{"id":"https://openalex.org/W4407158071","doi":"https://doi.org/10.1007/s11222-025-10569-y","title":"Anisotropic multidimensional smoothing using Bayesian tensor product P-splines","display_name":"Anisotropic multidimensional smoothing using Bayesian tensor product P-splines","publication_year":2025,"publication_date":"2025-02-05","ids":{"openalex":"https://openalex.org/W4407158071","doi":"https://doi.org/10.1007/s11222-025-10569-y"},"language":"en","primary_location":{"id":"doi:10.1007/s11222-025-10569-y","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s11222-025-10569-y","pdf_url":"https://link.springer.com/content/pdf/10.1007/s11222-025-10569-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":["crossref"],"open_access":{"is_oa":true,"oa_status":"hybrid","oa_url":"https://link.springer.com/content/pdf/10.1007/s11222-025-10569-y.pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5070548654","display_name":"Paul Bach","orcid":null},"institutions":[{"id":"https://openalex.org/I200332995","display_name":"TU Dortmund University","ror":"https://ror.org/01k97gp34","country_code":"DE","type":"education","lineage":["https://openalex.org/I200332995"]}],"countries":["DE"],"is_corresponding":true,"raw_author_name":"Paul Bach","raw_affiliation_strings":["Department of Statistics, TU Dortmund University, Dortmund, Germany"],"affiliations":[{"raw_affiliation_string":"Department of Statistics, TU Dortmund University, Dortmund, Germany","institution_ids":["https://openalex.org/I200332995"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5009563869","display_name":"Nadja Klein","orcid":"https://orcid.org/0000-0002-5072-5347"},"institutions":[{"id":"https://openalex.org/I102335020","display_name":"Karlsruhe Institute of Technology","ror":"https://ror.org/04t3en479","country_code":"DE","type":"education","lineage":["https://openalex.org/I102335020","https://openalex.org/I1305996414"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Nadja Klein","raw_affiliation_strings":["Scientific Computing Center, Karlsruhe Institute of Technology, Zirkel 2, 76131, Karlsruhe, Germany"],"affiliations":[{"raw_affiliation_string":"Scientific Computing Center, Karlsruhe Institute of Technology, Zirkel 2, 76131, Karlsruhe, Germany","institution_ids":["https://openalex.org/I102335020"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5070548654"],"corresponding_institution_ids":["https://openalex.org/I200332995"],"apc_list":{"value":2090,"currency":"EUR","value_usd":2690},"apc_paid":{"value":2090,"currency":"EUR","value_usd":2690},"fwci":0.0,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":{"value":0.01340485,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"35","issue":"2","first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10688","display_name":"Image and Signal Denoising Methods","score":0.9908000230789185,"subfield":{"id":"https://openalex.org/subfields/1707","display_name":"Computer Vision and Pattern Recognition"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T10688","display_name":"Image and Signal Denoising Methods","score":0.9908000230789185,"subfield":{"id":"https://openalex.org/subfields/1707","display_name":"Computer Vision and Pattern Recognition"},"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/T10136","display_name":"Statistical Methods and Inference","score":0.9837999939918518,"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/T10052","display_name":"Medical Image Segmentation Techniques","score":0.9830999970436096,"subfield":{"id":"https://openalex.org/subfields/1707","display_name":"Computer Vision and Pattern Recognition"},"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/tensor-product","display_name":"Tensor product","score":0.6970374584197998},{"id":"https://openalex.org/keywords/smoothing","display_name":"Smoothing","score":0.6404019594192505},{"id":"https://openalex.org/keywords/bayesian-probability","display_name":"Bayesian probability","score":0.5863139629364014},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5750436782836914},{"id":"https://openalex.org/keywords/anisotropy","display_name":"Anisotropy","score":0.4879316985607147},{"id":"https://openalex.org/keywords/tensor","display_name":"Tensor (intrinsic definition)","score":0.47989094257354736},{"id":"https://openalex.org/keywords/product","display_name":"Product (mathematics)","score":0.41746723651885986},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.4033302068710327},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.38589638471603394},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.38248106837272644},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.35698872804641724},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.2830876111984253},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.19446909427642822},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.19335824251174927},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.1696615219116211}],"concepts":[{"id":"https://openalex.org/C51255310","wikidata":"https://www.wikidata.org/wiki/Q1163016","display_name":"Tensor product","level":2,"score":0.6970374584197998},{"id":"https://openalex.org/C3770464","wikidata":"https://www.wikidata.org/wiki/Q775963","display_name":"Smoothing","level":2,"score":0.6404019594192505},{"id":"https://openalex.org/C107673813","wikidata":"https://www.wikidata.org/wiki/Q812534","display_name":"Bayesian probability","level":2,"score":0.5863139629364014},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5750436782836914},{"id":"https://openalex.org/C85725439","wikidata":"https://www.wikidata.org/wiki/Q466686","display_name":"Anisotropy","level":2,"score":0.4879316985607147},{"id":"https://openalex.org/C155281189","wikidata":"https://www.wikidata.org/wiki/Q3518150","display_name":"Tensor (intrinsic definition)","level":2,"score":0.47989094257354736},{"id":"https://openalex.org/C90673727","wikidata":"https://www.wikidata.org/wiki/Q901718","display_name":"Product (mathematics)","level":2,"score":0.41746723651885986},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.4033302068710327},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.38589638471603394},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.38248106837272644},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.35698872804641724},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.2830876111984253},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.19446909427642822},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.19335824251174927},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.1696615219116211},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1007/s11222-025-10569-y","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s11222-025-10569-y","pdf_url":"https://link.springer.com/content/pdf/10.1007/s11222-025-10569-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"}],"best_oa_location":{"id":"doi:10.1007/s11222-025-10569-y","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s11222-025-10569-y","pdf_url":"https://link.springer.com/content/pdf/10.1007/s11222-025-10569-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":[{"id":"https://openalex.org/G5040929572","display_name":null,"funder_award_id":"KL 3037/1-1","funder_id":"https://openalex.org/F4320320879","funder_display_name":"Deutsche Forschungsgemeinschaft"}],"funders":[{"id":"https://openalex.org/F4320320879","display_name":"Deutsche Forschungsgemeinschaft","ror":"https://ror.org/018mejw64"}],"has_content":{"grobid_xml":false,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4407158071.pdf"},"referenced_works_count":29,"referenced_works":["https://openalex.org/W32980360","https://openalex.org/W143236119","https://openalex.org/W1487825358","https://openalex.org/W1967247922","https://openalex.org/W2004900635","https://openalex.org/W2027505483","https://openalex.org/W2033279096","https://openalex.org/W2045293965","https://openalex.org/W2119047368","https://openalex.org/W2119160928","https://openalex.org/W2133785255","https://openalex.org/W2143339960","https://openalex.org/W2145514150","https://openalex.org/W2177956663","https://openalex.org/W2422618169","https://openalex.org/W2577537660","https://openalex.org/W2593046461","https://openalex.org/W2745428954","https://openalex.org/W2904813270","https://openalex.org/W2913257349","https://openalex.org/W2920804790","https://openalex.org/W2949227737","https://openalex.org/W2962683904","https://openalex.org/W2962890976","https://openalex.org/W3100886760","https://openalex.org/W3122629187","https://openalex.org/W4211049957","https://openalex.org/W4301014524","https://openalex.org/W4399569435"],"related_works":["https://openalex.org/W1978572805","https://openalex.org/W2383807498","https://openalex.org/W1997992934","https://openalex.org/W1987225439","https://openalex.org/W4238188170","https://openalex.org/W2125114371","https://openalex.org/W2019977573","https://openalex.org/W4386687603","https://openalex.org/W4307007469","https://openalex.org/W4288558775"],"abstract_inverted_index":{"Abstract":[0],"We":[1,125,141],"introduce":[2],"a":[3,37,48],"highly":[4],"efficient":[5,113],"fully":[6],"Bayesian":[7],"approach":[8,146],"for":[9,56,69,83,98,121,129],"anisotropic":[10],"multidimensional":[11],"smoothing.":[12],"The":[13],"main":[14],"challenge":[15],"in":[16,150,153],"this":[17,73,77],"context":[18],"is":[19],"the":[20,28,57,84,122,151],"Markov":[21],"chain":[22],"Monte":[23],"Carlo":[24],"(MCMC)":[25],"update":[26],"of":[27,59,155],"smoothing":[29,123],"parameters":[30],"as":[31],"their":[32],"full":[33],"conditional":[34],"posterior":[35],"comprises":[36],"pseudo-determinant":[38],"that":[39,143],"appears":[40],"to":[41,104,109,134],"be":[42],"intractable":[43],"at":[44],"first":[45,88],"sight.":[46],"As":[47],"consequence,":[49],"existing":[50],"implementations":[51],"are":[52,96],"computationally":[53],"feasible":[54],"only":[55],"estimation":[58],"two-dimensional":[60],"tensor":[61],"product":[62],"smooths,":[63],"which":[64,106],"is,":[65],"however,":[66],"too":[67],"restrictive":[68],"many":[70],"applications.":[71],"In":[72],"paper,":[74],"we":[75],"break":[76],"barrier":[78],"and":[79,86,89,101,132,137,158,161],"derive":[80,126],"closed-form":[81],"expressions":[82,95],"log-pseudo-determinant":[85],"its":[87,163],"second":[90],"order":[91],"partial":[92],"derivatives.":[93],"These":[94],"valid":[97],"arbitrary":[99],"dimension":[100],"very":[102],"fast":[103],"evaluate,":[105],"allows":[107],"us":[108],"set":[110],"up":[111],"an":[112,166],"MCMC":[114],"sampler":[115],"with":[116],"derivative-based":[117],"Metropolis\u2013Hastings":[118],"(MH)":[119],"updates":[120],"parameters.":[124],"simple":[127],"formulas":[128],"low-dimensional":[130],"slices":[131],"averages":[133],"facilitate":[135],"visualization":[136],"investigate":[138],"hyperprior":[139],"sensitivity.":[140],"show":[142],"our":[144],"new":[145],"outperforms":[147],"previous":[148],"suggestions":[149],"literature":[152],"terms":[154],"accuracy,":[156],"scalability":[157],"computational":[159],"cost":[160],"demonstrate":[162],"applicability":[164],"through":[165],"illustrating":[167],"temperature":[168],"data":[169],"example":[170],"from":[171],"spatio-temporal":[172],"statistics.":[173]},"counts_by_year":[],"updated_date":"2026-03-11T06:11:40.159057","created_date":"2025-10-10T00:00:00"}
