{"id":"https://openalex.org/W4220815390","doi":"https://doi.org/10.3390/e24040492","title":"Estimation of the Covariance Matrix in Hierarchical Bayesian Spatio-Temporal Modeling via Dimension Expansion","display_name":"Estimation of the Covariance Matrix in Hierarchical Bayesian Spatio-Temporal Modeling via Dimension Expansion","publication_year":2022,"publication_date":"2022-03-31","ids":{"openalex":"https://openalex.org/W4220815390","doi":"https://doi.org/10.3390/e24040492","pmid":"https://pubmed.ncbi.nlm.nih.gov/35455155"},"language":"en","primary_location":{"id":"doi:10.3390/e24040492","is_oa":true,"landing_page_url":"https://doi.org/10.3390/e24040492","pdf_url":"https://www.mdpi.com/1099-4300/24/4/492/pdf?version=1648721760","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","pubmed"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://www.mdpi.com/1099-4300/24/4/492/pdf?version=1648721760","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5103071701","display_name":"Bin Sun","orcid":"https://orcid.org/0000-0001-7057-8471"},"institutions":[{"id":"https://openalex.org/I192455969","display_name":"York University","ror":"https://ror.org/05fq50484","country_code":"CA","type":"education","lineage":["https://openalex.org/I192455969"]}],"countries":["CA"],"is_corresponding":false,"raw_author_name":"Bin Sun","raw_affiliation_strings":["Department of Mathematics and Statistics, York University, Toronto, ON M3J 1P3, Canada","Department of Mathematics and Statistics, York University, Toronto, ON M3J 1P3, Canada;"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics and Statistics, York University, Toronto, ON M3J 1P3, Canada","institution_ids":["https://openalex.org/I192455969"]},{"raw_affiliation_string":"Department of Mathematics and Statistics, York University, Toronto, ON M3J 1P3, Canada;","institution_ids":["https://openalex.org/I192455969"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5091325082","display_name":"Yuehua Wu","orcid":"https://orcid.org/0000-0002-8858-1289"},"institutions":[{"id":"https://openalex.org/I192455969","display_name":"York University","ror":"https://ror.org/05fq50484","country_code":"CA","type":"education","lineage":["https://openalex.org/I192455969"]}],"countries":["CA"],"is_corresponding":true,"raw_author_name":"Yuehua Wu","raw_affiliation_strings":["Department of Mathematics and Statistics, York University, Toronto, ON M3J 1P3, Canada","Department of Mathematics and Statistics, York University, Toronto, ON M3J 1P3, Canada;"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics and Statistics, York University, Toronto, ON M3J 1P3, Canada","institution_ids":["https://openalex.org/I192455969"]},{"raw_affiliation_string":"Department of Mathematics and Statistics, York University, Toronto, ON M3J 1P3, Canada;","institution_ids":["https://openalex.org/I192455969"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5091325082"],"corresponding_institution_ids":["https://openalex.org/I192455969"],"apc_list":{"value":2000,"currency":"CHF","value_usd":2165},"apc_paid":{"value":2000,"currency":"CHF","value_usd":2165},"fwci":0.1674,"has_fulltext":true,"cited_by_count":2,"citation_normalized_percentile":{"value":0.4030066,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":94},"biblio":{"volume":"24","issue":"4","first_page":"492","last_page":"492"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12120","display_name":"Air Quality Monitoring and Forecasting","score":0.9983999729156494,"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"}},"topics":[{"id":"https://openalex.org/T12120","display_name":"Air Quality Monitoring and Forecasting","score":0.9983999729156494,"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"}},{"id":"https://openalex.org/T10190","display_name":"Air Quality and Health Impacts","score":0.9977999925613403,"subfield":{"id":"https://openalex.org/subfields/2307","display_name":"Health, Toxicology and Mutagenesis"},"field":{"id":"https://openalex.org/fields/23","display_name":"Environmental Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T12095","display_name":"Vehicle emissions and performance","score":0.996999979019165,"subfield":{"id":"https://openalex.org/subfields/2203","display_name":"Automotive Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/covariance","display_name":"Covariance","score":0.639999508857727},{"id":"https://openalex.org/keywords/covariance-matrix","display_name":"Covariance matrix","score":0.6270822882652283},{"id":"https://openalex.org/keywords/dimension","display_name":"Dimension (graph theory)","score":0.5548567771911621},{"id":"https://openalex.org/keywords/missing-data","display_name":"Missing data","score":0.503875195980072},{"id":"https://openalex.org/keywords/bayesian-probability","display_name":"Bayesian probability","score":0.45773059129714966},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.4563009440898895},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.45053642988204956},{"id":"https://openalex.org/keywords/entropy","display_name":"Entropy (arrow of time)","score":0.44845694303512573},{"id":"https://openalex.org/keywords/estimation-of-covariance-matrices","display_name":"Estimation of covariance matrices","score":0.4269248843193054},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.42118653655052185},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.3894052505493164},{"id":"https://openalex.org/keywords/statistical-physics","display_name":"Statistical physics","score":0.3470109701156616},{"id":"https://openalex.org/keywords/data-mining","display_name":"Data mining","score":0.3399510979652405},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.28533828258514404}],"concepts":[{"id":"https://openalex.org/C178650346","wikidata":"https://www.wikidata.org/wiki/Q201984","display_name":"Covariance","level":2,"score":0.639999508857727},{"id":"https://openalex.org/C185142706","wikidata":"https://www.wikidata.org/wiki/Q1134404","display_name":"Covariance matrix","level":2,"score":0.6270822882652283},{"id":"https://openalex.org/C33676613","wikidata":"https://www.wikidata.org/wiki/Q13415176","display_name":"Dimension (graph theory)","level":2,"score":0.5548567771911621},{"id":"https://openalex.org/C9357733","wikidata":"https://www.wikidata.org/wiki/Q6878417","display_name":"Missing data","level":2,"score":0.503875195980072},{"id":"https://openalex.org/C107673813","wikidata":"https://www.wikidata.org/wiki/Q812534","display_name":"Bayesian probability","level":2,"score":0.45773059129714966},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.4563009440898895},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.45053642988204956},{"id":"https://openalex.org/C106301342","wikidata":"https://www.wikidata.org/wiki/Q4117933","display_name":"Entropy (arrow of time)","level":2,"score":0.44845694303512573},{"id":"https://openalex.org/C180877172","wikidata":"https://www.wikidata.org/wiki/Q5401390","display_name":"Estimation of covariance matrices","level":3,"score":0.4269248843193054},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.42118653655052185},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.3894052505493164},{"id":"https://openalex.org/C121864883","wikidata":"https://www.wikidata.org/wiki/Q677916","display_name":"Statistical physics","level":1,"score":0.3470109701156616},{"id":"https://openalex.org/C124101348","wikidata":"https://www.wikidata.org/wiki/Q172491","display_name":"Data mining","level":1,"score":0.3399510979652405},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.28533828258514404},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.0}],"mesh":[],"locations_count":5,"locations":[{"id":"doi:10.3390/e24040492","is_oa":true,"landing_page_url":"https://doi.org/10.3390/e24040492","pdf_url":"https://www.mdpi.com/1099-4300/24/4/492/pdf?version=1648721760","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":"pmid:35455155","is_oa":false,"landing_page_url":"https://pubmed.ncbi.nlm.nih.gov/35455155","pdf_url":null,"source":{"id":"https://openalex.org/S4306525036","display_name":"PubMed","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1299303238","host_organization_name":"National Institutes of Health","host_organization_lineage":["https://openalex.org/I1299303238"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Entropy (Basel, Switzerland)","raw_type":null},{"id":"pmh:oai:doaj.org/article:d9ecd996cfa04036b7d915f19ede2d91","is_oa":true,"landing_page_url":"https://doaj.org/article/d9ecd996cfa04036b7d915f19ede2d91","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":"cc-by-sa","license_id":"https://openalex.org/licenses/cc-by-sa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Entropy, Vol 24, Iss 4, p 492 (2022)","raw_type":"article"},{"id":"pmh:oai:mdpi.com:/1099-4300/24/4/492/","is_oa":true,"landing_page_url":"https://dx.doi.org/10.3390/e24040492","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; Volume 24; Issue 4; Pages: 492","raw_type":"Text"},{"id":"pmh:oai:pubmedcentral.nih.gov:9024874","is_oa":true,"landing_page_url":"https://www.ncbi.nlm.nih.gov/pmc/articles/9024874","pdf_url":null,"source":{"id":"https://openalex.org/S2764455111","display_name":"PubMed Central","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1299303238","host_organization_name":"National Institutes of Health","host_organization_lineage":["https://openalex.org/I1299303238"],"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 (Basel)","raw_type":"Text"}],"best_oa_location":{"id":"doi:10.3390/e24040492","is_oa":true,"landing_page_url":"https://doi.org/10.3390/e24040492","pdf_url":"https://www.mdpi.com/1099-4300/24/4/492/pdf?version=1648721760","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":[{"id":"https://metadata.un.org/sdg/15","score":0.5799999833106995,"display_name":"Life in Land"}],"awards":[],"funders":[],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4220815390.pdf","grobid_xml":"https://content.openalex.org/works/W4220815390.grobid-xml"},"referenced_works_count":10,"referenced_works":["https://openalex.org/W1573124210","https://openalex.org/W1824796321","https://openalex.org/W1982262289","https://openalex.org/W2004777611","https://openalex.org/W2047411924","https://openalex.org/W2058726491","https://openalex.org/W2172960773","https://openalex.org/W2326628520","https://openalex.org/W3164505946","https://openalex.org/W4293244076"],"related_works":["https://openalex.org/W2126916073","https://openalex.org/W2921280830","https://openalex.org/W2887132723","https://openalex.org/W2572601863","https://openalex.org/W2038723318","https://openalex.org/W1679731869","https://openalex.org/W1670628120","https://openalex.org/W3041177925","https://openalex.org/W2886934452","https://openalex.org/W2024369332"],"abstract_inverted_index":{"Ozone":[0],"concentrations":[1,10,40,135],"are":[2],"key":[3],"indicators":[4],"of":[5,30,47,146],"air":[6],"quality.":[7],"Modeling":[8],"ozone":[9,39,134],"is":[11,36,153,164],"challenging":[12],"because":[13],"they":[14],"change":[15],"both":[16],"spatially":[17],"and":[18,90,150,167],"temporally":[19],"with":[20],"complicated":[21],"structures.":[22],"Missing":[23],"data":[24],"bring":[25],"even":[26],"more":[27,165],"difficulties.":[28],"One":[29],"our":[31],"interests":[32],"in":[33,41,44,75,139],"this":[34],"paper":[35],"to":[37,61,106,112,119,132],"model":[38,105],"a":[42,52,67,103],"region":[43,142],"the":[45,58,63,73,80,83,121,130,133,140,147,151,161],"presence":[46],"missing":[48],"data.":[49],"We":[50],"propose":[51],"method":[53,70,131,149,163],"without":[54],"any":[55],"assumptions":[56],"on":[57,79,102],"correlation":[59],"structure":[60],"estimate":[62],"covariance":[64],"matrix":[65],"through":[66,155],"dimension":[68],"expansion":[69],"for":[71],"modeling":[72,87],"semivariograms":[74],"nonstationary":[76],"fields":[77],"based":[78,101],"estimations":[81],"from":[82],"hierarchical":[84],"Bayesian":[85],"spatio-temporal":[86],"technique":[88],"(Le":[89],"Zidek).":[91],"Further,":[92],"we":[93,128],"apply":[94,129],"an":[95],"entropy":[96,116],"criterion":[97,117],"(Jin":[98],"et":[99],"al.)":[100],"predictive":[104],"decide":[107],"if":[108],"new":[109],"stations":[110,138],"need":[111],"be":[113],"added.":[114],"This":[115],"helps":[118],"solve":[120],"environmental":[122],"network":[123],"design":[124],"problem.":[125],"For":[126],"demonstration,":[127],"at":[136],"25":[137],"Pittsburgh":[141],"studied.":[143],"The":[144],"comparison":[145],"proposed":[148,162],"one":[152],"provided":[154],"leave-one-out":[156],"cross-validation,":[157],"which":[158],"shows":[159],"that":[160],"general":[166],"applicable.":[168]},"counts_by_year":[{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":1}],"updated_date":"2026-06-20T20:08:15.867695","created_date":"2025-10-10T00:00:00"}