I presented my work at the Applied Mathematics and Computation Seminar at University of Massachusetta Amherst, Nonlinear Bayesian Update via Ensemble Kernel Regression with Clustering and Subsampling.
Bayesian updating is a fundamental tool for improving the statistical accuracy of uncertain systems using measurement data, with applications spanning numerical weather prediction, robotics, and neural network training. In this talk, I will review sample-based Bayesian update methods and examine their behavior under various assumptions on the prior distribution and measurement model. Building on this analysis, I will introduce a stable Bayesian update scheme designed to handle non-Gaussian statistics. The effectiveness of the proposed approach will be demonstrated through numerical examples, including nonlinear measurements in chaotic systems, robot localization, and PDE-constrained optimization.