{"id":"https://openalex.org/W1877880381","doi":"https://doi.org/10.1007/s11222-016-9649-y","title":"Comparison of Bayesian predictive methods for model selection","display_name":"Comparison of Bayesian predictive methods for model selection","publication_year":2016,"publication_date":"2016-04-07","ids":{"openalex":"https://openalex.org/W1877880381","doi":"https://doi.org/10.1007/s11222-016-9649-y","mag":"1877880381"},"language":"en","primary_location":{"id":"doi:10.1007/s11222-016-9649-y","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s11222-016-9649-y","pdf_url":"https://link.springer.com/content/pdf/10.1007%2Fs11222-016-9649-y.pdf","source":{"id":"https://openalex.org/S5437875","display_name":"Statistics and Computing","issn_l":"0960-3174","issn":["0960-3174","1573-1375"],"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":"Statistics and Computing","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%2Fs11222-016-9649-y.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5010412497","display_name":"Juho Piironen","orcid":"https://orcid.org/0000-0002-0784-8835"},"institutions":[{"id":"https://openalex.org/I9927081","display_name":"Aalto University","ror":"https://ror.org/020hwjq30","country_code":"FI","type":"education","lineage":["https://openalex.org/I9927081"]},{"id":"https://openalex.org/I32943570","display_name":"Helsinki Institute for Information Technology","ror":"https://ror.org/05kph4940","country_code":"FI","type":"facility","lineage":["https://openalex.org/I133731052","https://openalex.org/I32943570","https://openalex.org/I9927081"]}],"countries":["FI"],"is_corresponding":true,"raw_author_name":"Juho Piironen","raw_affiliation_strings":["Helsinki Institute for Information Technology HIIT, Department of Computer Science, Aalto University, Espoo, Finland"],"affiliations":[{"raw_affiliation_string":"Helsinki Institute for Information Technology HIIT, Department of Computer Science, Aalto University, Espoo, Finland","institution_ids":["https://openalex.org/I32943570","https://openalex.org/I9927081"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5047269552","display_name":"Aki Vehtari","orcid":"https://orcid.org/0000-0003-2164-9469"},"institutions":[{"id":"https://openalex.org/I32943570","display_name":"Helsinki Institute for Information Technology","ror":"https://ror.org/05kph4940","country_code":"FI","type":"facility","lineage":["https://openalex.org/I133731052","https://openalex.org/I32943570","https://openalex.org/I9927081"]},{"id":"https://openalex.org/I9927081","display_name":"Aalto University","ror":"https://ror.org/020hwjq30","country_code":"FI","type":"education","lineage":["https://openalex.org/I9927081"]}],"countries":["FI"],"is_corresponding":false,"raw_author_name":"Aki Vehtari","raw_affiliation_strings":["Helsinki Institute for Information Technology HIIT, Department of Computer Science, Aalto University, Espoo, Finland"],"affiliations":[{"raw_affiliation_string":"Helsinki Institute for Information Technology HIIT, Department of Computer Science, Aalto University, Espoo, Finland","institution_ids":["https://openalex.org/I32943570","https://openalex.org/I9927081"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5010412497"],"corresponding_institution_ids":["https://openalex.org/I32943570","https://openalex.org/I9927081"],"apc_list":{"value":2090,"currency":"EUR","value_usd":2690},"apc_paid":{"value":2090,"currency":"EUR","value_usd":2690},"fwci":31.8556,"has_fulltext":true,"cited_by_count":326,"citation_normalized_percentile":{"value":0.99744979,"is_in_top_1_percent":true,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":94,"max":100},"biblio":{"volume":"27","issue":"3","first_page":"711","last_page":"735"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10243","display_name":"Statistical Methods and Bayesian Inference","score":0.9955999851226807,"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":0.9955999851226807,"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/T10136","display_name":"Statistical Methods and Inference","score":0.9915000200271606,"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":0.9902999997138977,"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/overfitting","display_name":"Overfitting","score":0.8846254348754883},{"id":"https://openalex.org/keywords/model-selection","display_name":"Model selection","score":0.7418090105056763},{"id":"https://openalex.org/keywords/selection","display_name":"Selection (genetic algorithm)","score":0.6646355390548706},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.6196454763412476},{"id":"https://openalex.org/keywords/bayesian-probability","display_name":"Bayesian probability","score":0.5752289295196533},{"id":"https://openalex.org/keywords/machine-learning","display_name":"Machine learning","score":0.524125874042511},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.4867730140686035},{"id":"https://openalex.org/keywords/information-criteria","display_name":"Information Criteria","score":0.47529637813568115},{"id":"https://openalex.org/keywords/cross-validation","display_name":"Cross-validation","score":0.460757315158844},{"id":"https://openalex.org/keywords/bayesian-information-criterion","display_name":"Bayesian information criterion","score":0.4365254044532776},{"id":"https://openalex.org/keywords/variance","display_name":"Variance (accounting)","score":0.42320311069488525},{"id":"https://openalex.org/keywords/bayesian-inference","display_name":"Bayesian inference","score":0.41309696435928345},{"id":"https://openalex.org/keywords/data-mining","display_name":"Data mining","score":0.35976582765579224},{"id":"https://openalex.org/keywords/artificial-neural-network","display_name":"Artificial neural network","score":0.08999350666999817}],"concepts":[{"id":"https://openalex.org/C22019652","wikidata":"https://www.wikidata.org/wiki/Q331309","display_name":"Overfitting","level":3,"score":0.8846254348754883},{"id":"https://openalex.org/C93959086","wikidata":"https://www.wikidata.org/wiki/Q6888345","display_name":"Model selection","level":2,"score":0.7418090105056763},{"id":"https://openalex.org/C81917197","wikidata":"https://www.wikidata.org/wiki/Q628760","display_name":"Selection (genetic algorithm)","level":2,"score":0.6646355390548706},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.6196454763412476},{"id":"https://openalex.org/C107673813","wikidata":"https://www.wikidata.org/wiki/Q812534","display_name":"Bayesian probability","level":2,"score":0.5752289295196533},{"id":"https://openalex.org/C119857082","wikidata":"https://www.wikidata.org/wiki/Q2539","display_name":"Machine learning","level":1,"score":0.524125874042511},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.4867730140686035},{"id":"https://openalex.org/C2776709221","wikidata":"https://www.wikidata.org/wiki/Q6031040","display_name":"Information Criteria","level":3,"score":0.47529637813568115},{"id":"https://openalex.org/C27181475","wikidata":"https://www.wikidata.org/wiki/Q541014","display_name":"Cross-validation","level":2,"score":0.460757315158844},{"id":"https://openalex.org/C168136583","wikidata":"https://www.wikidata.org/wiki/Q1988242","display_name":"Bayesian information criterion","level":2,"score":0.4365254044532776},{"id":"https://openalex.org/C196083921","wikidata":"https://www.wikidata.org/wiki/Q7915758","display_name":"Variance (accounting)","level":2,"score":0.42320311069488525},{"id":"https://openalex.org/C160234255","wikidata":"https://www.wikidata.org/wiki/Q812535","display_name":"Bayesian inference","level":3,"score":0.41309696435928345},{"id":"https://openalex.org/C124101348","wikidata":"https://www.wikidata.org/wiki/Q172491","display_name":"Data mining","level":1,"score":0.35976582765579224},{"id":"https://openalex.org/C50644808","wikidata":"https://www.wikidata.org/wiki/Q192776","display_name":"Artificial neural network","level":2,"score":0.08999350666999817},{"id":"https://openalex.org/C144133560","wikidata":"https://www.wikidata.org/wiki/Q4830453","display_name":"Business","level":0,"score":0.0},{"id":"https://openalex.org/C121955636","wikidata":"https://www.wikidata.org/wiki/Q4116214","display_name":"Accounting","level":1,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1007/s11222-016-9649-y","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s11222-016-9649-y","pdf_url":"https://link.springer.com/content/pdf/10.1007%2Fs11222-016-9649-y.pdf","source":{"id":"https://openalex.org/S5437875","display_name":"Statistics and Computing","issn_l":"0960-3174","issn":["0960-3174","1573-1375"],"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":"Statistics and Computing","raw_type":"journal-article"},{"id":"pmh:oai:arXiv.org:1503.08650","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1503.08650","pdf_url":"https://arxiv.org/pdf/1503.08650","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:aaltodoc.aalto.fi:123456789/25209","is_oa":true,"landing_page_url":"https://research.aalto.fi/en/publications/14563119-44cc-4aa9-b0c5-1ffbf1191323","pdf_url":null,"source":{"id":"https://openalex.org/S4306401663","display_name":"Aaltodoc (Aalto University)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I9927081","host_organization_name":"Aalto University","host_organization_lineage":["https://openalex.org/I9927081"],"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":null,"raw_type":"publishedVersion"}],"best_oa_location":{"id":"doi:10.1007/s11222-016-9649-y","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s11222-016-9649-y","pdf_url":"https://link.springer.com/content/pdf/10.1007%2Fs11222-016-9649-y.pdf","source":{"id":"https://openalex.org/S5437875","display_name":"Statistics and Computing","issn_l":"0960-3174","issn":["0960-3174","1573-1375"],"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":"Statistics and Computing","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W1877880381.pdf","grobid_xml":"https://content.openalex.org/works/W1877880381.grobid-xml"},"referenced_works_count":62,"referenced_works":["https://openalex.org/W171292237","https://openalex.org/W1603903339","https://openalex.org/W1851360578","https://openalex.org/W1964804880","https://openalex.org/W1967396577","https://openalex.org/W1968353801","https://openalex.org/W1974315578","https://openalex.org/W1981299323","https://openalex.org/W1986672307","https://openalex.org/W1987223022","https://openalex.org/W1989706328","https://openalex.org/W1999974018","https://openalex.org/W2001994823","https://openalex.org/W2007069447","https://openalex.org/W2013718670","https://openalex.org/W2016219233","https://openalex.org/W2020599875","https://openalex.org/W2026357499","https://openalex.org/W2035035907","https://openalex.org/W2049228615","https://openalex.org/W2057331441","https://openalex.org/W2057765075","https://openalex.org/W2073610283","https://openalex.org/W2085297375","https://openalex.org/W2095827227","https://openalex.org/W2106706098","https://openalex.org/W2107956883","https://openalex.org/W2114169935","https://openalex.org/W2117135012","https://openalex.org/W2118001201","https://openalex.org/W2121943924","https://openalex.org/W2123222757","https://openalex.org/W2127874106","https://openalex.org/W2138936157","https://openalex.org/W2139474805","https://openalex.org/W2141007997","https://openalex.org/W2143684265","https://openalex.org/W2154776925","https://openalex.org/W2157801062","https://openalex.org/W2159347337","https://openalex.org/W2167191085","https://openalex.org/W2201264723","https://openalex.org/W2203714058","https://openalex.org/W2292751606","https://openalex.org/W2400086120","https://openalex.org/W2471967545","https://openalex.org/W2479236352","https://openalex.org/W2536729587","https://openalex.org/W2903900323","https://openalex.org/W2951093352","https://openalex.org/W3014064419","https://openalex.org/W3102998992","https://openalex.org/W3105620286","https://openalex.org/W3106385100","https://openalex.org/W4211177544","https://openalex.org/W4229849994","https://openalex.org/W4229914698","https://openalex.org/W4232632925","https://openalex.org/W4233936754","https://openalex.org/W4239353198","https://openalex.org/W4239966440","https://openalex.org/W4249506491"],"related_works":["https://openalex.org/W2114625140","https://openalex.org/W1968886786","https://openalex.org/W2607006239","https://openalex.org/W2509820422","https://openalex.org/W2963415778","https://openalex.org/W304661108","https://openalex.org/W3122388856","https://openalex.org/W1502087262","https://openalex.org/W2033907215","https://openalex.org/W1556261580"],"abstract_inverted_index":{"The":[0,53,201],"goal":[1],"of":[2,59,158,196,231],"this":[3],"paper":[4],"is":[5,69,87,142,162,169],"to":[6,71,76,93,173,185],"compare":[7],"several":[8,43],"widely":[9],"used":[10],"Bayesian":[11,130],"model":[12,17,119,131,141,161,192,207,223],"selection":[13,18,36,95,176,195,208,225],"methods":[14],"in":[15,80,100,154],"practical":[16],"problems,":[19],"highlight":[20],"their":[21],"differences":[22],"and":[23,39,41,49,98,193,226],"give":[24],"recommendations":[25],"about":[26],"the":[27,33,57,65,81,85,101,105,123,129,135,139,151,156,159,165,181,188,194,197,206,216,222,228,232],"preferred":[28],"approaches.":[29],"We":[30],"focus":[31],"on":[32,178],"variable":[34],"subset":[35],"for":[37,104,118,220],"regression":[38],"classification":[40],"perform":[42],"numerical":[44],"experiments":[45],"using":[46,213],"both":[47,219],"simulated":[48],"real":[50],"world":[51],"data.":[52],"results":[54,113],"show":[55],"that":[56,205],"optimization":[58],"a":[60,109,190],"utility":[61,82],"estimate":[62],"such":[63,127],"as":[64,128],"cross-validation":[66,214],"(CV)":[67],"score":[68],"liable":[70],"finding":[72],"overfitted":[73],"models":[74],"due":[75],"relatively":[77],"high":[78],"variance":[79],"estimates":[83],"when":[84],"data":[86],"scarce.":[88],"This":[89,167],"can":[90,146,209],"also":[91,187,203],"lead":[92],"substantial":[94],"induced":[96],"bias":[97],"optimism":[99],"performance":[102,230],"evaluation":[103],"selected":[106,234],"model.":[107,235],"From":[108],"predictive":[110,229],"viewpoint,":[111],"best":[112],"are":[114],"obtained":[115],"by":[116,121,150],"accounting":[117],"uncertainty":[120],"forming":[122],"full":[124,160],"encompassing":[125,140],"model,":[126],"averaging":[132],"solution":[133],"over":[134],"candidate":[136],"models.":[137],"If":[138],"too":[143],"complex,":[144],"it":[145],"be":[147],"robustly":[148],"simplified":[149],"projection":[152,182],"method,":[153],"which":[155],"information":[157],"projected":[163],"onto":[164],"submodels.":[166],"approach":[168],"substantially":[170],"less":[171],"prone":[172],"overfitting":[174],"than":[175],"based":[177],"CV-score.":[179],"Overall,":[180],"method":[183],"appears":[184],"outperform":[186],"maximum":[189],"posteriori":[191],"most":[198],"probable":[199],"variables.":[200],"study":[202],"demonstrates":[204],"greatly":[210],"benefit":[211],"from":[212],"outside":[215],"searching":[217],"process":[218],"guiding":[221],"size":[224],"assessing":[227],"finally":[233]},"counts_by_year":[{"year":2026,"cited_by_count":10},{"year":2025,"cited_by_count":28},{"year":2024,"cited_by_count":36},{"year":2023,"cited_by_count":36},{"year":2022,"cited_by_count":35},{"year":2021,"cited_by_count":49},{"year":2020,"cited_by_count":43},{"year":2019,"cited_by_count":40},{"year":2018,"cited_by_count":27},{"year":2017,"cited_by_count":11},{"year":2016,"cited_by_count":6},{"year":2015,"cited_by_count":3},{"year":2014,"cited_by_count":2}],"updated_date":"2026-04-03T22:45:19.894376","created_date":"2025-10-10T00:00:00"}