{"id":"https://openalex.org/W7204970588","doi":"https://doi.org/10.48550/arxiv.2608.29154","title":"Stochastic Bayes factors: why, when, and how","display_name":"Stochastic Bayes factors: why, when, and how","publication_year":2026,"publication_date":"2026-08-29","ids":{"openalex":"https://openalex.org/W7204970588","doi":"https://doi.org/10.48550/arxiv.2608.29154"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2608.29154","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2608.29154","pdf_url":"https://arxiv.org/pdf/2608.29154","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},"volume":null,"type":"preprint","is_traditional":true,"indexed_in":["arxiv","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/2608.29154","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5042215192","display_name":"Leonardo Egidi","orcid":"https://orcid.org/0000-0003-3211-905X","observed_orcids":["https://orcid.org/0000-0003-3211-905X"]},"institutions":[{"id":"https://openalex.org/I142444530","display_name":"University of Trieste","ror":"https://ror.org/02n742c10","country_code":"IT","type":"education","lineage":["https://openalex.org/I142444530"]},{"id":"https://openalex.org/I73142707","display_name":"Athens University of Economics and Business","ror":"https://ror.org/03s262162","country_code":"GR","type":"education","lineage":["https://openalex.org/I73142707"]}],"countries":["GR","IT"],"is_corresponding":false,"raw_author_name":"Egidi, Leonardo","raw_affiliation_strings":["Department of Economics, Business, Mathematics, and Statistics \"Bruno de Finetti\" , Via Valerio 4/1D , University of Trieste , Italy","professor of statistics , Department of Statistics , Athens University of Economics and Business , Athens , Greece,"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Economics, Business, Mathematics, and Statistics \"Bruno de Finetti\" , Via Valerio 4/1D , University of Trieste , Italy","institution_ids":["https://openalex.org/I142444530"]},{"raw_affiliation_string":"professor of statistics , Department of Statistics , Athens University of Economics and Business , Athens , Greece,","institution_ids":["https://openalex.org/I73142707"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5062615685","display_name":"Ioannis Ntzoufras","orcid":"https://orcid.org/0000-0002-7615-0334","observed_orcids":["https://orcid.org/0000-0002-7615-0334"]},"institutions":[{"id":"https://openalex.org/I142444530","display_name":"University of Trieste","ror":"https://ror.org/02n742c10","country_code":"IT","type":"education","lineage":["https://openalex.org/I142444530"]},{"id":"https://openalex.org/I73142707","display_name":"Athens University of Economics and Business","ror":"https://ror.org/03s262162","country_code":"GR","type":"education","lineage":["https://openalex.org/I73142707"]}],"countries":["GR","IT"],"is_corresponding":false,"raw_author_name":"Ntzoufras, Ioannis","raw_affiliation_strings":["Department of Statistics , Athens University of Economics and Business , 28is Oktovriou 76 , Athina 104 34 , Greece","associate professor of statistics , Department of Economics, Business, Mathematics, and Statistics \"Bruno de Finetti\" , University of Trieste , Trieste , Italy,"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Statistics , Athens University of Economics and Business , 28is Oktovriou 76 , Athina 104 34 , Greece","institution_ids":["https://openalex.org/I73142707"]},{"raw_affiliation_string":"associate professor of statistics , Department of Economics, Business, Mathematics, and Statistics \"Bruno de Finetti\" , University of Trieste , Trieste , Italy,","institution_ids":["https://openalex.org/I142444530"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":null,"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10243","display_name":"Statistical Methods and Bayesian Inference","score":0.9550999999046326,"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":0.9550999999046326,"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":0.013500000350177288,"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":0.01269999984651804,"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/bayes-factor","display_name":"Bayes factor","score":0.8859999775886536},{"id":"https://openalex.org/keywords/model-selection","display_name":"model selection","score":0.5640000104904175},{"id":"https://openalex.org/keywords/bayesian-hypothesis-testing","display_name":"Bayesian hypothesis testing","score":0.8199999928474426},{"id":"https://openalex.org/keywords/prior-uncertainty","display_name":"prior uncertainty","score":0.4650000035762787},{"id":"https://openalex.org/keywords/improper-priors","display_name":"improper priors","score":0.7540000081062317},{"id":"https://openalex.org/keywords/model-calibration","display_name":"model calibration","score":0.6790000200271606},{"id":"https://openalex.org/keywords/model-consistency","display_name":"model consistency","score":0.6290000081062317},{"id":"https://openalex.org/keywords/model-discrimination","display_name":"model discrimination","score":0.4819999933242798}],"concepts":[{"id":"https://openalex.org/C162376815","wikidata":"https://www.wikidata.org/wiki/Q2158281","display_name":"Frequentist inference","level":4,"score":0.794700026512146},{"id":"https://openalex.org/C142291917","wikidata":"https://www.wikidata.org/wiki/Q4165283","display_name":"Bayes factor","level":4,"score":0.673799991607666},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.6672000288963318},{"id":"https://openalex.org/C63479239","wikidata":"https://www.wikidata.org/wiki/Q7353546","display_name":"Robustness (evolution)","level":3,"score":0.5383999943733215},{"id":"https://openalex.org/C207201462","wikidata":"https://www.wikidata.org/wiki/Q182505","display_name":"Bayes' theorem","level":3,"score":0.5313000082969666},{"id":"https://openalex.org/C107673813","wikidata":"https://www.wikidata.org/wiki/Q812534","display_name":"Bayesian probability","level":2,"score":0.5270000100135803},{"id":"https://openalex.org/C9354725","wikidata":"https://www.wikidata.org/wiki/Q286017","display_name":"Operationalization","level":2,"score":0.4722999930381775},{"id":"https://openalex.org/C119857082","wikidata":"https://www.wikidata.org/wiki/Q2539","display_name":"Machine learning","level":1,"score":0.4253999888896942},{"id":"https://openalex.org/C177769412","wikidata":"https://www.wikidata.org/wiki/Q278090","display_name":"Prior probability","level":3,"score":0.4077000021934509},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.40560001134872437},{"id":"https://openalex.org/C521332185","wikidata":"https://www.wikidata.org/wiki/Q185816","display_name":"Analogy","level":2,"score":0.34790000319480896},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.34709998965263367},{"id":"https://openalex.org/C87007009","wikidata":"https://www.wikidata.org/wiki/Q210832","display_name":"Statistical hypothesis testing","level":2,"score":0.3416000008583069},{"id":"https://openalex.org/C32230216","wikidata":"https://www.wikidata.org/wiki/Q7882499","display_name":"Uncertainty quantification","level":2,"score":0.33239999413490295},{"id":"https://openalex.org/C2778648169","wikidata":"https://www.wikidata.org/wiki/Q967768","display_name":"Compatibility (geochemistry)","level":2,"score":0.33230000734329224},{"id":"https://openalex.org/C160234255","wikidata":"https://www.wikidata.org/wiki/Q812535","display_name":"Bayesian inference","level":3,"score":0.32679998874664307},{"id":"https://openalex.org/C114289077","wikidata":"https://www.wikidata.org/wiki/Q3284399","display_name":"Statistical model","level":2,"score":0.30480000376701355},{"id":"https://openalex.org/C124101348","wikidata":"https://www.wikidata.org/wiki/Q172491","display_name":"Data mining","level":1,"score":0.29490000009536743},{"id":"https://openalex.org/C43214815","wikidata":"https://www.wikidata.org/wiki/Q7310987","display_name":"Reliability (semiconductor)","level":3,"score":0.28700000047683716},{"id":"https://openalex.org/C101112237","wikidata":"https://www.wikidata.org/wiki/Q4874481","display_name":"Bayesian statistics","level":4,"score":0.28380000591278076},{"id":"https://openalex.org/C26517878","wikidata":"https://www.wikidata.org/wiki/Q228039","display_name":"Key (lock)","level":2,"score":0.26739999651908875},{"id":"https://openalex.org/C201729545","wikidata":"https://www.wikidata.org/wiki/Q2193887","display_name":"Reliability theory","level":3,"score":0.25859999656677246},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.2572999894618988},{"id":"https://openalex.org/C2780009758","wikidata":"https://www.wikidata.org/wiki/Q6804172","display_name":"Measure (data warehouse)","level":2,"score":0.2547000050544739}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2608.29154","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2608.29154","pdf_url":"https://arxiv.org/pdf/2608.29154","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},{"id":"doi:10.48550/arxiv.2608.29154","doi":"https://doi.org/10.48550/arxiv.2608.29154","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2608.29154","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:2608.29154","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2608.29154","pdf_url":"https://arxiv.org/pdf/2608.29154","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},"sustainable_development_goals":[],"study_designs":[],"awards":[],"funders":[],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7204970588.pdf","grobid_xml":"https://content.openalex.org/works/W7204970588.grobid-xml"},"referenced_works_count":1,"referenced_works":["https://openalex.org/W2467837763"],"related_works":["https://openalex.org/W2169267068","https://openalex.org/W7212341073","https://openalex.org/W3163707242","https://openalex.org/W2908121737","https://openalex.org/W7095741870","https://openalex.org/W2037737366","https://openalex.org/W4411317181","https://openalex.org/W2164394346","https://openalex.org/W7047858257","https://openalex.org/W1551467651"],"abstract_inverted_index":{"The":[0],"Bayes":[1,72],"factor":[2,73],"(BF)":[3],"is":[4,19,92,145],"a":[5,75,95,121,156,186],"central":[6],"tool":[7,188],"in":[8,50,155],"Bayesian":[9,140],"hypothesis":[10],"testing":[11],"and":[12,35,60,133,166,176],"model":[13,130,153,162,190],"selection,":[14],"yet":[15],"its":[16],"practical":[17],"use":[18],"often":[20],"challenged.":[21],"Classical":[22],"BFs":[23],"depend":[24],"heavily":[25],"on":[26],"prior":[27],"specification,":[28],"cannot":[29],"be":[30],"applied":[31],"with":[32,57],"improper":[33],"priors,":[34],"are":[36],"typically":[37],"interpreted":[38],"through":[39],"arbitrary":[40],"evidence":[41],"scales.":[42],"Moreover,":[43],"they":[44],"fail":[45],"to":[46,54,106,148,180],"capture":[47],"uncertainty":[48,85],"inherent":[49],"the":[51,70,80,90,99,102,150,171,181],"data,":[52],"leading":[53],"an":[55],"analogy":[56],"frequentist":[58],"p-values,":[59],"primarily":[61],"reflect":[62],"prior-predictive":[63],"rather":[64],"than":[65],"posterior-predictive":[66,118],"performance.":[67],"We":[68,124],"introduce":[69],"stochastic":[71],"(SBF),":[74],"new":[76],"framework":[77],"that":[78,107,136,170],"extends":[79],"BF":[81,100],"by":[82,184],"explicitly":[83],"incorporating":[84],"via":[86],"replicated":[87],"data.":[88],"Formally,":[89],"SBF":[91,172],"defined":[93],"as":[94,120],"push-forward":[96],"measure":[97],"transferring":[98],"from":[101],"observed":[103],"data":[104],"space":[105],"of":[108],"replications.":[109],"This":[110],"approach":[111],"generalizes":[112],"previous":[113],"calibration":[114],"proposals,":[115],"while":[116,159],"emphasizing":[117],"replication":[119],"robust":[122],"alternative.":[123],"establish":[125],"key":[126],"theoretical":[127],"properties,":[128],"including":[129],"consistency,":[131],"compatibility":[132],"dominance,":[134],"ensuring":[135],"SBFs":[137],"preserve":[138],"desirable":[139],"guarantees.":[141],"An":[142],"algorithmic":[143],"routine":[144],"then":[146],"proposed":[147],"operationalize":[149],"SBF,":[151],"guiding":[152],"discrimination":[154],"principled":[157],"way":[158],"naturally":[160],"providing":[161,185],"calibration.":[163],"Simulation":[164],"studies":[165],"real":[167],"applications":[168],"confirm":[169],"offers":[173],"improved":[174],"robustness":[175],"predictive":[177],"reliability":[178],"compared":[179],"classical":[182],"BF,":[183],"valuable":[187],"for":[189],"comparison.":[191]},"counts_by_year":[],"updated_date":"2026-11-07T11:25:07.637180","created_date":"2026-09-02T00:00:00"}