{"id":"https://openalex.org/W2006714754","doi":"https://doi.org/10.1109/isit.2013.6620615","title":"Some worst-case bounds for Bayesian estimators of discrete distributions","display_name":"Some worst-case bounds for Bayesian estimators of discrete distributions","publication_year":2013,"publication_date":"2013-07-01","ids":{"openalex":"https://openalex.org/W2006714754","doi":"https://doi.org/10.1109/isit.2013.6620615","mag":"2006714754"},"language":"en","primary_location":{"id":"doi:10.1109/isit.2013.6620615","is_oa":false,"landing_page_url":"https://doi.org/10.1109/isit.2013.6620615","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2013 IEEE International Symposium on Information Theory","raw_type":"proceedings-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/A5022350775","display_name":"Steffen Schober","orcid":null},"institutions":[{"id":"https://openalex.org/I196349391","display_name":"Universit\u00e4t Ulm","ror":"https://ror.org/032000t02","country_code":"DE","type":"education","lineage":["https://openalex.org/I196349391"]}],"countries":["DE"],"is_corresponding":true,"raw_author_name":"Steffen Schober","raw_affiliation_strings":["Institute of Communications Engineering, Ulm University, Ulm, Germany","Institute of Communication Engineering, Ulm University, Ulm, Germany"],"affiliations":[{"raw_affiliation_string":"Institute of Communications Engineering, Ulm University, Ulm, Germany","institution_ids":["https://openalex.org/I196349391"]},{"raw_affiliation_string":"Institute of Communication Engineering, Ulm University, Ulm, Germany","institution_ids":["https://openalex.org/I196349391"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5022350775"],"corresponding_institution_ids":["https://openalex.org/I196349391"],"apc_list":null,"apc_paid":null,"fwci":1.6066,"has_fulltext":false,"cited_by_count":10,"citation_normalized_percentile":{"value":0.84254348,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":97},"biblio":{"volume":"73","issue":null,"first_page":"2194","last_page":"2198"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10136","display_name":"Statistical Methods and Inference","score":0.9972000122070312,"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":0.9972000122070312,"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/T12072","display_name":"Machine Learning and Algorithms","score":0.9933000206947327,"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/T11901","display_name":"Bayesian Methods and Mixture Models","score":0.9923999905586243,"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/estimator","display_name":"Estimator","score":0.6908543109893799},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5015392303466797},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.4614379107952118},{"id":"https://openalex.org/keywords/distribution","display_name":"Distribution (mathematics)","score":0.4506974518299103},{"id":"https://openalex.org/keywords/bayesian-probability","display_name":"Bayesian probability","score":0.44759753346443176},{"id":"https://openalex.org/keywords/entropy","display_name":"Entropy (arrow of time)","score":0.43963223695755005},{"id":"https://openalex.org/keywords/dirichlet-distribution","display_name":"Dirichlet distribution","score":0.4374198019504547},{"id":"https://openalex.org/keywords/cardinality","display_name":"Cardinality (data modeling)","score":0.42569872736930847},{"id":"https://openalex.org/keywords/probability-distribution","display_name":"Probability distribution","score":0.4153427481651306},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.40055012702941895},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.3882863521575928},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.37419021129608154},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.3722105622291565},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.342486709356308},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.31392115354537964},{"id":"https://openalex.org/keywords/data-mining","display_name":"Data mining","score":0.120623379945755},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.1161891520023346},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.11601468920707703}],"concepts":[{"id":"https://openalex.org/C185429906","wikidata":"https://www.wikidata.org/wiki/Q1130160","display_name":"Estimator","level":2,"score":0.6908543109893799},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5015392303466797},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.4614379107952118},{"id":"https://openalex.org/C110121322","wikidata":"https://www.wikidata.org/wiki/Q865811","display_name":"Distribution (mathematics)","level":2,"score":0.4506974518299103},{"id":"https://openalex.org/C107673813","wikidata":"https://www.wikidata.org/wiki/Q812534","display_name":"Bayesian probability","level":2,"score":0.44759753346443176},{"id":"https://openalex.org/C106301342","wikidata":"https://www.wikidata.org/wiki/Q4117933","display_name":"Entropy (arrow of time)","level":2,"score":0.43963223695755005},{"id":"https://openalex.org/C169214877","wikidata":"https://www.wikidata.org/wiki/Q981016","display_name":"Dirichlet distribution","level":3,"score":0.4374198019504547},{"id":"https://openalex.org/C87117476","wikidata":"https://www.wikidata.org/wiki/Q362383","display_name":"Cardinality (data modeling)","level":2,"score":0.42569872736930847},{"id":"https://openalex.org/C149441793","wikidata":"https://www.wikidata.org/wiki/Q200726","display_name":"Probability distribution","level":2,"score":0.4153427481651306},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.40055012702941895},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.3882863521575928},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.37419021129608154},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.3722105622291565},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.342486709356308},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.31392115354537964},{"id":"https://openalex.org/C124101348","wikidata":"https://www.wikidata.org/wiki/Q172491","display_name":"Data mining","level":1,"score":0.120623379945755},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.1161891520023346},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.11601468920707703},{"id":"https://openalex.org/C182310444","wikidata":"https://www.wikidata.org/wiki/Q1332643","display_name":"Boundary value problem","level":2,"score":0.0},{"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:10.1109/isit.2013.6620615","is_oa":false,"landing_page_url":"https://doi.org/10.1109/isit.2013.6620615","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2013 IEEE International Symposium on Information Theory","raw_type":"proceedings-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":17,"referenced_works":["https://openalex.org/W1999120268","https://openalex.org/W2000163531","https://openalex.org/W2006681603","https://openalex.org/W2018891628","https://openalex.org/W2055403763","https://openalex.org/W2079715053","https://openalex.org/W2097173970","https://openalex.org/W2101985079","https://openalex.org/W2122882636","https://openalex.org/W2147962921","https://openalex.org/W2183235533","https://openalex.org/W2478708596","https://openalex.org/W2914447735","https://openalex.org/W2989661724","https://openalex.org/W4214636178","https://openalex.org/W6674669923","https://openalex.org/W6678323213"],"related_works":["https://openalex.org/W2002177687","https://openalex.org/W2058438338","https://openalex.org/W2019471580","https://openalex.org/W2941284322","https://openalex.org/W4224920876","https://openalex.org/W2168299207","https://openalex.org/W2124475651","https://openalex.org/W2585354854","https://openalex.org/W2064478620","https://openalex.org/W4308671316"],"abstract_inverted_index":{"Let":[0],"P":[1,42,54,144,156,216],"be":[2,76,96],"a":[3,8,16,34,92,123,194,214],"distribution":[4,41,83,155,215],"taking":[5],"values":[6],"in":[7,109,235],"finite":[9],"set":[10],"X":[11,23,29],"with":[12,160,184],"cardinality":[13],"K.":[14,236],"Given":[15],"sample":[17],"(X":[18],"<sub":[19,24,30,149,222],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"":[20,25,31,150,163,187,223],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">1</sub>":[21,151,224],",":[22,27,189],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">2</sub>":[26],"...,":[28],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">n</sub>":[32],")":[33],"fundamental":[35],"problem":[36],"is":[37,198,209,212,226],"to":[38,143],"estimate":[39],"the":[40,68,80,134,173,203,206,219],"and":[43,55,107,136,145,175],"its":[44],"entropy":[45,100],"H(P).":[46],"In":[47,111,127],"practical":[48],"applications":[49],"often":[50],"Bayesian":[51,120],"estimators":[52,121,132],"of":[53],"H(P)":[56],"are":[57],"used":[58],"as":[59,65,102,168],"they":[60],"may":[61],"give":[62,115],"better":[63,73],"results":[64,118],"for":[66,99,119,153],"example":[67],"maximum":[69],"likelihood":[70],"estimator.":[71],"The":[72],"performance":[74],"can":[75,95,139],"achieved":[77],"by":[78,104],"choosing":[79,91],"right":[81],"prior":[82,94,138,177,208],"on":[84,88],"all":[85],"possible":[86],"distributions":[87],"X.":[89],"But":[90],"wrong":[93],"disastrous,":[97],"especially":[98],"estimation,":[101],"demonstrated":[103],"Nemenman,":[105],"Shafee,":[106],"Bialek":[108],"2001.":[110],"this":[112,178],"work":[113],"we":[114,129],"asymptotic":[116],"worst-case":[117],"using":[122,133],"symmetric":[124],"Dirichlet":[125],"prior.":[126],"particular,":[128],"show":[130],"that":[131,201,218],"Laplace":[135,204],"Jeffrey":[137,207],"get":[140],"arbitrarily":[141],"close":[142],"H":[146],"(in":[147],"L":[148,221],"sense)":[152],"any":[154],"if":[157,181,202,231],"n":[158,169,182,232],"scales":[159,183,233],"K":[161,185],"<sup":[162,186],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">3/2+\u03b4</sup>":[164],",\u03b4":[165],">":[166,191],"0":[167],"\u2192":[170],"\u221e.":[171],"For":[172],"Perks":[174],"Minimax":[176],"holds":[179],"even":[180],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">1+\u03b4</sup>":[188],"\u03b4":[190],"0.":[192],"As":[193],"negative":[195],"result":[196],"it":[197],"further":[199],"shown":[200],"or":[205],"used,":[210],"there":[211],"always":[213],"such":[217],"expected":[220],"distance":[225],"bounded":[227],"away":[228],"from":[229],"zero":[230],"linear":[234]},"counts_by_year":[{"year":2021,"cited_by_count":1},{"year":2020,"cited_by_count":1},{"year":2018,"cited_by_count":1},{"year":2017,"cited_by_count":2},{"year":2015,"cited_by_count":3},{"year":2014,"cited_by_count":2}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
