{"id":"https://openalex.org/W3112621191","doi":"https://doi.org/10.1007/s00211-021-01266-9","title":"Non-asymptotic error estimates for the Laplace approximation in Bayesian inverse problems","display_name":"Non-asymptotic error estimates for the Laplace approximation in Bayesian inverse problems","publication_year":2022,"publication_date":"2022-01-15","ids":{"openalex":"https://openalex.org/W3112621191","doi":"https://doi.org/10.1007/s00211-021-01266-9","mag":"3112621191"},"language":"en","primary_location":{"id":"doi:10.1007/s00211-021-01266-9","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s00211-021-01266-9","pdf_url":"https://link.springer.com/content/pdf/10.1007/s00211-021-01266-9.pdf","source":{"id":"https://openalex.org/S4210205683","display_name":"Numerische Mathematik","issn_l":"0029-599X","issn":["0029-599X","0945-3245"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Numerische Mathematik","raw_type":"journal-article"},"type":"article","indexed_in":["arxiv","crossref"],"open_access":{"is_oa":true,"oa_status":"hybrid","oa_url":"https://link.springer.com/content/pdf/10.1007/s00211-021-01266-9.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5087514308","display_name":"Tapio Helin","orcid":"https://orcid.org/0000-0002-5788-0008"},"institutions":[{"id":"https://openalex.org/I63548447","display_name":"Lappeenranta-Lahti University of Technology","ror":"https://ror.org/0208vgz68","country_code":"FI","type":"education","lineage":["https://openalex.org/I63548447"]}],"countries":["FI"],"is_corresponding":true,"raw_author_name":"Tapio Helin","raw_affiliation_strings":["School of Engineering Science, LUT University, P.O. Box 20, 53851 Lappeenranta, Finland","School of Engineering Science, LUT University, P.O.\u00a0Box 20, 53851, Lappeenranta, Finland"],"raw_orcid":"https://orcid.org/0000-0002-5788-0008","affiliations":[{"raw_affiliation_string":"School of Engineering Science, LUT University, P.O. Box 20, 53851 Lappeenranta, Finland","institution_ids":["https://openalex.org/I63548447"]},{"raw_affiliation_string":"School of Engineering Science, LUT University, P.O.\u00a0Box 20, 53851, Lappeenranta, Finland","institution_ids":["https://openalex.org/I63548447"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5002617106","display_name":"Remo Kretschmann","orcid":"https://orcid.org/0000-0002-4856-955X"},"institutions":[{"id":"https://openalex.org/I25974101","display_name":"University of W\u00fcrzburg","ror":"https://ror.org/00fbnyb24","country_code":"DE","type":"education","lineage":["https://openalex.org/I25974101"]},{"id":"https://openalex.org/I63548447","display_name":"Lappeenranta-Lahti University of Technology","ror":"https://ror.org/0208vgz68","country_code":"FI","type":"education","lineage":["https://openalex.org/I63548447"]}],"countries":["DE","FI"],"is_corresponding":false,"raw_author_name":"Remo Kretschmann","raw_affiliation_strings":["Institute of Mathematics, University of Wrzburg, Emil-Fischer-Str. 30, 97074 Wrzburg, Germany","School of Engineering Science, LUT University, P.O. Box 20, 53851 Lappeenranta, Finland","School of Engineering Science, LUT University, P.O.\u00a0Box 20, 53851, Lappeenranta, Finland"],"raw_orcid":"https://orcid.org/0000-0002-4856-955X","affiliations":[{"raw_affiliation_string":"Institute of Mathematics, University of Wrzburg, Emil-Fischer-Str. 30, 97074 Wrzburg, Germany","institution_ids":["https://openalex.org/I25974101"]},{"raw_affiliation_string":"School of Engineering Science, LUT University, P.O. Box 20, 53851 Lappeenranta, Finland","institution_ids":["https://openalex.org/I63548447"]},{"raw_affiliation_string":"School of Engineering Science, LUT University, P.O.\u00a0Box 20, 53851, Lappeenranta, Finland","institution_ids":["https://openalex.org/I63548447"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5087514308"],"corresponding_institution_ids":["https://openalex.org/I63548447"],"apc_list":{"value":2390,"currency":"EUR","value_usd":2990},"apc_paid":{"value":2390,"currency":"EUR","value_usd":2990},"fwci":1.9727,"has_fulltext":true,"cited_by_count":9,"citation_normalized_percentile":{"value":0.86378894,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":98},"biblio":{"volume":"150","issue":"2","first_page":"521","last_page":"549"},"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":0.9994000196456909,"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":0.9994000196456909,"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/T12814","display_name":"Gaussian Processes and Bayesian Inference","score":0.9977999925613403,"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/T10136","display_name":"Statistical Methods and Inference","score":0.9968000054359436,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/laplaces-method","display_name":"Laplace's method","score":0.840778112411499},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7673377990722656},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.6074368953704834},{"id":"https://openalex.org/keywords/linearization","display_name":"Linearization","score":0.5822147727012634},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.5796337127685547},{"id":"https://openalex.org/keywords/laplace-transform","display_name":"Laplace transform","score":0.56849604845047},{"id":"https://openalex.org/keywords/inverse-problem","display_name":"Inverse problem","score":0.49480265378952026},{"id":"https://openalex.org/keywords/inverse","display_name":"Inverse","score":0.45750877261161804},{"id":"https://openalex.org/keywords/inverse-laplace-transform","display_name":"Inverse Laplace transform","score":0.4244154989719391},{"id":"https://openalex.org/keywords/linear-approximation","display_name":"Linear approximation","score":0.42078739404678345},{"id":"https://openalex.org/keywords/bayesian-probability","display_name":"Bayesian probability","score":0.41054093837738037},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.36286118626594543},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.12164518237113953}],"concepts":[{"id":"https://openalex.org/C22243797","wikidata":"https://www.wikidata.org/wiki/Q2058297","display_name":"Laplace's method","level":3,"score":0.840778112411499},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7673377990722656},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.6074368953704834},{"id":"https://openalex.org/C11210021","wikidata":"https://www.wikidata.org/wiki/Q1520713","display_name":"Linearization","level":3,"score":0.5822147727012634},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.5796337127685547},{"id":"https://openalex.org/C97937538","wikidata":"https://www.wikidata.org/wiki/Q199691","display_name":"Laplace transform","level":2,"score":0.56849604845047},{"id":"https://openalex.org/C135252773","wikidata":"https://www.wikidata.org/wiki/Q1567213","display_name":"Inverse problem","level":2,"score":0.49480265378952026},{"id":"https://openalex.org/C207467116","wikidata":"https://www.wikidata.org/wiki/Q4385666","display_name":"Inverse","level":2,"score":0.45750877261161804},{"id":"https://openalex.org/C60455284","wikidata":"https://www.wikidata.org/wiki/Q2162701","display_name":"Inverse Laplace transform","level":3,"score":0.4244154989719391},{"id":"https://openalex.org/C160824197","wikidata":"https://www.wikidata.org/wiki/Q2071054","display_name":"Linear approximation","level":3,"score":0.42078739404678345},{"id":"https://openalex.org/C107673813","wikidata":"https://www.wikidata.org/wiki/Q812534","display_name":"Bayesian probability","level":2,"score":0.41054093837738037},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.36286118626594543},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.12164518237113953},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"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/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1007/s00211-021-01266-9","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s00211-021-01266-9","pdf_url":"https://link.springer.com/content/pdf/10.1007/s00211-021-01266-9.pdf","source":{"id":"https://openalex.org/S4210205683","display_name":"Numerische Mathematik","issn_l":"0029-599X","issn":["0029-599X","0945-3245"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Numerische Mathematik","raw_type":"journal-article"},{"id":"pmh:oai:arXiv.org:2012.06603","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2012.06603","pdf_url":"https://arxiv.org/pdf/2012.06603","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":"pmh:oai:opus.bibliothek.uni-wuerzburg.de:26539","is_oa":true,"landing_page_url":"https://opus.bibliothek.uni-wuerzburg.de/frontdoor/index/index/docId/26539","pdf_url":null,"source":{"id":"https://openalex.org/S4306401635","display_name":"Online Publication Service of W\u00fcrzburg University (W\u00fcrzburg University)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I25974101","host_organization_name":"University of W\u00fcrzburg","host_organization_lineage":["https://openalex.org/I25974101"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"article"}],"best_oa_location":{"id":"doi:10.1007/s00211-021-01266-9","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s00211-021-01266-9","pdf_url":"https://link.springer.com/content/pdf/10.1007/s00211-021-01266-9.pdf","source":{"id":"https://openalex.org/S4210205683","display_name":"Numerische Mathematik","issn_l":"0029-599X","issn":["0029-599X","0945-3245"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Numerische Mathematik","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G1792994424","display_name":null,"funder_award_id":"326961","funder_id":"https://openalex.org/F4320321108","funder_display_name":"Academy of Finland"},{"id":"https://openalex.org/G2869523853","display_name":"Uncertainty quantification in non-linear inverse problems","funder_award_id":"326961","funder_id":"https://openalex.org/F4320321108","funder_display_name":"Academy of Finland"}],"funders":[{"id":"https://openalex.org/F4320321108","display_name":"Academy of Finland","ror":"https://ror.org/05k73zm37"},{"id":"https://openalex.org/F4320325356","display_name":"Julius-Maximilians-Universit\u00e4t W\u00fcrzburg","ror":"https://ror.org/00fbnyb24"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W3112621191.pdf","grobid_xml":"https://content.openalex.org/works/W3112621191.grobid-xml"},"referenced_works_count":37,"referenced_works":["https://openalex.org/W188867022","https://openalex.org/W651687795","https://openalex.org/W1460189015","https://openalex.org/W1531455566","https://openalex.org/W1535258871","https://openalex.org/W1663973292","https://openalex.org/W1972202090","https://openalex.org/W1983671004","https://openalex.org/W2009086942","https://openalex.org/W2026344384","https://openalex.org/W2032916024","https://openalex.org/W2046837553","https://openalex.org/W2057817591","https://openalex.org/W2069212578","https://openalex.org/W2081633643","https://openalex.org/W2101484286","https://openalex.org/W2144898279","https://openalex.org/W2149498546","https://openalex.org/W2170706425","https://openalex.org/W2303654018","https://openalex.org/W2621296450","https://openalex.org/W2627085529","https://openalex.org/W2671679770","https://openalex.org/W2764128407","https://openalex.org/W2809884308","https://openalex.org/W2962957435","https://openalex.org/W2964324126","https://openalex.org/W3007421735","https://openalex.org/W3029861853","https://openalex.org/W3043749415","https://openalex.org/W3098362959","https://openalex.org/W4230104858","https://openalex.org/W4241483739","https://openalex.org/W4247915326","https://openalex.org/W4256155303","https://openalex.org/W4301425558","https://openalex.org/W4303083268"],"related_works":["https://openalex.org/W3022275705","https://openalex.org/W1996624184","https://openalex.org/W3023736802","https://openalex.org/W3021788336","https://openalex.org/W2328813089","https://openalex.org/W2504967562","https://openalex.org/W2260908168","https://openalex.org/W3148077626","https://openalex.org/W3116142293","https://openalex.org/W4309989447"],"abstract_inverted_index":{"Abstract":[0],"In":[1,91],"this":[2,116],"paper":[3,130],"we":[4,62,93],"study":[5],"properties":[6],"of":[7,11,57,81,88,123,126,142],"the":[8,12,44,55,58,75,79,82,86,89,118,124,127,143],"Laplace":[9,45,119],"approximation":[10,46,120,148],"posterior":[13],"distribution":[14],"arising":[15],"in":[16,40,48,54,96,98,115,136],"nonlinear":[17,109,137],"Bayesian":[18,134],"inverse":[19,138],"problems.":[20],"Our":[21,111],"work":[22],"is":[23,37,104,122],"motivated":[24],"by":[25,106],"Schillings":[26],"et":[27],"al.":[28],"(Numer":[29],"Math":[30],"145:915\u2013971,":[31],"2020.":[32],"10.1007/s00211-020-01131-1":[33],"),":[34],"where":[35,140],"it":[36],"shown":[38],"that":[39,72,114],"such":[41],"a":[42,68,100,107],"setting":[43],"error":[47,65,121],"Hellinger":[49],"distance":[50],"converges":[51],"to":[52,78],"zero":[53],"order":[56],"noise":[59,70],"level.":[60],"Here,":[61],"prove":[63],"novel":[64],"estimates":[66],"for":[67],"given":[69],"level":[71],"also":[73],"quantify":[74],"effect":[76],"due":[77],"nonlinearity":[80],"forward":[83,102,144],"mapping":[84,103,145],"and":[85],"dimension":[87],"problem.":[90],"particular,":[92],"are":[94],"interested":[95],"settings":[97],"which":[99],"linear":[101],"perturbed":[105],"small":[108],"mapping.":[110],"results":[112],"indicate":[113],"case,":[117],"size":[125],"perturbation.":[128],"The":[129],"provides":[131],"insight":[132],"into":[133],"inference":[135],"problems,":[139],"linearization":[141],"has":[146],"suitable":[147],"properties.":[149]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":4},{"year":2023,"cited_by_count":2},{"year":2022,"cited_by_count":1}],"updated_date":"2026-03-27T05:58:40.876381","created_date":"2025-10-10T00:00:00"}
