Nonlinear Bayesian Update via Ensemble Kernel Regression with Clustering and Subsampling

• URL: http://arxiv.org/abs/2503.15160v1
• Date: Wed, 19 Mar 2025 12:35:28 GMT
• Title: Nonlinear Bayesian Update via Ensemble Kernel Regression with Clustering and Subsampling
• Authors: Yoonsang Lee,
• Abstract summary: We propose to extend traditional ensemble Kalman filtering to settings characterized by non-Gaussian priors and nonlinear measurement operators.<n>In this framework, the observed component is first denoised via a standard Kalman update, while the unobserved component is estimated using a nonlinear regression approach.
• Score: 0.87024326813104
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Nonlinear Bayesian update for a prior ensemble is proposed to extend traditional ensemble Kalman filtering to settings characterized by non-Gaussian priors and nonlinear measurement operators. In this framework, the observed component is first denoised via a standard Kalman update, while the unobserved component is estimated using a nonlinear regression approach based on kernel density estimation. The method incorporates a subsampling strategy to ensure stability and, when necessary, employs unsupervised clustering to refine the conditional estimate. Numerical experiments on Lorenz systems and a PDE-constrained inverse problem illustrate that the proposed nonlinear update can reduce estimation errors compared to standard linear updates, especially in highly nonlinear scenarios.

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