{"id":"https://openalex.org/W1964496517","doi":"https://doi.org/10.1109/tsp.2012.2184101","title":"Exact Sample Conditioned MSE Performance of the Bayesian MMSE Estimator for Classification Error\u2014Part I: Representation","display_name":"Exact Sample Conditioned MSE Performance of the Bayesian MMSE Estimator for Classification Error\u2014Part I: Representation","publication_year":2012,"publication_date":"2012-01-12","ids":{"openalex":"https://openalex.org/W1964496517","doi":"https://doi.org/10.1109/tsp.2012.2184101","mag":"1964496517"},"language":"en","primary_location":{"id":"doi:10.1109/tsp.2012.2184101","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tsp.2012.2184101","pdf_url":null,"source":{"id":"https://openalex.org/S168680287","display_name":"IEEE Transactions on Signal Processing","issn_l":"1053-587X","issn":["1053-587X","1941-0476"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319808","host_organization_name":"Institute of Electrical and Electronics Engineers","host_organization_lineage":["https://openalex.org/P4310319808"],"host_organization_lineage_names":["Institute of Electrical and Electronics Engineers"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Transactions on Signal Processing","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5037999551","display_name":"Lori A. Dalton","orcid":"https://orcid.org/0000-0001-8715-5723"},"institutions":[{"id":"https://openalex.org/I91045830","display_name":"Texas A&M University","ror":"https://ror.org/01f5ytq51","country_code":"US","type":"education","lineage":["https://openalex.org/I91045830"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Lori A. Dalton","raw_affiliation_strings":["Department of Electrical and Computer Engineering, Texas A and M University, College Station, TX, USA","Dept. of Electr. & Comput. Eng, Texas A&M Univ., College Station, TX, USA"],"affiliations":[{"raw_affiliation_string":"Department of Electrical and Computer Engineering, Texas A and M University, College Station, TX, USA","institution_ids":["https://openalex.org/I91045830"]},{"raw_affiliation_string":"Dept. of Electr. & Comput. Eng, Texas A&M Univ., College Station, TX, USA","institution_ids":["https://openalex.org/I91045830"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5112221423","display_name":"Edward R. Dougherty","orcid":null},"institutions":[{"id":"https://openalex.org/I1343551460","display_name":"The University of Texas MD Anderson Cancer Center","ror":"https://ror.org/04twxam07","country_code":"US","type":"funder","lineage":["https://openalex.org/I1343551460"]},{"id":"https://openalex.org/I4210104856","display_name":"Phoenix (United States)","ror":"https://ror.org/01ggenr10","country_code":"US","type":"company","lineage":["https://openalex.org/I4210104856"]},{"id":"https://openalex.org/I91045830","display_name":"Texas A&M University","ror":"https://ror.org/01f5ytq51","country_code":"US","type":"education","lineage":["https://openalex.org/I91045830"]},{"id":"https://openalex.org/I1284308235","display_name":"Translational Genomics Research Institute","ror":"https://ror.org/02hfpnk21","country_code":"US","type":"facility","lineage":["https://openalex.org/I1284308235"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Edward R. Dougherty","raw_affiliation_strings":["Computational Biology Division, Translational Genomics Research Institute Phoenix, Phoenix, AZ, USA","Department of Bioinformatics and Computational Biology, University of Texas M.D. Anderson Cancer Center, Houston, TX, USA","Department of Electrical and Computer Engineering, Texas A and M University, College Station, TX, USA","Dept. of Electr. & Comput. Eng, Texas A&M Univ., College Station, TX, USA"],"affiliations":[{"raw_affiliation_string":"Computational Biology Division, Translational Genomics Research Institute Phoenix, Phoenix, AZ, USA","institution_ids":["https://openalex.org/I1284308235","https://openalex.org/I4210104856"]},{"raw_affiliation_string":"Department of Bioinformatics and Computational Biology, University of Texas M.D. Anderson Cancer Center, Houston, TX, USA","institution_ids":["https://openalex.org/I1343551460"]},{"raw_affiliation_string":"Department of Electrical and Computer Engineering, Texas A and M University, College Station, TX, USA","institution_ids":["https://openalex.org/I91045830"]},{"raw_affiliation_string":"Dept. of Electr. & Comput. Eng, Texas A&M Univ., College Station, TX, USA","institution_ids":["https://openalex.org/I91045830"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5037999551"],"corresponding_institution_ids":["https://openalex.org/I91045830"],"apc_list":null,"apc_paid":null,"fwci":8.4116,"has_fulltext":false,"cited_by_count":39,"citation_normalized_percentile":{"value":0.97890947,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":90,"max":99},"biblio":{"volume":"60","issue":"5","first_page":"2575","last_page":"2587"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10136","display_name":"Statistical Methods and Inference","score":0.9944000244140625,"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/T10136","display_name":"Statistical Methods and Inference","score":0.9944000244140625,"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/T12535","display_name":"Machine Learning and Data Classification","score":0.9927999973297119,"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/T12814","display_name":"Gaussian Processes and Bayesian Inference","score":0.9817000031471252,"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/mean-squared-error","display_name":"Mean squared error","score":0.7505062818527222},{"id":"https://openalex.org/keywords/prior-probability","display_name":"Prior probability","score":0.6784322261810303},{"id":"https://openalex.org/keywords/estimator","display_name":"Estimator","score":0.6350677013397217},{"id":"https://openalex.org/keywords/minimum-mean-square-error","display_name":"Minimum mean square error","score":0.607398271560669},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5861383676528931},{"id":"https://openalex.org/keywords/bayesian-probability","display_name":"Bayesian probability","score":0.465457022190094},{"id":"https://openalex.org/keywords/bias-of-an-estimator","display_name":"Bias of an estimator","score":0.4488280117511749},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.4457135498523712},{"id":"https://openalex.org/keywords/pattern-recognition","display_name":"Pattern recognition (psychology)","score":0.4417746067047119},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.3671191930770874},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.35871344804763794},{"id":"https://openalex.org/keywords/minimum-variance-unbiased-estimator","display_name":"Minimum-variance unbiased estimator","score":0.2893611192703247}],"concepts":[{"id":"https://openalex.org/C139945424","wikidata":"https://www.wikidata.org/wiki/Q1940696","display_name":"Mean squared error","level":2,"score":0.7505062818527222},{"id":"https://openalex.org/C177769412","wikidata":"https://www.wikidata.org/wiki/Q278090","display_name":"Prior probability","level":3,"score":0.6784322261810303},{"id":"https://openalex.org/C185429906","wikidata":"https://www.wikidata.org/wiki/Q1130160","display_name":"Estimator","level":2,"score":0.6350677013397217},{"id":"https://openalex.org/C90652560","wikidata":"https://www.wikidata.org/wiki/Q11091747","display_name":"Minimum mean square error","level":3,"score":0.607398271560669},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5861383676528931},{"id":"https://openalex.org/C107673813","wikidata":"https://www.wikidata.org/wiki/Q812534","display_name":"Bayesian probability","level":2,"score":0.465457022190094},{"id":"https://openalex.org/C191393472","wikidata":"https://www.wikidata.org/wiki/Q15222032","display_name":"Bias of an estimator","level":4,"score":0.4488280117511749},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.4457135498523712},{"id":"https://openalex.org/C153180895","wikidata":"https://www.wikidata.org/wiki/Q7148389","display_name":"Pattern recognition (psychology)","level":2,"score":0.4417746067047119},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.3671191930770874},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.35871344804763794},{"id":"https://openalex.org/C165646398","wikidata":"https://www.wikidata.org/wiki/Q3755281","display_name":"Minimum-variance unbiased estimator","level":3,"score":0.2893611192703247}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1109/tsp.2012.2184101","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tsp.2012.2184101","pdf_url":null,"source":{"id":"https://openalex.org/S168680287","display_name":"IEEE Transactions on Signal Processing","issn_l":"1053-587X","issn":["1053-587X","1941-0476"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319808","host_organization_name":"Institute of Electrical and Electronics Engineers","host_organization_lineage":["https://openalex.org/P4310319808"],"host_organization_lineage_names":["Institute of Electrical and Electronics Engineers"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Transactions on Signal Processing","raw_type":"journal-article"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.418.3521","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.418.3521","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://gsp.tamu.edu/Publications/journal-publications/exact-mse-performance-of-the-bayesian-mmse-estimator-for-classification-error-2013-part-ii-performance-analysis-and-applications/files/ieee_mse_ii.pdf","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.418.4287","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.418.4287","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://gsp.tamu.edu/Publications/journal-publications/exact-mse-performance-of-the-bayesian-mmse-estimator-for-classification-error-2013-part-i-representation/files/ieee_mse_i.pdf","raw_type":"text"}],"best_oa_location":null,"sustainable_development_goals":[{"display_name":"Peace, Justice and strong institutions","score":0.5899999737739563,"id":"https://metadata.un.org/sdg/16"}],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":36,"referenced_works":["https://openalex.org/W651097206","https://openalex.org/W659391916","https://openalex.org/W1564947197","https://openalex.org/W1842498742","https://openalex.org/W1965878388","https://openalex.org/W1970886386","https://openalex.org/W1980879760","https://openalex.org/W1995368377","https://openalex.org/W2009778625","https://openalex.org/W2020181407","https://openalex.org/W2026628137","https://openalex.org/W2047458638","https://openalex.org/W2049898120","https://openalex.org/W2057658881","https://openalex.org/W2061122220","https://openalex.org/W2096552892","https://openalex.org/W2104738901","https://openalex.org/W2108806834","https://openalex.org/W2113169045","https://openalex.org/W2127947512","https://openalex.org/W2134258050","https://openalex.org/W2137586026","https://openalex.org/W2143707047","https://openalex.org/W2144285986","https://openalex.org/W2146403040","https://openalex.org/W2152670498","https://openalex.org/W2159638256","https://openalex.org/W2166162270","https://openalex.org/W2315537806","https://openalex.org/W2328425686","https://openalex.org/W2904853484","https://openalex.org/W3015240874","https://openalex.org/W4230803260","https://openalex.org/W4232383088","https://openalex.org/W4300033818","https://openalex.org/W6679784660"],"related_works":["https://openalex.org/W2562263695","https://openalex.org/W2075897667","https://openalex.org/W2015518264","https://openalex.org/W2135187896","https://openalex.org/W2147201983","https://openalex.org/W2795035211","https://openalex.org/W2160108762","https://openalex.org/W1718066205","https://openalex.org/W1513121561","https://openalex.org/W2356451205"],"abstract_inverted_index":{"In":[0,13,107,170],"recent":[1],"years,":[2],"biomedicine":[3],"has":[4,147],"been":[5],"faced":[6],"with":[7,95,104],"difficult":[8],"high-throughput":[9],"small-sample":[10],"classification":[11,94,100],"problems.":[12],"such":[14],"settings,":[15],"classifier":[16,132],"error":[17,37,60,82,137,145,181],"estimation":[18,45,146],"becomes":[19],"a":[20,43,53,58,78,113,148,160],"critical":[21],"issue":[22],"because":[23],"training":[24],"and":[25,98,187],"testing":[26],"must":[27],"be":[28],"done":[29],"on":[30,123],"the":[31,40,48,70,73,118,124,131,135,174,180,189],"same":[32],"data.":[33],"A":[34],"recently":[35],"proposed":[36],"estimator":[38],"places":[39],"problem":[41],"in":[42,47,57,64,77,151],"signal":[44],"framework":[46,155],"presence":[49],"of":[50,72,101,112,127,130,164,173,179],"uncertainty,":[51],"permitting":[52],"rigorous":[54],"solution":[55],"optimal":[56],"minimum-mean-square":[59],"sense.":[61],"The":[62],"uncertainty":[63],"this":[65,108],"model":[66],"is":[67],"relative":[68],"to":[69,81,159,192],"parameters":[71],"feature-label":[74],"distributions,":[75],"resulting":[76],"Bayesian":[79,136,141,144],"approach":[80],"estimation.":[83],"Closed":[84],"form":[85],"solutions":[86],"are":[87],"available":[88],"for":[89,139],"two":[90],"important":[91],"problems:":[92],"discrete":[93],"Dirichlet":[96],"priors":[97],"linear":[99],"Gaussian":[102],"distributions":[103],"normal-inverse-Wishart":[105],"priors.":[106],"work,":[109],"Part":[110,171],"I":[111],"two-part":[114],"study,":[115],"we":[116,176],"introduce":[117],"theoretical":[119],"mean-square-error":[120],"(MSE)":[121],"conditioned":[122],"observed":[125,168],"sample":[126],"any":[128],"estimate":[129],"error,":[133],"including":[134],"estimator,":[138,182],"both":[140],"models.":[142],"Thus,":[143],"unique":[149],"advantage":[150],"that":[152],"its":[153],"mathematical":[154],"naturally":[156],"gives":[157],"rise":[158],"practical":[161],"expected":[162],"measure":[163],"performance":[165],"given":[166],"an":[167],"sample.":[169],"II":[172],"study":[175],"examine":[177],"consistency":[178],"demonstrate":[183],"various":[184],"MSE":[185,191],"properties,":[186],"apply":[188],"conditional":[190],"censored":[193],"sampling.":[194]},"counts_by_year":[{"year":2023,"cited_by_count":1},{"year":2020,"cited_by_count":2},{"year":2019,"cited_by_count":3},{"year":2018,"cited_by_count":2},{"year":2017,"cited_by_count":1},{"year":2015,"cited_by_count":11},{"year":2014,"cited_by_count":2},{"year":2013,"cited_by_count":8},{"year":2012,"cited_by_count":6}],"updated_date":"2026-04-04T16:13:02.066488","created_date":"2025-10-10T00:00:00"}