{"id":"https://openalex.org/W1710526942","doi":"https://doi.org/10.1137/140981319","title":"Analysis of the Ensemble and Polynomial Chaos Kalman Filters in Bayesian Inverse Problems","display_name":"Analysis of the Ensemble and Polynomial Chaos Kalman Filters in Bayesian Inverse Problems","publication_year":2015,"publication_date":"2015-01-01","ids":{"openalex":"https://openalex.org/W1710526942","doi":"https://doi.org/10.1137/140981319","mag":"1710526942"},"language":"en","primary_location":{"id":"doi:10.1137/140981319","is_oa":false,"landing_page_url":"https://doi.org/10.1137/140981319","pdf_url":null,"source":{"id":"https://openalex.org/S2911293512","display_name":"SIAM/ASA Journal on Uncertainty Quantification","issn_l":"2166-2525","issn":["2166-2525"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM/ASA Journal on Uncertainty Quantification","raw_type":"journal-article"},"type":"preprint","indexed_in":["arxiv","crossref","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/1504.03529","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5084624008","display_name":"Oliver G. Ernst","orcid":"https://orcid.org/0000-0002-0176-7321"},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Oliver G. Ernst","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5049132140","display_name":"Bj\u00f6rn Sprungk","orcid":"https://orcid.org/0000-0001-8359-6863"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Bj\u00f6rn Sprungk","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5085830380","display_name":"Hans-J\u00f6rg Starkloff","orcid":"https://orcid.org/0000-0001-9704-0700"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Hans-J\u00f6rg Starkloff","raw_affiliation_strings":[],"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5084624008"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":1.7865,"has_fulltext":true,"cited_by_count":6,"citation_normalized_percentile":{"value":0.88289654,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":97},"biblio":{"volume":"3","issue":"1","first_page":"823","last_page":"851"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10711","display_name":"Target Tracking and Data Fusion in Sensor Networks","score":0.9901999831199646,"subfield":{"id":"https://openalex.org/subfields/1702","display_name":"Artificial Intelligence"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T10711","display_name":"Target Tracking and Data Fusion in Sensor Networks","score":0.9901999831199646,"subfield":{"id":"https://openalex.org/subfields/1702","display_name":"Artificial Intelligence"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T12814","display_name":"Gaussian Processes and Bayesian Inference","score":0.979200005531311,"subfield":{"id":"https://openalex.org/subfields/1702","display_name":"Artificial Intelligence"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11918","display_name":"Forecasting Techniques and Applications","score":0.9790999889373779,"subfield":{"id":"https://openalex.org/subfields/1803","display_name":"Management Science and Operations Research"},"field":{"id":"https://openalex.org/fields/18","display_name":"Decision Sciences"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/kalman-filter","display_name":"Kalman filter","score":0.687113344669342},{"id":"https://openalex.org/keywords/ensemble-kalman-filter","display_name":"Ensemble Kalman filter","score":0.6603156924247742},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6114420294761658},{"id":"https://openalex.org/keywords/bayesian-probability","display_name":"Bayesian probability","score":0.5822920203208923},{"id":"https://openalex.org/keywords/polynomial-chaos","display_name":"Polynomial chaos","score":0.4989631175994873},{"id":"https://openalex.org/keywords/context","display_name":"Context (archaeology)","score":0.4924067258834839},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.47851669788360596},{"id":"https://openalex.org/keywords/polynomial","display_name":"Polynomial","score":0.47819140553474426},{"id":"https://openalex.org/keywords/estimator","display_name":"Estimator","score":0.47816377878189087},{"id":"https://openalex.org/keywords/random-variable","display_name":"Random variable","score":0.4699326455593109},{"id":"https://openalex.org/keywords/data-assimilation","display_name":"Data assimilation","score":0.44284331798553467},{"id":"https://openalex.org/keywords/bayes-theorem","display_name":"Bayes' theorem","score":0.43426191806793213},{"id":"https://openalex.org/keywords/extended-kalman-filter","display_name":"Extended Kalman filter","score":0.4267389178276062},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.39921313524246216},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.3616694211959839},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.3591310381889343},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.24599486589431763},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.08661407232284546},{"id":"https://openalex.org/keywords/monte-carlo-method","display_name":"Monte Carlo method","score":0.06797194480895996}],"concepts":[{"id":"https://openalex.org/C157286648","wikidata":"https://www.wikidata.org/wiki/Q846780","display_name":"Kalman filter","level":2,"score":0.687113344669342},{"id":"https://openalex.org/C79334102","wikidata":"https://www.wikidata.org/wiki/Q3072268","display_name":"Ensemble Kalman filter","level":4,"score":0.6603156924247742},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6114420294761658},{"id":"https://openalex.org/C107673813","wikidata":"https://www.wikidata.org/wiki/Q812534","display_name":"Bayesian probability","level":2,"score":0.5822920203208923},{"id":"https://openalex.org/C197656079","wikidata":"https://www.wikidata.org/wiki/Q17147719","display_name":"Polynomial chaos","level":3,"score":0.4989631175994873},{"id":"https://openalex.org/C2779343474","wikidata":"https://www.wikidata.org/wiki/Q3109175","display_name":"Context (archaeology)","level":2,"score":0.4924067258834839},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.47851669788360596},{"id":"https://openalex.org/C90119067","wikidata":"https://www.wikidata.org/wiki/Q43260","display_name":"Polynomial","level":2,"score":0.47819140553474426},{"id":"https://openalex.org/C185429906","wikidata":"https://www.wikidata.org/wiki/Q1130160","display_name":"Estimator","level":2,"score":0.47816377878189087},{"id":"https://openalex.org/C122123141","wikidata":"https://www.wikidata.org/wiki/Q176623","display_name":"Random variable","level":2,"score":0.4699326455593109},{"id":"https://openalex.org/C24552861","wikidata":"https://www.wikidata.org/wiki/Q2670177","display_name":"Data assimilation","level":2,"score":0.44284331798553467},{"id":"https://openalex.org/C207201462","wikidata":"https://www.wikidata.org/wiki/Q182505","display_name":"Bayes' theorem","level":3,"score":0.43426191806793213},{"id":"https://openalex.org/C206833254","wikidata":"https://www.wikidata.org/wiki/Q5421817","display_name":"Extended Kalman filter","level":3,"score":0.4267389178276062},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.39921313524246216},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.3616694211959839},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.3591310381889343},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.24599486589431763},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.08661407232284546},{"id":"https://openalex.org/C19499675","wikidata":"https://www.wikidata.org/wiki/Q232207","display_name":"Monte Carlo method","level":2,"score":0.06797194480895996},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0},{"id":"https://openalex.org/C151730666","wikidata":"https://www.wikidata.org/wiki/Q7205","display_name":"Paleontology","level":1,"score":0.0},{"id":"https://openalex.org/C153294291","wikidata":"https://www.wikidata.org/wiki/Q25261","display_name":"Meteorology","level":1,"score":0.0}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.1137/140981319","is_oa":false,"landing_page_url":"https://doi.org/10.1137/140981319","pdf_url":null,"source":{"id":"https://openalex.org/S2911293512","display_name":"SIAM/ASA Journal on Uncertainty Quantification","issn_l":"2166-2525","issn":["2166-2525"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM/ASA Journal on Uncertainty Quantification","raw_type":"journal-article"},{"id":"pmh:oai:arXiv.org:1504.03529","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1504.03529","pdf_url":"https://arxiv.org/pdf/1504.03529","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},{"id":"mag:1710526942","is_oa":true,"landing_page_url":"https://arxiv.org/pdf/1504.03529v1","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"arXiv (Cornell University)","raw_type":null},{"id":"doi:10.48550/arxiv.1504.03529","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.1504.03529","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"article"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:1504.03529","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1504.03529","pdf_url":"https://arxiv.org/pdf/1504.03529","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W1710526942.pdf","grobid_xml":"https://content.openalex.org/works/W1710526942.grobid-xml"},"referenced_works_count":36,"referenced_works":["https://openalex.org/W3979328","https://openalex.org/W255324976","https://openalex.org/W654155693","https://openalex.org/W1570089119","https://openalex.org/W1593244281","https://openalex.org/W1656951490","https://openalex.org/W1969575045","https://openalex.org/W1988520084","https://openalex.org/W1990386944","https://openalex.org/W1991131983","https://openalex.org/W2009104157","https://openalex.org/W2017170340","https://openalex.org/W2027060966","https://openalex.org/W2032916024","https://openalex.org/W2042722852","https://openalex.org/W2054247041","https://openalex.org/W2064991026","https://openalex.org/W2087158441","https://openalex.org/W2096567125","https://openalex.org/W2102125272","https://openalex.org/W2102835525","https://openalex.org/W2105934661","https://openalex.org/W2128931495","https://openalex.org/W2140002539","https://openalex.org/W2143534834","https://openalex.org/W2149498546","https://openalex.org/W2150062983","https://openalex.org/W2157098139","https://openalex.org/W2158987262","https://openalex.org/W2161442523","https://openalex.org/W2179860363","https://openalex.org/W2322464541","https://openalex.org/W2479909395","https://openalex.org/W2503900448","https://openalex.org/W2610857016","https://openalex.org/W3038830718"],"related_works":["https://openalex.org/W3024664683","https://openalex.org/W2940190618","https://openalex.org/W1541047959","https://openalex.org/W2065620939","https://openalex.org/W2891400210","https://openalex.org/W2189405583","https://openalex.org/W1987784373","https://openalex.org/W2057661804","https://openalex.org/W2022022158","https://openalex.org/W3193097237","https://openalex.org/W2781708691","https://openalex.org/W110881745","https://openalex.org/W2141562047","https://openalex.org/W2089746802","https://openalex.org/W1989510446","https://openalex.org/W2989722226","https://openalex.org/W2048686071","https://openalex.org/W2805981122","https://openalex.org/W2590870493","https://openalex.org/W2972409374"],"abstract_inverted_index":{"We":[0,32,79],"analyze":[1],"the":[2,38,47,54,75,98,101,108,126],"ensemble":[3,58],"and":[4,50],"polynomial":[5,61],"chaos":[6],"Kalman":[7,122],"filters":[8,45],"applied":[9],"to":[10,69,90,97],"nonlinear":[11],"stationary":[12,23],"Bayesian":[13,48,103],"inverse":[14,104],"problems.":[15],"In":[16],"a":[17,34,70,91],"sequential":[18],"data":[19],"assimilation":[20],"setting,":[21],"such":[22],"problems":[24],"arise":[25],"in":[26,46,53],"each":[27],"step":[28],"of":[29,37,56,100,119,128],"either":[30],"filter.":[31],"give":[33],"new":[35],"interpretation":[36],"approximations":[39,66],"produced":[40],"by":[41,107],"these":[42,120],"two":[43],"popular":[44],"context":[49],"prove":[51],"that,":[52],"limit":[55],"large":[57],"or":[59,114],"high":[60],"degree,":[62],"both":[63],"methods":[64,124],"yield":[65],"which":[67],"converge":[68],"well-defined":[71],"random":[72,77],"variable":[73,85],"termed":[74],"analysis":[76,84],"variable.":[78],"then":[80],"show":[81],"that":[82],"this":[83],"is":[86],"more":[87],"closely":[88],"related":[89],"specific":[92],"linear":[93],"Bayes":[94],"estimator":[95],"than":[96],"solution":[99],"associated":[102],"problem":[105],"given":[106],"posterior":[109],"measure.":[110],"This":[111],"suggests":[112],"limited":[113],"at":[115],"least":[116],"guarded":[117],"use":[118],"generalized":[121],"filter":[123],"for":[125],"purpose":[127],"uncertainty":[129],"quantification.":[130]},"counts_by_year":[{"year":2024,"cited_by_count":1},{"year":2022,"cited_by_count":1},{"year":2017,"cited_by_count":3},{"year":2016,"cited_by_count":1}],"updated_date":"2026-03-20T23:20:44.827607","created_date":"2025-10-10T00:00:00"}