{"id":3990,"date":"2013-03-21T22:54:14","date_gmt":"2013-03-22T02:54:14","guid":{"rendered":"http:\/\/mseas.mit.edu\/?p=3990"},"modified":"2024-01-08T15:35:26","modified_gmt":"2024-01-08T20:35:26","slug":"bayesian-inference-of-stochastic-dynamical-models","status":"publish","type":"post","link":"https:\/\/mseas.mit.edu\/?p=3990","title":{"rendered":"Bayesian inference of stochastic dynamical models"},"content":{"rendered":"A new methodology for Bayesian inference of stochastic dynamical models is developed.\nThe methodology leverages the dynamically orthogonal (DO) evolution equations\nfor reduced-dimension uncertainty evolution and the Gaussian mixture model\nDO filtering algorithm for nonlinear reduced-dimension state variable inference to\nperform parallelized computation of marginal likelihoods for multiple candidate models,\nenabling efficient Bayesian update of model distributions. The methodology also\nemploys reduced-dimension state augmentation to accommodate models featuring uncertain\nparameters. The methodology is applied successfully to two high-dimensional,\nnonlinear simulated fluid and ocean systems. Successful joint inference of an uncertain\nspatial geometry, one uncertain model parameter, and 0(105) uncertain state\nvariables is achieved for the first. Successful joint inference of an uncertain stochastic\ndynamical equation and 0(105) uncertain state variables is achieved for the second.\nExtensions to adaptive modeling and adaptive sampling are discussed.","protected":false},"excerpt":{"rendered":"<p>A new methodology for Bayesian inference of stochastic dynamical models is developed. The methodology leverages the dynamically orthogonal (DO) evolution equations for reduced-dimension uncertainty evolution and the Gaussian mixture model DO filtering algorithm for nonlinear reduced-dimension state variable inference to perform parallelized computation of marginal likelihoods for multiple candidate models, enabling efficient Bayesian update of [&hellip;]<\/p>\n","protected":false},"author":2,"featured_media":0,"comment_status":"open","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[42,5,44],"tags":[],"class_list":["post-3990","post","type-post","status-publish","format-standard","hentry","category-meche-theses","category-publications","category-masters-theses"],"_links":{"self":[{"href":"https:\/\/mseas.mit.edu\/index.php?rest_route=\/wp\/v2\/posts\/3990","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/mseas.mit.edu\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/mseas.mit.edu\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/mseas.mit.edu\/index.php?rest_route=\/wp\/v2\/users\/2"}],"replies":[{"embeddable":true,"href":"https:\/\/mseas.mit.edu\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=3990"}],"version-history":[{"count":2,"href":"https:\/\/mseas.mit.edu\/index.php?rest_route=\/wp\/v2\/posts\/3990\/revisions"}],"predecessor-version":[{"id":6625,"href":"https:\/\/mseas.mit.edu\/index.php?rest_route=\/wp\/v2\/posts\/3990\/revisions\/6625"}],"wp:attachment":[{"href":"https:\/\/mseas.mit.edu\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=3990"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/mseas.mit.edu\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=3990"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/mseas.mit.edu\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=3990"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}