I presented at Frontiers in Computational Mathematics, a conference in honor of Bjorn Engquist’s 80th birthday.
It was a nice opportunity to see old friends and colleagues at Austin.
Ensemble-based Bayesian updates play a crucial role in estimating system states with uncertainty by assimilating observational data. Applications such as numerical weather prediction, UAV localization, and epidemiology are well-known examples of the effectiveness of ensemble-based Bayesian methods. The use of ensembles in Bayesian updates addresses the challenge of estimating the system’s prior distribution, which is often complicated by nonlinear dynamics and computationally intensive prediction models, frequently resulting in non-Gaussian distributions. While nonparametric particle filters are versatile in handling nonGaussian systems, ensemble filters that assume Gaussian priors have demonstrated greater robustness in high-dimensional settings. This talk will explore the stabilizing effect of the Gaussian assumption in ensemble filters and propose extensions to enhance their accuracy and convergence speed, particularly in the context of solving inverse problems.
