Tuesday 23 Nov 2021: Contributions to high dimensional nonlinear data assimilation
Jana de Wiljes - University Potsdam
Harrison 101 13:30-14:30
The seamless integration of large data sets into computational models is one of the central challenges for the mathematical sciences of the 21st century. Despite the fact that the underlying assumptions do not hold for many applications, Gaussian approximative filters are considered state of the art as they have been successfully implemented for highly nonlinear settings with large dimensional state spaces. Moreover several recent studies have been devoted to showing accuracy of such filters in terms of tracking ability for nonlinear evolution models and we will present one of these results given in the form of distinct bounds for certain filter variants. While the robustness of such Gaussian approximative filters is undeniable there has been considerable aspiration to design filters that can achieve even higher levels of accuracy while maintaining an appropriate level of robustness and stability. Here we will discuss a family of such filters that do not require a parametrization of the posterior distribution and can be combined with traditional Gaussian filters via a likelihood split.