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In this paper, we exploit the gradient flow structure of continuous-time formulations of Bayesian inference in terms of their numerical time-stepping.
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Amezcua, J., Kalnay, E., Ide, K. & Reich, S. (2014), ‘Ensemble transform Kalman-Bucy filters’, Q.J.R. Meteor. Soc
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Crisan, D. & Xiong, J. (2010), ‘Approximate McKean-Vlasov representation for a class of SPDEs’, Stochastics
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Daum, F. & Huang, J. (2011), Particle filter for nonlinear filters, in
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Reich, S. (2011), ‘A dynamical systems framework for intermittent data assimilation’, BIT Numer Math
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Bergemann, K. & Reich, S. (2012), ‘An ensemble Kalman–Bucy filter for continuous data assimilation’, Meteorolog. Zeitschrift
2012
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Emerik, A. & Reynolds, A. (2012), ‘Ensemble smoother with multiple data assimilation’, Computers & Geosciences
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Chen, Y. & Oliver, D. (2013), ‘Levenberg-Marquardt forms of the iterative ensemble smoother for efficient history matching and uncertainty quantification’, Computational Geoscience
2013
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2016
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Blömker, D., Schillings, C. & Wacker, P. (2018), ‘A strongly convergent numerical scheme for ensemble Kalman inversion’, SIAM J. Numer. Anal
2018
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de Wiljes, J., Reich, S. & Stannat, W. (2018), ‘Long-time stability and accuracy of the ensemble Kalman–Bucy filter for fully observed processes and small measurement noise’, SIAM J. Appl. Dyn. Syst
2018
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Detommaso, G., Cui, T., Spantini, A., Marzouk, Y. & Scheichl, R. (2018), A Stein variational Newton method, in
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Ollivier, Y. (2018), ‘Online natural gradient as a Kalman filter’, Electronic Journal of Statistics
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Reich, S. (2019), ‘Data assimilation: The Schrödinger perspective’, Acta Numerica
2019
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