{"id":"https://openalex.org/W3020567546","doi":"https://doi.org/10.1137/19m1263534","title":"On Multilevel Best Linear Unbiased Estimators","display_name":"On Multilevel Best Linear Unbiased Estimators","publication_year":2020,"publication_date":"2020-01-01","ids":{"openalex":"https://openalex.org/W3020567546","doi":"https://doi.org/10.1137/19m1263534","mag":"3020567546"},"language":"en","primary_location":{"id":"doi:10.1137/19m1263534","is_oa":false,"landing_page_url":"https://doi.org/10.1137/19m1263534","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":"article","indexed_in":["crossref"],"open_access":{"is_oa":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5027342433","display_name":"Daniel Schaden","orcid":"https://orcid.org/0000-0003-2419-2839"},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Daniel Schaden","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5015636859","display_name":"Elisabeth Ullmann","orcid":"https://orcid.org/0000-0002-5699-7394"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Elisabeth Ullmann","raw_affiliation_strings":[],"raw_orcid":"https://orcid.org/0000-0002-5699-7394","affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5027342433"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":2.889,"has_fulltext":false,"cited_by_count":41,"citation_normalized_percentile":{"value":0.9252881,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":95,"max":99},"biblio":{"volume":"8","issue":"2","first_page":"601","last_page":"635"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10928","display_name":"Probabilistic and Robust Engineering Design","score":0.9991000294685364,"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"}},"topics":[{"id":"https://openalex.org/T10928","display_name":"Probabilistic and Robust Engineering Design","score":0.9991000294685364,"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"}},{"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/T12056","display_name":"Markov Chains and Monte Carlo Methods","score":0.9939000010490417,"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/estimator","display_name":"Estimator","score":0.7748081088066101},{"id":"https://openalex.org/keywords/minimum-variance-unbiased-estimator","display_name":"Minimum-variance unbiased estimator","score":0.715848445892334},{"id":"https://openalex.org/keywords/control-variates","display_name":"Control variates","score":0.6948494911193848},{"id":"https://openalex.org/keywords/bias-of-an-estimator","display_name":"Bias of an estimator","score":0.6693975329399109},{"id":"https://openalex.org/keywords/steins-unbiased-risk-estimate","display_name":"Stein's unbiased risk estimate","score":0.6568001508712769},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6460679769515991},{"id":"https://openalex.org/keywords/variance-reduction","display_name":"Variance reduction","score":0.5751798152923584},{"id":"https://openalex.org/keywords/efficient-estimator","display_name":"Efficient estimator","score":0.5373799800872803},{"id":"https://openalex.org/keywords/best-linear-unbiased-prediction","display_name":"Best linear unbiased prediction","score":0.5203220844268799},{"id":"https://openalex.org/keywords/monte-carlo-method","display_name":"Monte Carlo method","score":0.47785279154777527},{"id":"https://openalex.org/keywords/linear-model","display_name":"Linear model","score":0.46904951333999634},{"id":"https://openalex.org/keywords/multilevel-model","display_name":"Multilevel model","score":0.4630544185638428},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.4612167775630951},{"id":"https://openalex.org/keywords/efficiency","display_name":"Efficiency","score":0.4379108250141144},{"id":"https://openalex.org/keywords/mean-squared-error","display_name":"Mean squared error","score":0.4174298644065857},{"id":"https://openalex.org/keywords/linear-regression","display_name":"Linear regression","score":0.41742801666259766},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.39330583810806274},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.22514879703521729},{"id":"https://openalex.org/keywords/hybrid-monte-carlo","display_name":"Hybrid Monte Carlo","score":0.10932955145835876},{"id":"https://openalex.org/keywords/markov-chain-monte-carlo","display_name":"Markov chain Monte Carlo","score":0.0930311381816864}],"concepts":[{"id":"https://openalex.org/C185429906","wikidata":"https://www.wikidata.org/wiki/Q1130160","display_name":"Estimator","level":2,"score":0.7748081088066101},{"id":"https://openalex.org/C165646398","wikidata":"https://www.wikidata.org/wiki/Q3755281","display_name":"Minimum-variance unbiased estimator","level":3,"score":0.715848445892334},{"id":"https://openalex.org/C121683094","wikidata":"https://www.wikidata.org/wiki/Q3554721","display_name":"Control variates","level":5,"score":0.6948494911193848},{"id":"https://openalex.org/C191393472","wikidata":"https://www.wikidata.org/wiki/Q15222032","display_name":"Bias of an estimator","level":4,"score":0.6693975329399109},{"id":"https://openalex.org/C134962040","wikidata":"https://www.wikidata.org/wiki/Q7606742","display_name":"Stein's unbiased risk estimate","level":5,"score":0.6568001508712769},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6460679769515991},{"id":"https://openalex.org/C62644790","wikidata":"https://www.wikidata.org/wiki/Q3454689","display_name":"Variance reduction","level":3,"score":0.5751798152923584},{"id":"https://openalex.org/C35594927","wikidata":"https://www.wikidata.org/wiki/Q2265984","display_name":"Efficient estimator","level":4,"score":0.5373799800872803},{"id":"https://openalex.org/C103545067","wikidata":"https://www.wikidata.org/wiki/Q796265","display_name":"Best linear unbiased prediction","level":3,"score":0.5203220844268799},{"id":"https://openalex.org/C19499675","wikidata":"https://www.wikidata.org/wiki/Q232207","display_name":"Monte Carlo method","level":2,"score":0.47785279154777527},{"id":"https://openalex.org/C163175372","wikidata":"https://www.wikidata.org/wiki/Q3339222","display_name":"Linear model","level":2,"score":0.46904951333999634},{"id":"https://openalex.org/C53059260","wikidata":"https://www.wikidata.org/wiki/Q374758","display_name":"Multilevel model","level":2,"score":0.4630544185638428},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.4612167775630951},{"id":"https://openalex.org/C17648541","wikidata":"https://www.wikidata.org/wiki/Q2265984","display_name":"Efficiency","level":3,"score":0.4379108250141144},{"id":"https://openalex.org/C139945424","wikidata":"https://www.wikidata.org/wiki/Q1940696","display_name":"Mean squared error","level":2,"score":0.4174298644065857},{"id":"https://openalex.org/C48921125","wikidata":"https://www.wikidata.org/wiki/Q10861030","display_name":"Linear regression","level":2,"score":0.41742801666259766},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.39330583810806274},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.22514879703521729},{"id":"https://openalex.org/C13153151","wikidata":"https://www.wikidata.org/wiki/Q1639846","display_name":"Hybrid Monte Carlo","level":4,"score":0.10932955145835876},{"id":"https://openalex.org/C111350023","wikidata":"https://www.wikidata.org/wiki/Q1191869","display_name":"Markov chain Monte Carlo","level":3,"score":0.0930311381816864},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.0},{"id":"https://openalex.org/C81917197","wikidata":"https://www.wikidata.org/wiki/Q628760","display_name":"Selection (genetic algorithm)","level":2,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1137/19m1263534","is_oa":false,"landing_page_url":"https://doi.org/10.1137/19m1263534","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"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G1277698726","display_name":null,"funder_award_id":"188264188/GRK1754","funder_id":"https://openalex.org/F4320320879","funder_display_name":"Deutsche Forschungsgemeinschaft"}],"funders":[{"id":"https://openalex.org/F4320320879","display_name":"Deutsche Forschungsgemeinschaft","ror":"https://ror.org/018mejw64"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":16,"referenced_works":["https://openalex.org/W1941377048","https://openalex.org/W1991681863","https://openalex.org/W1995573301","https://openalex.org/W2014945091","https://openalex.org/W2135459060","https://openalex.org/W2163715525","https://openalex.org/W2275145915","https://openalex.org/W2529348500","https://openalex.org/W2603909564","https://openalex.org/W2811395263","https://openalex.org/W2893228383","https://openalex.org/W2915943053","https://openalex.org/W2963136325","https://openalex.org/W2963492671","https://openalex.org/W2964025847","https://openalex.org/W3102699604"],"related_works":["https://openalex.org/W2035998077","https://openalex.org/W2349547417","https://openalex.org/W4239491110","https://openalex.org/W2910434125","https://openalex.org/W1984619412","https://openalex.org/W2059813665","https://openalex.org/W3092888124","https://openalex.org/W2036535888","https://openalex.org/W2356451205","https://openalex.org/W3020567546"],"abstract_inverted_index":{"We":[0,39,77],"present":[1],"a":[2,14,21,35,58,65,73,102],"general":[3],"variance":[4,47,66,108],"reduction":[5],"technique":[6],"for":[7,72,106],"the":[8,11,32,43,50,107,124,138],"estimation":[9,33],"of":[10,13,17,23,52,109,142],"expectation":[12],"scalar-valued":[15],"quantity":[16,141],"interest":[18,143],"associated":[19,44],"with":[20],"family":[22],"model":[24],"evaluations.":[25],"The":[26,130],"key":[27],"idea":[28],"is":[29,144],"to":[30,82],"reformulate":[31],"as":[34,87],"linear":[36,53,111],"regression":[37],"problem.":[38],"then":[40],"show":[41,116],"that":[42,117],"estimators":[45],"are":[46,132],"minimal":[48],"within":[49],"class":[51],"unbiased":[54,70,112],"estimators.":[55],"By":[56],"solving":[57],"sample":[59],"allocation":[60],"problem":[61],"we":[62,100],"further":[63],"construct":[64],"minimal,":[67],"linear,":[68],"and":[69,94,115],"estimator":[71,81,114,119],"given":[74],"computational":[75],"budget.":[76],"compare":[78],"our":[79,118],"proposed":[80],"other":[83],"multilevel":[84,88,113],"estimators,":[85],"such":[86],"Monte":[89,92],"Carlo,":[90,93],"multifidelity":[91],"approximate":[95],"control":[96],"variates.":[97],"In":[98],"addition,":[99],"provide":[101],"sharp":[103],"lower":[104],"bound":[105,122],"any":[110],"approaches":[120],"this":[121],"in":[123],"infinite":[125],"low":[126],"fidelity":[127],"data":[128],"limit.":[129],"results":[131],"illustrated":[133],"by":[134,146],"numerical":[135],"experiments":[136],"where":[137],"underlying":[139],"output":[140],"generated":[145],"an":[147],"elliptic":[148],"partial":[149],"differential":[150],"equation.":[151]},"counts_by_year":[{"year":2026,"cited_by_count":3},{"year":2025,"cited_by_count":11},{"year":2024,"cited_by_count":10},{"year":2023,"cited_by_count":11},{"year":2022,"cited_by_count":3},{"year":2021,"cited_by_count":3}],"updated_date":"2026-04-25T08:17:42.794288","created_date":"2025-10-10T00:00:00"}