{"id":"https://openalex.org/W4324100080","doi":"https://doi.org/10.1137/22m1510121","title":"On the Error Rate of Importance Sampling with Randomized Quasi-Monte Carlo","display_name":"On the Error Rate of Importance Sampling with Randomized Quasi-Monte Carlo","publication_year":2023,"publication_date":"2023-03-10","ids":{"openalex":"https://openalex.org/W4324100080","doi":"https://doi.org/10.1137/22m1510121"},"language":"en","primary_location":{"id":"doi:10.1137/22m1510121","is_oa":false,"landing_page_url":"https://doi.org/10.1137/22m1510121","pdf_url":null,"source":{"id":"https://openalex.org/S203348814","display_name":"SIAM Journal on Numerical Analysis","issn_l":"0036-1429","issn":["0036-1429","1095-7170"],"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 Journal on Numerical Analysis","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/A5058665232","display_name":"Zhijian He","orcid":"https://orcid.org/0000-0002-0730-5953"},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Zhijian He","raw_affiliation_strings":["Corresponding author. School of Mathematics, South China University of Technology, Guangzhou 510641, People\u2019s Republic of China"],"affiliations":[{"raw_affiliation_string":"Corresponding author. School of Mathematics, South China University of Technology, Guangzhou 510641, People\u2019s Republic of China","institution_ids":[]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5037655503","display_name":"Zheng Zhan","orcid":"https://orcid.org/0000-0002-3882-5484"},"institutions":[{"id":"https://openalex.org/I99065089","display_name":"Tsinghua University","ror":"https://ror.org/03cve4549","country_code":"CN","type":"education","lineage":["https://openalex.org/I99065089"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Zhan Zheng","raw_affiliation_strings":["Department of Mathematical Sciences, Tsinghua University, Beijing 100084, People\u2019s Republic of China","Department of Mathematical Sciences, Tsinghua University, Beijing 100084, People's Republic of China"],"affiliations":[{"raw_affiliation_string":"Department of Mathematical Sciences, Tsinghua University, Beijing 100084, People\u2019s Republic of China","institution_ids":["https://openalex.org/I99065089"]},{"raw_affiliation_string":"Department of Mathematical Sciences, Tsinghua University, Beijing 100084, People's Republic of China","institution_ids":["https://openalex.org/I99065089"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5101625376","display_name":"Xiaoqun Wang","orcid":"https://orcid.org/0000-0003-3440-2617"},"institutions":[{"id":"https://openalex.org/I99065089","display_name":"Tsinghua University","ror":"https://ror.org/03cve4549","country_code":"CN","type":"education","lineage":["https://openalex.org/I99065089"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Xiaoqun Wang","raw_affiliation_strings":["Department of Mathematical Sciences, Tsinghua University, Beijing 100084, People\u2019s Republic of China","Department of Mathematical Sciences, Tsinghua University, Beijing 100084, People's Republic of China"],"affiliations":[{"raw_affiliation_string":"Department of Mathematical Sciences, Tsinghua University, Beijing 100084, People\u2019s Republic of China","institution_ids":["https://openalex.org/I99065089"]},{"raw_affiliation_string":"Department of Mathematical Sciences, Tsinghua University, Beijing 100084, People's Republic of China","institution_ids":["https://openalex.org/I99065089"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5058665232"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":3.2237,"has_fulltext":false,"cited_by_count":8,"citation_normalized_percentile":{"value":0.90936405,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":90,"max":98},"biblio":{"volume":"61","issue":"2","first_page":"515","last_page":"538"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12404","display_name":"Mathematical Approximation and Integration","score":0.9998999834060669,"subfield":{"id":"https://openalex.org/subfields/2612","display_name":"Numerical Analysis"},"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/T12404","display_name":"Mathematical Approximation and Integration","score":0.9998999834060669,"subfield":{"id":"https://openalex.org/subfields/2612","display_name":"Numerical Analysis"},"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":0.9908999800682068,"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":0.9872000217437744,"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":0.7289041876792908},{"id":"https://openalex.org/keywords/quasi-monte-carlo-method","display_name":"Quasi-Monte Carlo method","score":0.641520619392395},{"id":"https://openalex.org/keywords/monte-carlo-method","display_name":"Monte Carlo method","score":0.6339066028594971},{"id":"https://openalex.org/keywords/rate-of-convergence","display_name":"Rate of convergence","score":0.5390369892120361},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.5044635534286499},{"id":"https://openalex.org/keywords/gaussian","display_name":"Gaussian","score":0.4899822771549225},{"id":"https://openalex.org/keywords/importance-sampling","display_name":"Importance sampling","score":0.48965388536453247},{"id":"https://openalex.org/keywords/monte-carlo-integration","display_name":"Monte Carlo integration","score":0.4409090578556061},{"id":"https://openalex.org/keywords/covariance","display_name":"Covariance","score":0.4177306890487671},{"id":"https://openalex.org/keywords/hybrid-monte-carlo","display_name":"Hybrid Monte Carlo","score":0.31767886877059937},{"id":"https://openalex.org/keywords/markov-chain-monte-carlo","display_name":"Markov chain Monte Carlo","score":0.2289961278438568},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.20212554931640625},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.1322856843471527},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.07425755262374878}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7289041876792908},{"id":"https://openalex.org/C63320529","wikidata":"https://www.wikidata.org/wiki/Q7269435","display_name":"Quasi-Monte Carlo method","level":5,"score":0.641520619392395},{"id":"https://openalex.org/C19499675","wikidata":"https://www.wikidata.org/wiki/Q232207","display_name":"Monte Carlo method","level":2,"score":0.6339066028594971},{"id":"https://openalex.org/C57869625","wikidata":"https://www.wikidata.org/wiki/Q1783502","display_name":"Rate of convergence","level":3,"score":0.5390369892120361},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5044635534286499},{"id":"https://openalex.org/C163716315","wikidata":"https://www.wikidata.org/wiki/Q901177","display_name":"Gaussian","level":2,"score":0.4899822771549225},{"id":"https://openalex.org/C52740198","wikidata":"https://www.wikidata.org/wiki/Q1539564","display_name":"Importance sampling","level":3,"score":0.48965388536453247},{"id":"https://openalex.org/C132725507","wikidata":"https://www.wikidata.org/wiki/Q39879","display_name":"Monte Carlo integration","level":5,"score":0.4409090578556061},{"id":"https://openalex.org/C178650346","wikidata":"https://www.wikidata.org/wiki/Q201984","display_name":"Covariance","level":2,"score":0.4177306890487671},{"id":"https://openalex.org/C13153151","wikidata":"https://www.wikidata.org/wiki/Q1639846","display_name":"Hybrid Monte Carlo","level":4,"score":0.31767886877059937},{"id":"https://openalex.org/C111350023","wikidata":"https://www.wikidata.org/wiki/Q1191869","display_name":"Markov chain Monte Carlo","level":3,"score":0.2289961278438568},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.20212554931640625},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.1322856843471527},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.07425755262374878},{"id":"https://openalex.org/C31258907","wikidata":"https://www.wikidata.org/wiki/Q1301371","display_name":"Computer network","level":1,"score":0.0},{"id":"https://openalex.org/C127162648","wikidata":"https://www.wikidata.org/wiki/Q16858953","display_name":"Channel (broadcasting)","level":2,"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":1,"locations":[{"id":"doi:10.1137/22m1510121","is_oa":false,"landing_page_url":"https://doi.org/10.1137/22m1510121","pdf_url":null,"source":{"id":"https://openalex.org/S203348814","display_name":"SIAM Journal on Numerical Analysis","issn_l":"0036-1429","issn":["0036-1429","1095-7170"],"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 Journal on Numerical Analysis","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G1735207325","display_name":null,"funder_award_id":"12071154","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G3260297835","display_name":null,"funder_award_id":"2021A1515010275","funder_id":"https://openalex.org/F4320337111","funder_display_name":"Basic and Applied Basic Research Foundation of Guangdong Province"},{"id":"https://openalex.org/G3990281000","display_name":null,"funder_award_id":"202102020407","funder_id":"https://openalex.org/F4320334898","funder_display_name":"Guangzhou Science and Technology Program key projects"},{"id":"https://openalex.org/G4519327660","display_name":null,"funder_award_id":"720711119","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"}],"funders":[{"id":"https://openalex.org/F4320321001","display_name":"National Natural Science Foundation of China","ror":"https://ror.org/01h0zpd94"},{"id":"https://openalex.org/F4320334898","display_name":"Guangzhou Science and Technology Program key projects","ror":"https://ror.org/00tjzgn92"},{"id":"https://openalex.org/F4320337111","display_name":"Basic and Applied Basic Research Foundation of Guangdong Province","ror":null}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":32,"referenced_works":["https://openalex.org/W34142743","https://openalex.org/W39759813","https://openalex.org/W598051755","https://openalex.org/W1533955387","https://openalex.org/W1572757349","https://openalex.org/W1577789187","https://openalex.org/W1862031973","https://openalex.org/W1965440168","https://openalex.org/W1973738368","https://openalex.org/W1976544585","https://openalex.org/W1981512668","https://openalex.org/W1998105223","https://openalex.org/W2006722592","https://openalex.org/W2023711160","https://openalex.org/W2024626809","https://openalex.org/W2090692107","https://openalex.org/W2097511294","https://openalex.org/W2124189866","https://openalex.org/W2124763785","https://openalex.org/W2146299225","https://openalex.org/W2151084831","https://openalex.org/W2153750152","https://openalex.org/W2228579993","https://openalex.org/W2527484249","https://openalex.org/W2751681773","https://openalex.org/W2962757710","https://openalex.org/W2963880462","https://openalex.org/W2964193315","https://openalex.org/W3043749415","https://openalex.org/W3120073684","https://openalex.org/W3125876763","https://openalex.org/W4300580367"],"related_works":["https://openalex.org/W4294677683","https://openalex.org/W590971457","https://openalex.org/W1548972748","https://openalex.org/W4367155567","https://openalex.org/W4327802989","https://openalex.org/W3565757","https://openalex.org/W86393192","https://openalex.org/W2077096961","https://openalex.org/W2949594430","https://openalex.org/W2984753240"],"abstract_inverted_index":{".Importance":[0],"sampling":[1,12,238],"(IS)":[2],"is":[3,25,81,239,276,282,285,331],"valuable":[4],"in":[5,76,159],"reducing":[6],"the":[7,60,78,91,95,101,105,118,144,155,168,177,194,211,233,244,250,254,260,278,287,291,297],"variance":[8,234],"of":[9,42,48,63,104,127,157,204,216,235,246,296,313],"Monte":[10,49,236,314],"Carlo":[11,32,50,237,315],"for":[13,67,130,199,230],"many":[14],"areas,":[15],"including":[16],"finance,":[17],"rare":[18],"event":[19],"simulation,":[20],"and":[21,27,100,266,293,308],"Bayesian":[22],"inference.":[23],"It":[24],"natural":[26],"obvious":[28],"to":[29,37,72,153,175,304],"combine":[30],"quasi-Monte":[31],"(QMC)":[33],"methods":[34],"with":[35,51,70,117,139,316,328,336],"IS":[36,66,79,106,158,212,220,319,327],"achieve":[38],"a":[39,45,73,82,122,140,171,181,214,223],"faster":[40],"rate":[41,252,279],"convergence.":[43],"However,":[44],"naive":[46,311],"replacement":[47,312],"QMC":[52,116,231,317],"may":[53,221],"not":[54,286],"work":[55],"well.":[56],"This":[57,284],"paper":[58],"investigates":[59],"convergence":[61],"rates":[62],"randomized":[64,115],"QMC-based":[65],"estimating":[68],"integrals":[69],"respect":[71],"Gaussian":[74,83,119,208,337],"measure,":[75],"which":[77],"measure":[80,217],"or":[84],"\\(t\\)":[85,141,329],"distribution.":[86],"We":[87,241,299],"prove":[88],"that":[89,167,324,335],"if":[90,289],"target":[92,178],"function":[93,179],"satisfies":[94],"so-called":[96],"boundary":[97],"growth":[98,340],"condition":[99],"covariance":[102],"matrix":[103],"density":[107],"has":[108,121,188,256],"eigenvalues":[109,189],"no":[110],"smaller":[111,190],"than":[112,191,334],"1,":[113,192],"then":[114],"proposal":[120,145],"root":[123],"mean":[124],"squared":[125],"error":[126,251],"\\(O(N^{-1+\\epsilon":[128,280],"})\\)":[129,281],"arbitrarily":[131],"small":[132],"\\(\\epsilon":[133],"\\gt":[134],"0\\)":[135],".":[136],"Similar":[137],"results":[138,322],"distribution":[142],"as":[143,210],"are":[146],"also":[147,242,300],"established.":[148],"These":[149],"sufficient":[150],"conditions":[151],"help":[152],"assess":[154],"effectiveness":[156],"QMC.":[160,200],"For":[161],"some":[162,302],"particular":[163],"applications,":[164],"we":[165],"find":[166],"Laplace":[169,219,326],"IS,":[170],"very":[172],"general":[173],"approach":[174],"approximate":[176],"by":[180,264],"quadratic":[182],"Taylor":[183],"approximation":[184],"around":[185],"its":[186],"mode,":[187],"making":[193],"resulting":[195],"integrand":[196,225,255],"less":[197],"favorable":[198,224],"From":[201],"this":[202],"point":[203],"view,":[205],"when":[206,253],"using":[207,325],"distributions":[209,330],"proposal,":[213],"change":[215],"via":[218],"transform":[222],"into":[226],"an":[227],"unfavorable":[228],"one":[229],"although":[232],"reduced.":[240],"study":[243],"effect":[245],"positivization":[247,262],"tricks":[248],"on":[249],"mixed":[257],"sign.":[258],"If":[259],"smooth":[261],"proposed":[263],"Owen":[265],"Zhou":[267],"(J.":[268],"Amer.":[269],"Statist.":[270],"Assoc.,":[271],"95":[272],"(2000),":[273],"pp.":[274],"135\u2013143)":[275],"used,":[277],"retained.":[283],"case":[288],"taking":[290],"positive":[292],"negative":[294],"parts":[295],"integrand.":[298],"give":[301],"examples":[303],"verify":[305],"our":[306],"propositions":[307],"warn":[309],"against":[310],"under":[318],"proposals.":[320],"Numerical":[321],"suggest":[323],"more":[332],"robust":[333],"distributions.Keywordsimportance":[338],"samplingboundary":[339],"conditionquasi-Monte":[341],"CarloMSC":[342],"codes41A6365D3097N40":[343]},"counts_by_year":[{"year":2025,"cited_by_count":3},{"year":2024,"cited_by_count":4},{"year":2023,"cited_by_count":1}],"updated_date":"2026-04-09T08:11:56.329763","created_date":"2025-10-10T00:00:00"}