{"id":"https://openalex.org/W2306777281","doi":"https://doi.org/10.6339/jds.2008.06(2).401","title":"A Bayesian Approach to Zero-Numerator Problems Using Hierarchical Models","display_name":"A Bayesian Approach to Zero-Numerator Problems Using Hierarchical Models","publication_year":2021,"publication_date":"2021-07-11","ids":{"openalex":"https://openalex.org/W2306777281","doi":"https://doi.org/10.6339/jds.2008.06(2).401","mag":"2306777281"},"language":"en","primary_location":{"id":"doi:10.6339/jds.2008.06(2).401","doi":"https://doi.org/10.6339/jds.2008.06(2).401","is_oa":true,"landing_page_url":"https://doi.org/10.6339/jds.2008.06(2).401","pdf_url":"https://jds-online.org/journal/JDS/article/996/file/pdf","source":{"id":"https://openalex.org/S2764553900","display_name":"Journal of Data Science","issn_l":"1680-743X","issn":["1680-743X","1683-8602"],"is_oa":true,"is_in_doaj":true,"is_core":false,"listed_in":["anvur-scientific","doaj","norway-1"],"host_organization":"https://openalex.org/P4327988825","host_organization_name":"People's University of China","host_organization_lineage":["https://openalex.org/P4327988825"],"host_organization_lineage_names":["People's University of China"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Data Science","raw_type":"journal-article"},"volume":null,"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"diamond","oa_url":"https://jds-online.org/journal/JDS/article/996/file/pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5060889456","display_name":"Zhongxue Chen","orcid":"https://orcid.org/0000-0003-2537-7843","observed_orcids":["https://orcid.org/0000-0003-2537-7843"]},"institutions":[{"id":"https://openalex.org/I178169726","display_name":"Southern Methodist University","ror":"https://ror.org/042tdr378","country_code":"US","type":"education","lineage":["https://openalex.org/I178169726"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Zhongxue Chen","raw_affiliation_strings":["Department of Statistical Science Southern Methodist University 3225 Daniel Avenue P.O. Box 750332 Dallas, Texas 75275, USA","Southern Methodist University"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Statistical Science Southern Methodist University 3225 Daniel Avenue P.O. Box 750332 Dallas, Texas 75275, USA","institution_ids":["https://openalex.org/I178169726"]},{"raw_affiliation_string":"Southern Methodist University","institution_ids":["https://openalex.org/I178169726"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5041148495","display_name":"Monnie McGee","orcid":"https://orcid.org/0000-0001-9150-7832","observed_orcids":["https://orcid.org/0000-0001-9150-7832"]},"institutions":[{"id":"https://openalex.org/I178169726","display_name":"Southern Methodist University","ror":"https://ror.org/042tdr378","country_code":"US","type":"education","lineage":["https://openalex.org/I178169726"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Monnie McGee","raw_affiliation_strings":["Department of Statistical Science Southern Methodist University 3225 Daniel Avenue P.O. Box 750332 Dallas, Texas 75275, USA","Southern Methodist University"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Statistical Science Southern Methodist University 3225 Daniel Avenue P.O. Box 750332 Dallas, Texas 75275, USA","institution_ids":["https://openalex.org/I178169726"]},{"raw_affiliation_string":"Southern Methodist University","institution_ids":["https://openalex.org/I178169726"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I178169726"],"apc_list":null,"apc_paid":null,"fwci":0.3717,"has_fulltext":true,"cited_by_count":16,"citation_normalized_percentile":{"value":0.5578264,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":88,"max":97},"biblio":{"volume":"6","issue":"2","first_page":"261","last_page":"268"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10243","display_name":"Statistical Methods and Bayesian Inference","score":0.7890999913215637,"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/T10243","display_name":"Statistical Methods and Bayesian Inference","score":0.7890999913215637,"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/T10968","display_name":"Statistical Distribution Estimation and Applications","score":0.15860000252723694,"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/T13500","display_name":"Probability and Statistical Research","score":0.03999999910593033,"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/rule-of-three","display_name":"rule of three","score":0.8059999942779541},{"id":"https://openalex.org/keywords/upper-confidence-bound","display_name":"upper confidence bound","score":0.6349999904632568},{"id":"https://openalex.org/keywords/bayesian-hierarchical-model","display_name":"Bayesian hierarchical model","score":0.7120000123977661},{"id":"https://openalex.org/keywords/beta-prior","display_name":"beta prior","score":0.9300000071525574},{"id":"https://openalex.org/keywords/posterior-distribution","display_name":"posterior distribution","score":0.6940000057220459}],"concepts":[{"id":"https://openalex.org/C177769412","wikidata":"https://www.wikidata.org/wiki/Q278090","display_name":"Prior probability","level":3,"score":0.8566051721572876},{"id":"https://openalex.org/C107673813","wikidata":"https://www.wikidata.org/wiki/Q812534","display_name":"Bayesian probability","level":2,"score":0.7452133893966675},{"id":"https://openalex.org/C2780813799","wikidata":"https://www.wikidata.org/wiki/Q3274237","display_name":"Zero (linguistics)","level":2,"score":0.716299831867218},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6501690745353699},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.5571340918540955},{"id":"https://openalex.org/C57830394","wikidata":"https://www.wikidata.org/wiki/Q278079","display_name":"Posterior probability","level":3,"score":0.4904637038707733},{"id":"https://openalex.org/C191413810","wikidata":"https://www.wikidata.org/wiki/Q17100952","display_name":"Bayesian hierarchical modeling","level":4,"score":0.4874587059020996},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.46822497248649597},{"id":"https://openalex.org/C21621910","wikidata":"https://www.wikidata.org/wiki/Q756254","display_name":"Beta distribution","level":2,"score":0.44538843631744385},{"id":"https://openalex.org/C144986985","wikidata":"https://www.wikidata.org/wiki/Q871236","display_name":"Hierarchical database model","level":2,"score":0.41235798597335815},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.36467084288597107},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.35970214009284973},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.3397446274757385},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.33580970764160156},{"id":"https://openalex.org/C160234255","wikidata":"https://www.wikidata.org/wiki/Q812535","display_name":"Bayesian inference","level":3,"score":0.3335091471672058},{"id":"https://openalex.org/C149782125","wikidata":"https://www.wikidata.org/wiki/Q160039","display_name":"Econometrics","level":1,"score":0.32224225997924805},{"id":"https://openalex.org/C124101348","wikidata":"https://www.wikidata.org/wiki/Q172491","display_name":"Data mining","level":1,"score":0.17507687211036682},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.06226751208305359},{"id":"https://openalex.org/C41895202","wikidata":"https://www.wikidata.org/wiki/Q8162","display_name":"Linguistics","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}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.6339/jds.2008.06(2).401","doi":"https://doi.org/10.6339/jds.2008.06(2).401","is_oa":true,"landing_page_url":"https://doi.org/10.6339/jds.2008.06(2).401","pdf_url":"https://jds-online.org/journal/JDS/article/996/file/pdf","source":{"id":"https://openalex.org/S2764553900","display_name":"Journal of Data Science","issn_l":"1680-743X","issn":["1680-743X","1683-8602"],"is_oa":true,"is_in_doaj":true,"is_core":false,"listed_in":["anvur-scientific","doaj","norway-1"],"host_organization":"https://openalex.org/P4327988825","host_organization_name":"People's University of China","host_organization_lineage":["https://openalex.org/P4327988825"],"host_organization_lineage_names":["People's University of China"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Data Science","raw_type":"journal-article"}],"best_oa_location":{"id":"doi:10.6339/jds.2008.06(2).401","doi":"https://doi.org/10.6339/jds.2008.06(2).401","is_oa":true,"landing_page_url":"https://doi.org/10.6339/jds.2008.06(2).401","pdf_url":"https://jds-online.org/journal/JDS/article/996/file/pdf","source":{"id":"https://openalex.org/S2764553900","display_name":"Journal of Data Science","issn_l":"1680-743X","issn":["1680-743X","1683-8602"],"is_oa":true,"is_in_doaj":true,"is_core":false,"listed_in":["anvur-scientific","doaj","norway-1"],"host_organization":"https://openalex.org/P4327988825","host_organization_name":"People's University of China","host_organization_lineage":["https://openalex.org/P4327988825"],"host_organization_lineage_names":["People's University of China"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Data Science","raw_type":"journal-article"},"sustainable_development_goals":[],"study_designs":[],"awards":[],"funders":[],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2306777281.pdf","grobid_xml":"https://content.openalex.org/works/W2306777281.grobid-xml"},"referenced_works_count":7,"referenced_works":["https://openalex.org/W1983311265","https://openalex.org/W2030794561","https://openalex.org/W2041729493","https://openalex.org/W2061003478","https://openalex.org/W4241470522","https://openalex.org/W4256642426","https://openalex.org/W6753645147"],"related_works":["https://openalex.org/W1983311265","https://openalex.org/W3112565331","https://openalex.org/W2796272744","https://openalex.org/W2347359446","https://openalex.org/W1736905758","https://openalex.org/W6944741964","https://openalex.org/W2278514930","https://openalex.org/W2526089277","https://openalex.org/W2571681777","https://openalex.org/W2388260686"],"abstract_inverted_index":{"The":[0],"rule":[1],"of":[2,15],"three":[3],"gives":[4],"3/n":[5],"as":[6,38],"the":[7,12,16,45,48,56],"upper":[8],"95%":[9],"bound":[10,21],"for":[11,47,74],"success":[13],"rate":[14],"zero-numerator":[17,76],"problems.":[18,77],"However,":[19,43],"this":[20,62],"is":[22,28,50],"usu":[23],"ally":[24],"conservative":[25],"although":[26],"it":[27],"useful":[29],"in":[30],"practice.":[31],"Some":[32],"Bayesian":[33],"methods":[34],"with":[35],"beta":[36],"distributions":[37],"priors":[39,49],"have":[40],"been":[41],"studied.":[42],"choosing":[44],"parameters":[46],"subjective":[51],"and":[52],"can":[53],"severely":[54],"impact":[55],"corre":[57],"sponding":[58],"posterior":[59],"distributions.":[60],"In":[61],"paper,":[63],"some":[64],"hierarchical":[65],"models":[66],"are":[67],"proposed,":[68],"which":[69],"provide":[70],"practitioners":[71],"other":[72],"options":[73],"those":[75]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2022,"cited_by_count":2},{"year":2020,"cited_by_count":1},{"year":2017,"cited_by_count":3},{"year":2015,"cited_by_count":3},{"year":2013,"cited_by_count":2},{"year":2012,"cited_by_count":2}],"updated_date":"2026-10-30T12:39:25.321706","created_date":"2016-06-24T00:00:00"}
