transform algorithms for nonlinear smoothing problems},
  series = {SIAM journal on scientific computing},
  volume    = {42},
  journal   = {SIAM journal on scientific computing},
  number    = {1},
  publisher = {Society for Industrial and Applied Mathematics},
  address   = {Philadelphia},
  issn      = {1064-8275},
  doi       = {10.1137/19M1239544},
  pages     = {A87 -- A114},
  year      = {2020},
  abstract  = {Several numerical tools designed to overcome the challenges of smoothing in a non-linear and non-Gaussian setting are investigated for a class of particle smoothers. The considered family of smoothers is induced by the class of linear ensemble transform filters which contains classical filters such as the stochastic ensemble Kalman filter, the ensemble square root filter, and the recently introduced nonlinear ensemble transform filter. Further the ensemble transform particle smoother is introduced and particularly highlighted as it is consistent in the particle limit and does not require assumptions with respect to the family of the posterior distribution. The linear update pattern of the considered class of linear ensemble transform smoothers allows one to implement important supplementary techniques such as adaptive spread corrections, hybrid formulations, and localization in order to facilitate their application to complex estimation problems. These additional features are derived and numerically investigated for a sequence of increasingly challenging test problems.},
  language  = {en}
}
@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{BourneCushingLiuetal.2018,
  author    = {Bourne, D. P. and Cushing, D. and Liu, S. and M{\"u}nch, Florentin and Peyerimhoff, Norbert},
  title     = {Ollivier-Ricci idleness functions of graphs},
  series = {SIAM Journal on Discrete Mathematics},
  volume    = {32},
  journal   = {SIAM Journal on Discrete Mathematics},
  number    = {2},
  publisher = {Society for Industrial and Applied Mathematics},
  address   = {Philadelphia},
  issn      = {0895-4801},
  doi       = {10.1137/17M1134469},
  pages     = {1408 -- 1424},
  year      = {2018},
  abstract  = {We study the Ollivier-Ricci curvature of graphs as a function of the chosen idleness. We show that this idleness function is concave and piecewise linear with at most three linear parts, and at most two linear parts in the case of a regular graph. We then apply our result to show that the idleness function of the Cartesian product of two regular graphs is completely determined by the idleness functions of the factors.},
  language  = {en}
}