{"about":{"site":"https://codewithpapers.app","non_affiliation":"Code with Papers and Syntology are not affiliated with, endorsed by, or sponsored by Papers with Code, Meta, or the pwc-archive mirror.","licence":"CC BY-SA 4.0","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","attribution":"https://codewithpapers.app/attribution","modified":"archive material modified by Syntology; see the attribution page"},"url":"/paper/newton-based-maximum-likelihood-estimation-in","title":"Newton-based maximum likelihood estimation in nonlinear state space models","arxiv_id":"1502.03655","date":"2015-02-12","proceeding":null,"authors":["Manon Kok","Johan Dahlin","Thomas B. Schön","Adrian Wills"],"abstract":"Maximum likelihood (ML) estimation using Newton's method in nonlinear state\nspace models (SSMs) is a challenging problem due to the analytical\nintractability of the log-likelihood and its gradient and Hessian. We estimate\nthe gradient and Hessian using Fisher's identity in combination with a\nsmoothing algorithm. We explore two approximations of the log-likelihood and of\nthe solution of the smoothing problem. The first is a linearization\napproximation which is computationally cheap, but the accuracy typically varies\nbetween models. The second is a sampling approximation which is asymptotically\nvalid for any SSM but is more computationally costly. We demonstrate our\napproach for ML parameter estimation on simulated data from two different SSMs\nwith encouraging results.","url_abs":"http://arxiv.org/abs/1502.03655v2","url_pdf":"http://arxiv.org/pdf/1502.03655v2.pdf","source":{"archive":"pwc-archive (Hugging Face), CC BY-SA 4.0","snapshot":"2025-07-28","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","row_kind":"abstracts"},"code_links":[{"paper_slug":"newton-based-maximum-likelihood-estimation-in","repo_url":"https://github.com/compops/newton-sysid2015","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":1,"framework":"none","reach":null}],"tasks":[{"task_slug":"state-space-models","task_name":"State Space Models"},{"task_slug":"parameter-estimation","task_name":"parameter estimation"},{"task_slug":null,"task_name":"valid"}],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":null,"mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}