{"id":2523,"date":"2025-03-20T07:03:19","date_gmt":"2025-03-20T07:03:19","guid":{"rendered":"https:\/\/mailitics.com\/index.php\/2025\/03\/20\/2503-15160\/"},"modified":"2025-03-20T07:03:19","modified_gmt":"2025-03-20T07:03:19","slug":"2503-15160","status":"publish","type":"post","link":"https:\/\/mailitics.com\/index.php\/2025\/03\/20\/2503-15160\/","title":{"rendered":"Nonlinear Bayesian Update via Ensemble Kernel Regression with Clustering and Subsampling"},"content":{"rendered":"<p>    Nonlinear Bayesian Update via Ensemble Kernel Regression with Clustering and Subsampling<br \/>\n \t<BR><br \/>\n<BR><\/BR><br \/>\n    <!-- no image --><br \/>\n \t<BR><br \/>\n<BR><\/BR><\/p>\n<div>arXiv:2503.15160v1 Announce Type: new<br \/>\nAbstract: 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.<\/div>\n<p> \t<BR><br \/>\n <BR><\/BR><br \/>\n    Yoonsang Lee<br \/>\n \t<BR><br \/>\n<BR><\/BR><br \/>\n<a href=\"https:\/\/arxiv.org\/abs\/2503.15160\">Go to original source<\/a><br \/>\n \t<BR><br \/>\n <BR><\/BR><\/p>\n","protected":false},"excerpt":{"rendered":"<p>Nonlinear Bayesian Update via Ensemble Kernel Regression with Clustering and Subsampling arXiv:2503.15160v1 Announce Type: new 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, [&hellip;]<\/p>\n","protected":false},"author":2,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[62,420,190,112,191],"tags":[671,587,1434],"class_list":["post-2523","post","type-post","status-publish","format-standard","hentry","category-aimldsaimlds","category-math-pr","category-math-st","category-stat-ml","category-stat-th","tag-ensemble","tag-nonlinear","tag-update"],"_links":{"self":[{"href":"https:\/\/mailitics.com\/index.php\/wp-json\/wp\/v2\/posts\/2523"}],"collection":[{"href":"https:\/\/mailitics.com\/index.php\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/mailitics.com\/index.php\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/mailitics.com\/index.php\/wp-json\/wp\/v2\/users\/2"}],"replies":[{"embeddable":true,"href":"https:\/\/mailitics.com\/index.php\/wp-json\/wp\/v2\/comments?post=2523"}],"version-history":[{"count":0,"href":"https:\/\/mailitics.com\/index.php\/wp-json\/wp\/v2\/posts\/2523\/revisions"}],"wp:attachment":[{"href":"https:\/\/mailitics.com\/index.php\/wp-json\/wp\/v2\/media?parent=2523"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/mailitics.com\/index.php\/wp-json\/wp\/v2\/categories?post=2523"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/mailitics.com\/index.php\/wp-json\/wp\/v2\/tags?post=2523"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}