{"id":"https://openalex.org/W4402604443","doi":"https://doi.org/10.1080/10618600.2024.2404711","title":"Approximate Cross-Validated Mean Estimates for Bayesian Hierarchical Regression Models","display_name":"Approximate Cross-Validated Mean Estimates for Bayesian Hierarchical Regression Models","publication_year":2024,"publication_date":"2024-09-18","ids":{"openalex":"https://openalex.org/W4402604443","doi":"https://doi.org/10.1080/10618600.2024.2404711","pmid":"https://pubmed.ncbi.nlm.nih.gov/40771436"},"language":"en","primary_location":{"id":"doi:10.1080/10618600.2024.2404711","is_oa":true,"landing_page_url":"https://doi.org/10.1080/10618600.2024.2404711","pdf_url":null,"source":{"id":"https://openalex.org/S76159266","display_name":"Journal of Computational and Graphical Statistics","issn_l":"1061-8600","issn":["1061-8600","1537-2715"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320547","host_organization_name":"Taylor & Francis","host_organization_lineage":["https://openalex.org/P4310320547"],"host_organization_lineage_names":["Taylor & Francis"],"type":"journal"},"license":"cc-by-sa","license_id":"https://openalex.org/licenses/cc-by-sa","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Computational and Graphical Statistics","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","pubmed"],"open_access":{"is_oa":true,"oa_status":"hybrid","oa_url":"https://doi.org/10.1080/10618600.2024.2404711","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5016013192","display_name":"A. Q. Zhang","orcid":"https://orcid.org/0000-0002-7086-693X"},"institutions":[{"id":"https://openalex.org/I130769515","display_name":"Pennsylvania State University","ror":"https://ror.org/04p491231","country_code":"US","type":"education","lineage":["https://openalex.org/I130769515"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Amy Zhang","raw_affiliation_strings":["Department of Statistics, The Pennsylvania State University","Department of Statistics, Pennsylvania State University","Department of Statistics, Pennsylvania State University and"],"raw_orcid":"https://orcid.org/0000-0002-7086-693X","affiliations":[{"raw_affiliation_string":"Department of Statistics, The Pennsylvania State University","institution_ids":["https://openalex.org/I130769515"]},{"raw_affiliation_string":"Department of Statistics, Pennsylvania State University","institution_ids":["https://openalex.org/I130769515"]},{"raw_affiliation_string":"Department of Statistics, Pennsylvania State University and","institution_ids":["https://openalex.org/I130769515"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5031529176","display_name":"Michael J. Daniels","orcid":"https://orcid.org/0000-0002-9856-9486"},"institutions":[{"id":"https://openalex.org/I33213144","display_name":"University of Florida","ror":"https://ror.org/02y3ad647","country_code":"US","type":"education","lineage":["https://openalex.org/I33213144"]},{"id":"https://openalex.org/I4210092944","display_name":"Dalian University","ror":"https://ror.org/00g2ypp58","country_code":"CN","type":"education","lineage":["https://openalex.org/I4210092944"]}],"countries":["CN","US"],"is_corresponding":false,"raw_author_name":"Michael J. Daniels","raw_affiliation_strings":["Department of Statistics, University of Florida","Department of Statistics, University of Florida and Changcheng Li School of Mathematical Sciences, Dalian University of Technology and Le Bao Department of Statistics, Pennsylvania State University"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Statistics, University of Florida","institution_ids":["https://openalex.org/I33213144"]},{"raw_affiliation_string":"Department of Statistics, University of Florida and Changcheng Li School of Mathematical Sciences, Dalian University of Technology and Le Bao Department of Statistics, Pennsylvania State University","institution_ids":["https://openalex.org/I4210092944"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5008489600","display_name":"Changcheng Li","orcid":"https://orcid.org/0000-0002-3092-3303"},"institutions":[{"id":"https://openalex.org/I27357992","display_name":"Dalian University of Technology","ror":"https://ror.org/023hj5876","country_code":"CN","type":"education","lineage":["https://openalex.org/I27357992"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Changcheng Li","raw_affiliation_strings":["School of Mathematical Sciences, Dalian University of Technology"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Mathematical Sciences, Dalian University of Technology","institution_ids":["https://openalex.org/I27357992"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5010808240","display_name":"Le Bao","orcid":"https://orcid.org/0000-0003-0191-5918"},"institutions":[{"id":"https://openalex.org/I130769515","display_name":"Pennsylvania State University","ror":"https://ror.org/04p491231","country_code":"US","type":"education","lineage":["https://openalex.org/I130769515"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Le Bao","raw_affiliation_strings":["Department of Statistics, The Pennsylvania State University","Department of Statistics, Pennsylvania State University"],"raw_orcid":"https://orcid.org/0000-0003-0191-5918","affiliations":[{"raw_affiliation_string":"Department of Statistics, The Pennsylvania State University","institution_ids":["https://openalex.org/I130769515"]},{"raw_affiliation_string":"Department of Statistics, Pennsylvania State University","institution_ids":["https://openalex.org/I130769515"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5010808240"],"corresponding_institution_ids":["https://openalex.org/I130769515"],"apc_list":null,"apc_paid":null,"fwci":0.5042,"has_fulltext":true,"cited_by_count":1,"citation_normalized_percentile":{"value":0.67613932,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":94,"max":97},"biblio":{"volume":"34","issue":"2","first_page":"488","last_page":"497"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10136","display_name":"Statistical Methods and Inference","score":0.9995999932289124,"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/T10136","display_name":"Statistical Methods and Inference","score":0.9995999932289124,"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/T10243","display_name":"Statistical Methods and Bayesian Inference","score":0.9988999962806702,"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/T11901","display_name":"Bayesian Methods and Mixture Models","score":0.9979000091552734,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.5434046983718872},{"id":"https://openalex.org/keywords/bayesian-probability","display_name":"Bayesian probability","score":0.5350708961486816},{"id":"https://openalex.org/keywords/regression","display_name":"Regression","score":0.46541380882263184},{"id":"https://openalex.org/keywords/regression-analysis","display_name":"Regression analysis","score":0.45809441804885864},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.4478342831134796},{"id":"https://openalex.org/keywords/bayesian-hierarchical-modeling","display_name":"Bayesian hierarchical modeling","score":0.4226870834827423},{"id":"https://openalex.org/keywords/multilevel-model","display_name":"Multilevel model","score":0.4217481017112732},{"id":"https://openalex.org/keywords/bayesian-linear-regression","display_name":"Bayesian linear regression","score":0.41533300280570984},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.41209501028060913},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.3378240764141083},{"id":"https://openalex.org/keywords/econometrics","display_name":"Econometrics","score":0.3366378843784332},{"id":"https://openalex.org/keywords/bayesian-inference","display_name":"Bayesian inference","score":0.2969876527786255}],"concepts":[{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.5434046983718872},{"id":"https://openalex.org/C107673813","wikidata":"https://www.wikidata.org/wiki/Q812534","display_name":"Bayesian probability","level":2,"score":0.5350708961486816},{"id":"https://openalex.org/C83546350","wikidata":"https://www.wikidata.org/wiki/Q1139051","display_name":"Regression","level":2,"score":0.46541380882263184},{"id":"https://openalex.org/C152877465","wikidata":"https://www.wikidata.org/wiki/Q208042","display_name":"Regression analysis","level":2,"score":0.45809441804885864},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.4478342831134796},{"id":"https://openalex.org/C191413810","wikidata":"https://www.wikidata.org/wiki/Q17100952","display_name":"Bayesian hierarchical modeling","level":4,"score":0.4226870834827423},{"id":"https://openalex.org/C53059260","wikidata":"https://www.wikidata.org/wiki/Q374758","display_name":"Multilevel model","level":2,"score":0.4217481017112732},{"id":"https://openalex.org/C37903108","wikidata":"https://www.wikidata.org/wiki/Q4874474","display_name":"Bayesian linear regression","level":4,"score":0.41533300280570984},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.41209501028060913},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.3378240764141083},{"id":"https://openalex.org/C149782125","wikidata":"https://www.wikidata.org/wiki/Q160039","display_name":"Econometrics","level":1,"score":0.3366378843784332},{"id":"https://openalex.org/C160234255","wikidata":"https://www.wikidata.org/wiki/Q812535","display_name":"Bayesian inference","level":3,"score":0.2969876527786255}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1080/10618600.2024.2404711","is_oa":true,"landing_page_url":"https://doi.org/10.1080/10618600.2024.2404711","pdf_url":null,"source":{"id":"https://openalex.org/S76159266","display_name":"Journal of Computational and Graphical Statistics","issn_l":"1061-8600","issn":["1061-8600","1537-2715"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320547","host_organization_name":"Taylor & Francis","host_organization_lineage":["https://openalex.org/P4310320547"],"host_organization_lineage_names":["Taylor & Francis"],"type":"journal"},"license":"cc-by-sa","license_id":"https://openalex.org/licenses/cc-by-sa","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Computational and Graphical Statistics","raw_type":"journal-article"},{"id":"pmid:40771436","is_oa":false,"landing_page_url":"https://pubmed.ncbi.nlm.nih.gov/40771436","pdf_url":null,"source":{"id":"https://openalex.org/S4306525036","display_name":"PubMed","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1299303238","host_organization_name":"National Institutes of Health","host_organization_lineage":["https://openalex.org/I1299303238"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of computational and graphical statistics : a joint publication of American Statistical Association, Institute of Mathematical Statistics, Interface Foundation of North America","raw_type":null},{"id":"pmh:oai:pubmedcentral.nih.gov:12327438","is_oa":true,"landing_page_url":"https://www.ncbi.nlm.nih.gov/pmc/articles/12327438","pdf_url":"https://pmc.ncbi.nlm.nih.gov/articles/PMC12327438/pdf/nihms-2025082.pdf","source":{"id":"https://openalex.org/S2764455111","display_name":"PubMed Central","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1299303238","host_organization_name":"National Institutes of Health","host_organization_lineage":["https://openalex.org/I1299303238"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by-sa","license_id":"https://openalex.org/licenses/cc-by-sa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"J Comput Graph Stat","raw_type":"Text"}],"best_oa_location":{"id":"doi:10.1080/10618600.2024.2404711","is_oa":true,"landing_page_url":"https://doi.org/10.1080/10618600.2024.2404711","pdf_url":null,"source":{"id":"https://openalex.org/S76159266","display_name":"Journal of Computational and Graphical Statistics","issn_l":"1061-8600","issn":["1061-8600","1537-2715"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320547","host_organization_name":"Taylor & Francis","host_organization_lineage":["https://openalex.org/P4310320547"],"host_organization_lineage_names":["Taylor & Francis"],"type":"journal"},"license":"cc-by-sa","license_id":"https://openalex.org/licenses/cc-by-sa","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Computational and Graphical Statistics","raw_type":"journal-article"},"sustainable_development_goals":[{"id":"https://metadata.un.org/sdg/13","score":0.47999998927116394,"display_name":"Climate action"}],"awards":[{"id":"https://openalex.org/G160003332","display_name":null,"funder_award_id":"R01AI136664","funder_id":"https://openalex.org/F4320332161","funder_display_name":"National Institutes of Health"},{"id":"https://openalex.org/G2365518779","display_name":null,"funder_award_id":"R56AI120812-01A1","funder_id":"https://openalex.org/F4320332161","funder_display_name":"National Institutes of Health"},{"id":"https://openalex.org/G2544398089","display_name":null,"funder_award_id":"R01 HL158963","funder_id":"https://openalex.org/F4320337338","funder_display_name":"National Heart, Lung, and Blood Institute"},{"id":"https://openalex.org/G3929892274","display_name":null,"funder_award_id":"R01AI170249","funder_id":"https://openalex.org/F4320332161","funder_display_name":"National Institutes of Health"},{"id":"https://openalex.org/G4664904886","display_name":null,"funder_award_id":"R56 AI120812","funder_id":"https://openalex.org/F4320337355","funder_display_name":"National Institute of Allergy and Infectious Diseases"},{"id":"https://openalex.org/G5142011116","display_name":null,"funder_award_id":"R01HL158963","funder_id":"https://openalex.org/F4320332161","funder_display_name":"National Institutes of Health"},{"id":"https://openalex.org/G5778208618","display_name":null,"funder_award_id":"R01 AI170249","funder_id":"https://openalex.org/F4320337355","funder_display_name":"National Institute of Allergy and Infectious Diseases"},{"id":"https://openalex.org/G604344734","display_name":null,"funder_award_id":"R01 HL166324","funder_id":"https://openalex.org/F4320337338","funder_display_name":"National Heart, Lung, and Blood Institute"},{"id":"https://openalex.org/G8962555888","display_name":null,"funder_award_id":"R01 AI136664","funder_id":"https://openalex.org/F4320337355","funder_display_name":"National Institute of Allergy and Infectious Diseases"}],"funders":[{"id":"https://openalex.org/F4320332161","display_name":"National Institutes of Health","ror":"https://ror.org/01cwqze88"},{"id":"https://openalex.org/F4320337338","display_name":"National Heart, Lung, and Blood Institute","ror":"https://ror.org/012pb6c26"},{"id":"https://openalex.org/F4320337355","display_name":"National Institute of Allergy and Infectious Diseases","ror":"https://ror.org/043z4tv69"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":33,"referenced_works":["https://openalex.org/W136174036","https://openalex.org/W1536497620","https://openalex.org/W1545319692","https://openalex.org/W1851360578","https://openalex.org/W1981552604","https://openalex.org/W1982585616","https://openalex.org/W2014581807","https://openalex.org/W2044645601","https://openalex.org/W2050551672","https://openalex.org/W2090373435","https://openalex.org/W2101756511","https://openalex.org/W2112995480","https://openalex.org/W2115067168","https://openalex.org/W2128709328","https://openalex.org/W2144898279","https://openalex.org/W2150847344","https://openalex.org/W2160624840","https://openalex.org/W2168016523","https://openalex.org/W2169762407","https://openalex.org/W2577537660","https://openalex.org/W2756421408","https://openalex.org/W2803543245","https://openalex.org/W2903718010","https://openalex.org/W2911352402","https://openalex.org/W2980880174","https://openalex.org/W3036840984","https://openalex.org/W3102024356","https://openalex.org/W3104887532","https://openalex.org/W4252268551","https://openalex.org/W4399608067","https://openalex.org/W4399648311","https://openalex.org/W6635963195","https://openalex.org/W6755603394"],"related_works":["https://openalex.org/W2121035573","https://openalex.org/W786367546","https://openalex.org/W4220780651","https://openalex.org/W3119278052","https://openalex.org/W4281746790","https://openalex.org/W1579935274","https://openalex.org/W3175939413","https://openalex.org/W186208444","https://openalex.org/W4214773488","https://openalex.org/W2032094637"],"abstract_inverted_index":{"We":[0,77,129],"introduce":[1],"a":[2,44,86],"novel":[3],"procedure":[4],"for":[5,10,19,65,74,114,155],"obtaining":[6],"cross-validated":[7],"predictive":[8,50],"estimates":[9,124],"Bayesian":[11],"hierarchical":[12],"regression":[13],"models":[14,115],"(BHRMs).":[15],"BHRMs":[16],"are":[17],"popular":[18],"modeling":[20],"complex":[21,117],"dependence":[22],"structures":[23],"(e.g.,":[24],"Gaussian":[25,28],"processes":[26],"and":[27,69,88,104,143,146,159],"Markov":[29],"random":[30],"fields)":[31],"but":[32],"can":[33],"be":[34],"computationally":[35,61],"expensive":[36],"to":[37,47,59,85,101,126],"run.":[38],"Cross-validation":[39],"(CV)":[40],"is,":[41],"therefore,":[42],"not":[43],"common":[45],"practice":[46],"evaluate":[48],"the":[49,57,79,95,107,134,148],"performance":[51,150],"of":[52,109,136],"BHRMs.":[53,76],"Our":[54,98],"method":[55,138],"circumvents":[56],"need":[58],"rerun":[60],"costly":[62],"estimation":[63],"methods":[64,154],"each":[66],"cross-validation":[67],"fold":[68],"makes":[70],"CV":[71,80,103,156],"more":[72,112],"feasible":[73],"large":[75],"shift":[78],"problem":[81,91],"from":[82],"probability-based":[83],"sampling":[84],"familiar":[87],"straightforward":[89],"optimization":[90],"by":[92],"conditioning":[93],"on":[94,139],"variance-covariance":[96],"parameters.":[97],"approximation":[99],"applies":[100],"leave-one-out":[102],"leave-one-cluster-out":[105],"CV,":[106],"latter":[108],"which":[110],"is":[111],"appropriate":[113],"with":[116,151],"dependencies.":[118],"In":[119],"many":[120],"cases,":[121],"this":[122],"produces":[123],"equivalent":[125],"full":[127],"CV.":[128],"provide":[130],"theoretical":[131],"results,":[132],"demonstrate":[133],"efficacy":[135],"our":[137],"publicly":[140],"available":[141,163],"data":[142],"in":[144],"simulations,":[145],"compare":[147],"model":[149],"several":[152],"competing":[153],"approximation.":[157],"Code":[158],"other":[160],"supplementary":[161],"materials":[162],"online.":[164]},"counts_by_year":[{"year":2026,"cited_by_count":1}],"updated_date":"2026-07-27T08:26:11.824852","created_date":"2025-10-10T00:00:00"}
