{"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/bayesian-nonparametric-spectral-estimation","title":"Bayesian Nonparametric Spectral Estimation","arxiv_id":"1809.02196","date":"2018-09-06","proceeding":"NeurIPS 2018 12","authors":["Felipe Tobar"],"abstract":"Spectral estimation (SE) aims to identify how the energy of a signal (e.g., a\ntime series) is distributed across different frequencies. This can become\nparticularly challenging when only partial and noisy observations of the signal\nare available, where current methods fail to handle uncertainty appropriately.\nIn this context, we propose a joint probabilistic model for signals,\nobservations and spectra, where SE is addressed as an exact inference problem.\nAssuming a Gaussian process prior over the signal, we apply Bayes' rule to find\nthe analytic posterior distribution of the spectrum given a set of\nobservations. Besides its expressiveness and natural account of spectral\nuncertainty, the proposed model also provides a functional-form representation\nof the power spectral density, which can be optimised efficiently. Comparison\nwith previous approaches, in particular against Lomb-Scargle, is addressed\ntheoretically and also experimentally in three different scenarios. Code and\ndemo available at https://github.com/GAMES-UChile/BayesianSpectralEstimation.","url_abs":"http://arxiv.org/abs/1809.02196v2","url_pdf":"http://arxiv.org/pdf/1809.02196v2.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":"bayesian-nonparametric-spectral-estimation","repo_url":"https://github.com/GAMES-UChile/BayesianSpectralEstimation","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":0,"framework":"none","reach":null}],"tasks":[{"task_slug":"time-series-1","task_name":"Time Series"},{"task_slug":"time-series","task_name":"Time Series Analysis"}],"methods":[{"method_slug":"gaussian-process","method_name":"Gaussian Process"}],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"syntology_url":null,"atlas_url":null,"mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}