{"id":"https://openalex.org/W2117155780","doi":"https://doi.org/10.3390/e17063898","title":"General Hyperplane Prior Distributions Based on Geometric Invariances for Bayesian Multivariate Linear Regression","display_name":"General Hyperplane Prior Distributions Based on Geometric Invariances for Bayesian Multivariate Linear Regression","publication_year":2015,"publication_date":"2015-06-10","ids":{"openalex":"https://openalex.org/W2117155780","doi":"https://doi.org/10.3390/e17063898","mag":"2117155780"},"language":"en","primary_location":{"id":"doi:10.3390/e17063898","is_oa":true,"landing_page_url":"https://doi.org/10.3390/e17063898","pdf_url":"https://www.mdpi.com/1099-4300/17/6/3898/pdf?version=1433931213","source":{"id":"https://openalex.org/S195231649","display_name":"Entropy","issn_l":"1099-4300","issn":["1099-4300"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Entropy","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://www.mdpi.com/1099-4300/17/6/3898/pdf?version=1433931213","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5024026339","display_name":"U. von Toussaint","orcid":"https://orcid.org/0000-0002-8867-1014"},"institutions":[{"id":"https://openalex.org/I4210139716","display_name":"Max Planck Institute for Plasma Physics","ror":"https://ror.org/03taest98","country_code":"DE","type":"facility","lineage":["https://openalex.org/I149899117","https://openalex.org/I4210139716"]}],"countries":["DE"],"is_corresponding":true,"raw_author_name":"Udo Von Toussaint","raw_affiliation_strings":["Max-Planck-Institute for Plasmaphysics, Boltzmannstrasse 2, 85748 Garching, Germany"],"raw_orcid":"https://orcid.org/0000-0002-8867-1014","affiliations":[{"raw_affiliation_string":"Max-Planck-Institute for Plasmaphysics, Boltzmannstrasse 2, 85748 Garching, Germany","institution_ids":["https://openalex.org/I4210139716"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5024026339"],"corresponding_institution_ids":["https://openalex.org/I4210139716"],"apc_list":{"value":2000,"currency":"CHF","value_usd":2165},"apc_paid":{"value":2000,"currency":"CHF","value_usd":2165},"fwci":1.0219,"has_fulltext":true,"cited_by_count":5,"citation_normalized_percentile":{"value":0.79187067,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":96},"biblio":{"volume":"17","issue":"6","first_page":"3898","last_page":"3912"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11871","display_name":"Advanced Statistical Methods and Models","score":0.9966999888420105,"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/T11871","display_name":"Advanced Statistical Methods and Models","score":0.9966999888420105,"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":0.9955000281333923,"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"}},{"id":"https://openalex.org/T10770","display_name":"Soil Geostatistics and Mapping","score":0.988099992275238,"subfield":{"id":"https://openalex.org/subfields/2305","display_name":"Environmental Engineering"},"field":{"id":"https://openalex.org/fields/23","display_name":"Environmental Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/hyperplane","display_name":"Hyperplane","score":0.8591020107269287},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.744907557964325},{"id":"https://openalex.org/keywords/multivariate-statistics","display_name":"Multivariate statistics","score":0.7144716382026672},{"id":"https://openalex.org/keywords/bayesian-multivariate-linear-regression","display_name":"Bayesian multivariate linear regression","score":0.6458653807640076},{"id":"https://openalex.org/keywords/invariant","display_name":"Invariant (physics)","score":0.5353501439094543},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.48519662022590637},{"id":"https://openalex.org/keywords/multivariate-normal-distribution","display_name":"Multivariate normal distribution","score":0.48409807682037354},{"id":"https://openalex.org/keywords/prior-probability","display_name":"Prior probability","score":0.47440478205680847},{"id":"https://openalex.org/keywords/distribution","display_name":"Distribution (mathematics)","score":0.4622516334056854},{"id":"https://openalex.org/keywords/bayesian-probability","display_name":"Bayesian probability","score":0.4287962317466736},{"id":"https://openalex.org/keywords/linear-regression","display_name":"Linear regression","score":0.40040475130081177},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.2918504774570465},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.26876071095466614},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.22213691473007202}],"concepts":[{"id":"https://openalex.org/C68693459","wikidata":"https://www.wikidata.org/wiki/Q657586","display_name":"Hyperplane","level":2,"score":0.8591020107269287},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.744907557964325},{"id":"https://openalex.org/C161584116","wikidata":"https://www.wikidata.org/wiki/Q1952580","display_name":"Multivariate statistics","level":2,"score":0.7144716382026672},{"id":"https://openalex.org/C64946054","wikidata":"https://www.wikidata.org/wiki/Q4874476","display_name":"Bayesian multivariate linear regression","level":3,"score":0.6458653807640076},{"id":"https://openalex.org/C190470478","wikidata":"https://www.wikidata.org/wiki/Q2370229","display_name":"Invariant (physics)","level":2,"score":0.5353501439094543},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.48519662022590637},{"id":"https://openalex.org/C177384507","wikidata":"https://www.wikidata.org/wiki/Q1149000","display_name":"Multivariate normal distribution","level":3,"score":0.48409807682037354},{"id":"https://openalex.org/C177769412","wikidata":"https://www.wikidata.org/wiki/Q278090","display_name":"Prior probability","level":3,"score":0.47440478205680847},{"id":"https://openalex.org/C110121322","wikidata":"https://www.wikidata.org/wiki/Q865811","display_name":"Distribution (mathematics)","level":2,"score":0.4622516334056854},{"id":"https://openalex.org/C107673813","wikidata":"https://www.wikidata.org/wiki/Q812534","display_name":"Bayesian probability","level":2,"score":0.4287962317466736},{"id":"https://openalex.org/C48921125","wikidata":"https://www.wikidata.org/wiki/Q10861030","display_name":"Linear regression","level":2,"score":0.40040475130081177},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.2918504774570465},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.26876071095466614},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.22213691473007202},{"id":"https://openalex.org/C37914503","wikidata":"https://www.wikidata.org/wiki/Q156495","display_name":"Mathematical physics","level":1,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.3390/e17063898","is_oa":true,"landing_page_url":"https://doi.org/10.3390/e17063898","pdf_url":"https://www.mdpi.com/1099-4300/17/6/3898/pdf?version=1433931213","source":{"id":"https://openalex.org/S195231649","display_name":"Entropy","issn_l":"1099-4300","issn":["1099-4300"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Entropy","raw_type":"journal-article"},{"id":"pmh:oai:doaj.org/article:eccfddce2493419286df3041335e4a5f","is_oa":false,"landing_page_url":"https://doaj.org/article/eccfddce2493419286df3041335e4a5f","pdf_url":null,"source":{"id":"https://openalex.org/S4306401280","display_name":"DOAJ (DOAJ: Directory of Open Access Journals)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Entropy, Vol 17, Iss 6, Pp 3898-3912 (2015)","raw_type":"article"},{"id":"pmh:oai:mdpi.com:/1099-4300/17/6/3898/","is_oa":true,"landing_page_url":"http://dx.doi.org/10.3390/e17063898","pdf_url":null,"source":{"id":"https://openalex.org/S4306400947","display_name":"MDPI (MDPI AG)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I4210097602","host_organization_name":"Multidisciplinary Digital Publishing Institute (Switzerland)","host_organization_lineage":["https://openalex.org/I4210097602"],"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":"Entropy","raw_type":"Text"}],"best_oa_location":{"id":"doi:10.3390/e17063898","is_oa":true,"landing_page_url":"https://doi.org/10.3390/e17063898","pdf_url":"https://www.mdpi.com/1099-4300/17/6/3898/pdf?version=1433931213","source":{"id":"https://openalex.org/S195231649","display_name":"Entropy","issn_l":"1099-4300","issn":["1099-4300"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Entropy","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2117155780.pdf","grobid_xml":"https://content.openalex.org/works/W2117155780.grobid-xml"},"referenced_works_count":13,"referenced_works":["https://openalex.org/W191167826","https://openalex.org/W2020494710","https://openalex.org/W2100495367","https://openalex.org/W2145339207","https://openalex.org/W2154500048","https://openalex.org/W2156273867","https://openalex.org/W2157714590","https://openalex.org/W2294604761","https://openalex.org/W2493977830","https://openalex.org/W3015217870","https://openalex.org/W3088091123","https://openalex.org/W4249186015","https://openalex.org/W4249230118"],"related_works":["https://openalex.org/W2606692828","https://openalex.org/W4309298396","https://openalex.org/W2074089485","https://openalex.org/W2378624038","https://openalex.org/W2140265721","https://openalex.org/W2348421592","https://openalex.org/W3199622279","https://openalex.org/W3035695858","https://openalex.org/W2349373437","https://openalex.org/W2349542682"],"abstract_inverted_index":{"Based":[0],"on":[1],"geometric":[2],"invariance":[3],"properties,":[4],"we":[5],"derive":[6],"an":[7],"explicit":[8],"prior":[9,24,52],"distribution":[10,33,53],"for":[11],"the":[12,20,41,55],"parameters":[13],"of":[14,22,34,44],"multivariate":[15],"linear":[16],"regression":[17],"problems":[18],"in":[19,37,63],"absence":[21],"further":[23],"information.":[25],"The":[26,50],"problem":[27],"is":[28,48],"formulated":[29],"as":[30],"a":[31],"rotationally-invariant":[32],"\\(L\\)-dimensional":[35],"hyperplanes":[36],"\\(N\\)":[38],"dimensions,":[39],"and":[40],"associated":[42],"system":[43],"partial":[45],"differential":[46],"equations":[47],"solved.":[49],"derived":[51],"generalizes":[54],"already":[56],"known":[57],"special":[58],"cases,":[59],"e.g.,":[60],"2D":[61],"plane":[62],"three":[64],"dimensions.":[65]},"counts_by_year":[{"year":2023,"cited_by_count":1},{"year":2021,"cited_by_count":1},{"year":2016,"cited_by_count":1},{"year":2015,"cited_by_count":2}],"updated_date":"2026-05-21T06:26:12.895304","created_date":"2025-10-10T00:00:00"}