@InProceedings{JCFHASUV-2026,
    author="Carrillo, J. A. and Hoffmann, F. and Stuart, A. M. and Vaes, U.",
    editor="Oishi, Shin'ichi and Okamoto, Hisashi and Hayami, Ken",
    title="Statistical Accuracy of Approximate Filtering Methods",
    booktitle="Recent Developments in Industrial and Applied Mathematics",
    year="2026",
    publisher="Springer Nature Singapore",
    address="Singapore",
    pages="295--306",
    abstract="Estimating the statistics of the state of a dynamical system, from partial and noisy observations, is both mathematically challenging and finds wide application. Furthermore, the applications are of great societal importance, including problems such as probabilistic weather forecasting (Kalnay 2003) and prediction of epidemics (Keeling and Eames 2005). Particle filters provide a well-founded approach to the problem, leading to provably accurate approximations of the statistics (Doucet et al. 2001). However these methods perform poorly in high dimensions (Bickel et al. 2008; Snyder et al. 2008). In 1994 the idea of ensemble Kalman filtering was introduced (Evensen 1994) leading to a methodology that has been widely adopted in the geophysical sciences (van Leeuwen et al. 2019) and also finds application to quite general inverse problems (Iglesias et al. 2013). However, ensemble Kalman filters have defied rigorous analysis of their statistical accuracy, except in the linear Gaussian setting (Le Gland et al. 2011; Mandel et al. 2011). In this article we describe recent work which takes first steps to analyze the statistical accuracy of ensemble Kalman filters beyond the linear Gaussian setting (Carrillo et al. 2022). The subject is inherently technical, as it involves the evolution of probability measures according to a nonlinear and nonautonomous dynamical system; and the approximation of this evolution. It can nonetheless be presented in a fairly accessible fashion, understandable with basic knowledge of dynamical systems, numerical analysis and probability. We undertake such a presentation here.",
    isbn="978-981-95-1446-5"
}