{"id":"https://openalex.org/W2584252732","doi":"https://doi.org/10.1137/16m1105384","title":"Gaussian Approximations for Probability Measures on $R^d$","display_name":"Gaussian Approximations for Probability Measures on $R^d$","publication_year":2017,"publication_date":"2017-01-01","ids":{"openalex":"https://openalex.org/W2584252732","doi":"https://doi.org/10.1137/16m1105384","mag":"2584252732"},"language":"en","primary_location":{"id":"doi:10.1137/16m1105384","is_oa":true,"landing_page_url":"https://doi.org/10.1137/16m1105384","pdf_url":"https://epubs.siam.org/doi/pdf/10.1137/16M1105384","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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM/ASA Journal on Uncertainty Quantification","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"hybrid","oa_url":"https://epubs.siam.org/doi/pdf/10.1137/16M1105384","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5080770658","display_name":"Yulong Lu","orcid":"https://orcid.org/0000-0003-2914-414X"},"institutions":[{"id":"https://openalex.org/I39555362","display_name":"University of Warwick","ror":"https://ror.org/01a77tt86","country_code":"GB","type":"education","lineage":["https://openalex.org/I39555362"]}],"countries":["GB"],"is_corresponding":true,"raw_author_name":"Yulong Lu","raw_affiliation_strings":["Mathematics Institute, University of Warwick, Coventry, CV4 7AL, UK"],"affiliations":[{"raw_affiliation_string":"Mathematics Institute, University of Warwick, Coventry, CV4 7AL, UK","institution_ids":["https://openalex.org/I39555362"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5032114852","display_name":"Andrew M. Stuart","orcid":"https://orcid.org/0000-0001-9091-7266"},"institutions":[{"id":"https://openalex.org/I122411786","display_name":"California Institute of Technology","ror":"https://ror.org/05dxps055","country_code":"US","type":"education","lineage":["https://openalex.org/I122411786"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Andrew Stuart","raw_affiliation_strings":["Computing and Mathematical Sciences, California Institute of Technology, Pasadena, CA 91125"],"affiliations":[{"raw_affiliation_string":"Computing and Mathematical Sciences, California Institute of Technology, Pasadena, CA 91125","institution_ids":["https://openalex.org/I122411786"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5001883810","display_name":"Hendrik Weber","orcid":"https://orcid.org/0000-0003-3969-230X"},"institutions":[{"id":"https://openalex.org/I39555362","display_name":"University of Warwick","ror":"https://ror.org/01a77tt86","country_code":"GB","type":"education","lineage":["https://openalex.org/I39555362"]}],"countries":["GB"],"is_corresponding":false,"raw_author_name":"Hendrik Weber","raw_affiliation_strings":["Mathematics Institute, University of Warwick, Coventry, CV4 7AL, UK"],"affiliations":[{"raw_affiliation_string":"Mathematics Institute, University of Warwick, Coventry, CV4 7AL, UK","institution_ids":["https://openalex.org/I39555362"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5080770658"],"corresponding_institution_ids":["https://openalex.org/I39555362"],"apc_list":null,"apc_paid":null,"fwci":2.0986,"has_fulltext":false,"cited_by_count":22,"citation_normalized_percentile":{"value":0.89733309,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":97},"biblio":{"volume":"5","issue":"1","first_page":"1136","last_page":"1165"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12056","display_name":"Markov Chains and Monte Carlo Methods","score":0.9994999766349792,"subfield":{"id":"https://openalex.org/subfields/2613","display_name":"Statistics and Probability"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T12056","display_name":"Markov Chains and Monte Carlo Methods","score":0.9994999766349792,"subfield":{"id":"https://openalex.org/subfields/2613","display_name":"Statistics and Probability"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10136","display_name":"Statistical Methods and Inference","score":0.9979000091552734,"subfield":{"id":"https://openalex.org/subfields/2613","display_name":"Statistics and Probability"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10928","display_name":"Probabilistic and Robust Engineering Design","score":0.9975000023841858,"subfield":{"id":"https://openalex.org/subfields/1804","display_name":"Statistics, Probability and Uncertainty"},"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/mathematics","display_name":"Mathematics","score":0.7745622396469116},{"id":"https://openalex.org/keywords/measure","display_name":"Measure (data warehouse)","score":0.6200931072235107},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.5620555877685547},{"id":"https://openalex.org/keywords/probability-measure","display_name":"Probability measure","score":0.5428699254989624},{"id":"https://openalex.org/keywords/randomness","display_name":"Randomness","score":0.5372275114059448},{"id":"https://openalex.org/keywords/limit","display_name":"Limit (mathematics)","score":0.5328030586242676},{"id":"https://openalex.org/keywords/divergence","display_name":"Divergence (linguistics)","score":0.5269169211387634},{"id":"https://openalex.org/keywords/kullback\u2013leibler-divergence","display_name":"Kullback\u2013Leibler divergence","score":0.5214923620223999},{"id":"https://openalex.org/keywords/gaussian","display_name":"Gaussian","score":0.49318450689315796},{"id":"https://openalex.org/keywords/frequentist-inference","display_name":"Frequentist inference","score":0.44134238362312317},{"id":"https://openalex.org/keywords/gaussian-noise","display_name":"Gaussian noise","score":0.42439988255500793},{"id":"https://openalex.org/keywords/bayesian-probability","display_name":"Bayesian probability","score":0.35775330662727356},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.3308340311050415},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.25961238145828247},{"id":"https://openalex.org/keywords/bayesian-inference","display_name":"Bayesian inference","score":0.18322253227233887},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.1309385597705841},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.0903637707233429},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.0768493115901947}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7745622396469116},{"id":"https://openalex.org/C2780009758","wikidata":"https://www.wikidata.org/wiki/Q6804172","display_name":"Measure (data warehouse)","level":2,"score":0.6200931072235107},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5620555877685547},{"id":"https://openalex.org/C21031990","wikidata":"https://www.wikidata.org/wiki/Q355020","display_name":"Probability measure","level":2,"score":0.5428699254989624},{"id":"https://openalex.org/C125112378","wikidata":"https://www.wikidata.org/wiki/Q176640","display_name":"Randomness","level":2,"score":0.5372275114059448},{"id":"https://openalex.org/C151201525","wikidata":"https://www.wikidata.org/wiki/Q177239","display_name":"Limit (mathematics)","level":2,"score":0.5328030586242676},{"id":"https://openalex.org/C207390915","wikidata":"https://www.wikidata.org/wiki/Q1230525","display_name":"Divergence (linguistics)","level":2,"score":0.5269169211387634},{"id":"https://openalex.org/C171752962","wikidata":"https://www.wikidata.org/wiki/Q255166","display_name":"Kullback\u2013Leibler divergence","level":2,"score":0.5214923620223999},{"id":"https://openalex.org/C163716315","wikidata":"https://www.wikidata.org/wiki/Q901177","display_name":"Gaussian","level":2,"score":0.49318450689315796},{"id":"https://openalex.org/C162376815","wikidata":"https://www.wikidata.org/wiki/Q2158281","display_name":"Frequentist inference","level":4,"score":0.44134238362312317},{"id":"https://openalex.org/C4199805","wikidata":"https://www.wikidata.org/wiki/Q2725903","display_name":"Gaussian noise","level":2,"score":0.42439988255500793},{"id":"https://openalex.org/C107673813","wikidata":"https://www.wikidata.org/wiki/Q812534","display_name":"Bayesian probability","level":2,"score":0.35775330662727356},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.3308340311050415},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.25961238145828247},{"id":"https://openalex.org/C160234255","wikidata":"https://www.wikidata.org/wiki/Q812535","display_name":"Bayesian inference","level":3,"score":0.18322253227233887},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.1309385597705841},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.0903637707233429},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0768493115901947},{"id":"https://openalex.org/C41895202","wikidata":"https://www.wikidata.org/wiki/Q8162","display_name":"Linguistics","level":1,"score":0.0},{"id":"https://openalex.org/C77088390","wikidata":"https://www.wikidata.org/wiki/Q8513","display_name":"Database","level":1,"score":0.0},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"score":0.0},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1137/16m1105384","is_oa":true,"landing_page_url":"https://doi.org/10.1137/16m1105384","pdf_url":"https://epubs.siam.org/doi/pdf/10.1137/16M1105384","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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM/ASA Journal on Uncertainty Quantification","raw_type":"journal-article"},{"id":"pmh:oai:wrap.warwick.ac.uk:89495","is_oa":false,"landing_page_url":null,"pdf_url":null,"source":{"id":"https://openalex.org/S4306400665","display_name":"Warwick Research Archive Portal (University of Warwick)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I39555362","host_organization_name":"University of Warwick","host_organization_lineage":["https://openalex.org/I39555362"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"acceptedVersion","is_accepted":true,"is_published":false,"raw_source_name":"","raw_type":"Journal Article"},{"id":"pmh:oai:authors.library.caltech.edu:73114","is_oa":false,"landing_page_url":"https://resolver.caltech.edu/CaltechAUTHORS:20161221-163341129","pdf_url":null,"source":{"id":"https://openalex.org/S4306402161","display_name":"CaltechAUTHORS (California Institute of Technology)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I122411786","host_organization_name":"California Institute of Technology","host_organization_lineage":["https://openalex.org/I122411786"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"Article"}],"best_oa_location":{"id":"doi:10.1137/16m1105384","is_oa":true,"landing_page_url":"https://doi.org/10.1137/16m1105384","pdf_url":"https://epubs.siam.org/doi/pdf/10.1137/16M1105384","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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM/ASA Journal on Uncertainty Quantification","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G1166036910","display_name":null,"funder_award_id":"EP/HO23364/1","funder_id":"https://openalex.org/F4320334627","funder_display_name":"Engineering and Physical Sciences Research Council"},{"id":"https://openalex.org/G1854682607","display_name":null,"funder_award_id":"EP/K034154/1","funder_id":"https://openalex.org/F4320334627","funder_display_name":"Engineering and Physical Sciences Research Council"},{"id":"https://openalex.org/G8027000134","display_name":null,"funder_award_id":"UF140187","funder_id":"https://openalex.org/F4320320006","funder_display_name":"Royal Society"}],"funders":[{"id":"https://openalex.org/F4320320006","display_name":"Royal Society","ror":"https://ror.org/03wnrjx87"},{"id":"https://openalex.org/F4320332180","display_name":"Defense Advanced Research Projects Agency","ror":"https://ror.org/02caytj08"},{"id":"https://openalex.org/F4320334627","display_name":"Engineering and Physical Sciences Research Council","ror":"https://ror.org/0439y7842"},{"id":"https://openalex.org/F4320337345","display_name":"Office of Naval Research","ror":"https://ror.org/00rk2pe57"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2584252732.pdf","grobid_xml":"https://content.openalex.org/works/W2584252732.grobid-xml"},"referenced_works_count":33,"referenced_works":["https://openalex.org/W260216039","https://openalex.org/W649818166","https://openalex.org/W1524622012","https://openalex.org/W1976068406","https://openalex.org/W1995672551","https://openalex.org/W2001102637","https://openalex.org/W2004060143","https://openalex.org/W2014863861","https://openalex.org/W2016373742","https://openalex.org/W2024376461","https://openalex.org/W2027608755","https://openalex.org/W2060209743","https://openalex.org/W2062532221","https://openalex.org/W2087122499","https://openalex.org/W2091552984","https://openalex.org/W2111117254","https://openalex.org/W2112609371","https://openalex.org/W2120340025","https://openalex.org/W2123597716","https://openalex.org/W2126304434","https://openalex.org/W2127339814","https://openalex.org/W2144540906","https://openalex.org/W2149498546","https://openalex.org/W2158446701","https://openalex.org/W2344708621","https://openalex.org/W2745055376","https://openalex.org/W2962906676","https://openalex.org/W3100176265","https://openalex.org/W3101357194","https://openalex.org/W3101842270","https://openalex.org/W3102516841","https://openalex.org/W3105462721","https://openalex.org/W4293052541"],"related_works":["https://openalex.org/W3124023584","https://openalex.org/W1506744765","https://openalex.org/W193226913","https://openalex.org/W2168076595","https://openalex.org/W2290754432","https://openalex.org/W1559405175","https://openalex.org/W2116258251","https://openalex.org/W2742348189","https://openalex.org/W2963863608","https://openalex.org/W1865390738"],"abstract_inverted_index":{"This":[0],"paper":[1],"concerns":[2],"the":[3,13,23,26,54,59,77,97,101,105,112,115,125],"approximation":[4],"of":[5,25,37,46,80,91,100,114],"probability":[6],"measures":[7,39],"on":[8],"$\\mathbb{R}^d$":[9],"with":[10,29],"respect":[11,30],"to":[12,31,75],"Kullback--Leibler":[14],"divergence.":[15],"Given":[16],"an":[17],"admissible":[18],"target":[19],"measure,":[20],"we":[21,95,117],"show":[22,96],"existence":[24],"best":[27,48],"approximation,":[28],"this":[32,62],"divergence,":[33],"from":[34],"certain":[35],"sets":[36],"Gaussian":[38,41],"and":[40],"mixtures.":[42],"The":[43,69],"asymptotic":[44,98],"behavior":[45,64],"such":[47],"approximations":[49],"is":[50,65,72],"then":[51,73],"studied":[52],"in":[53,84,104],"small":[55,106],"parameter":[56],"limit":[57],"where":[58],"measure":[60,103],"concentrates;":[61],"asympotic":[63],"characterized":[66],"using":[67],"$\\Gamma$-convergence.":[68],"theory":[70],"developed":[71],"applied":[74],"understand":[76],"frequentist":[78],"consistency":[79],"Bayesian":[81],"inverse":[82],"problems":[83],"finite":[85],"dimensions.":[86],"For":[87],"a":[88,119],"fixed":[89],"realization":[90],"additive":[92],"observational":[93],"noise,":[94,116],"normality":[99],"posterior":[102,126],"noise":[107],"limit.":[108],"Taking":[109],"into":[110],"account":[111],"randomness":[113],"prove":[118],"Bernstein--Von":[120],"Mises":[121],"type":[122],"result":[123],"for":[124],"measure.":[127]},"counts_by_year":[{"year":2025,"cited_by_count":3},{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":4},{"year":2021,"cited_by_count":4},{"year":2020,"cited_by_count":3},{"year":2019,"cited_by_count":3},{"year":2018,"cited_by_count":2},{"year":2017,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2017-02-10T00:00:00"}
