{"id":"https://openalex.org/W225101284","doi":null,"title":"Aspects of Exchangeable Partitions and Trees","display_name":"Aspects of Exchangeable Partitions and Trees","publication_year":2011,"publication_date":"2011-01-01","ids":{"openalex":"https://openalex.org/W225101284","mag":"225101284"},"language":"en","primary_location":{"id":"pmh:oai:escholarship.org/ark:/13030/qt5419p8xt","doi":null,"is_oa":true,"landing_page_url":"https://escholarship.org/uc/item/5419p8xt","pdf_url":"https://escholarship.org/uc/item/5419p8xt","source":{"id":"https://openalex.org/S4306400115","display_name":"eScholarship (California Digital Library)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I2801248553","host_organization_name":"California Digital Library","host_organization_lineage":["https://openalex.org/I2801248553"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"etd"},"volume":null,"type":"dissertation","is_traditional":true,"indexed_in":[],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://escholarship.org/uc/item/5419p8xt","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5033193321","display_name":"Chris Haulk","orcid":null,"observed_orcids":[]},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Christopher Kenneth Haulk","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":["https://openalex.org/A5033193321"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":true,"cited_by_count":3,"citation_normalized_percentile":null,"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11152","display_name":"Stochastic processes and statistical mechanics","score":0.95169997215271,"subfield":{"id":"https://openalex.org/subfields/2610","display_name":"Mathematical Physics"},"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/T11152","display_name":"Stochastic processes and statistical mechanics","score":0.95169997215271,"subfield":{"id":"https://openalex.org/subfields/2610","display_name":"Mathematical Physics"},"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/T13500","display_name":"Probability and Statistical Research","score":0.016200000420212746,"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/T10948","display_name":"Advanced Combinatorial Mathematics","score":0.004399999976158142,"subfield":{"id":"https://openalex.org/subfields/2607","display_name":"Discrete Mathematics and Combinatorics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/exchangeability","display_name":"exchangeability","score":0.8889999985694885},{"id":"https://openalex.org/keywords/de-finetti-s-theorem","display_name":"de Finetti's theorem","score":0.7049999833106995},{"id":"https://openalex.org/keywords/hierarchy","display_name":"hierarchy","score":0.9129999876022339},{"id":"https://openalex.org/keywords/fragmentation-processes","display_name":"fragmentation processes","score":0.9800000190734863},{"id":"https://openalex.org/keywords/hierarchical-clustering","display_name":"hierarchical clustering","score":0.9990000128746033},{"id":"https://openalex.org/keywords/scaling-limits","display_name":"scaling limits","score":0.6110000014305115}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8216179013252258},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.6559978723526001},{"id":"https://openalex.org/C21308566","wikidata":"https://www.wikidata.org/wiki/Q7169365","display_name":"Permutation (music)","level":2,"score":0.5061501860618591},{"id":"https://openalex.org/C122123141","wikidata":"https://www.wikidata.org/wiki/Q176623","display_name":"Random variable","level":2,"score":0.5006246566772461},{"id":"https://openalex.org/C200985842","wikidata":"https://www.wikidata.org/wiki/Q3375503","display_name":"Random permutation","level":3,"score":0.4829696714878082},{"id":"https://openalex.org/C2777299769","wikidata":"https://www.wikidata.org/wiki/Q3707858","display_name":"Type (biology)","level":2,"score":0.43475353717803955},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.42004355788230896},{"id":"https://openalex.org/C113174947","wikidata":"https://www.wikidata.org/wiki/Q2859736","display_name":"Tree (set theory)","level":2,"score":0.41183558106422424},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.18059206008911133},{"id":"https://openalex.org/C128622974","wikidata":"https://www.wikidata.org/wiki/Q849512","display_name":"Symmetric group","level":2,"score":0.13866785168647766},{"id":"https://openalex.org/C24890656","wikidata":"https://www.wikidata.org/wiki/Q82811","display_name":"Acoustics","level":1,"score":0.0},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0},{"id":"https://openalex.org/C18903297","wikidata":"https://www.wikidata.org/wiki/Q7150","display_name":"Ecology","level":1,"score":0.0},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"pmh:oai:escholarship.org/ark:/13030/qt5419p8xt","doi":null,"is_oa":true,"landing_page_url":"https://escholarship.org/uc/item/5419p8xt","pdf_url":"https://escholarship.org/uc/item/5419p8xt","source":{"id":"https://openalex.org/S4306400115","display_name":"eScholarship (California Digital Library)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I2801248553","host_organization_name":"California Digital Library","host_organization_lineage":["https://openalex.org/I2801248553"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"etd"},{"id":"pmh:qt5419p8xt","doi":null,"is_oa":true,"landing_page_url":"http://www.escholarship.org/uc/item/5419p8xt","pdf_url":"http://www.escholarship.org/uc/item/5419p8xt","source":{"id":"https://openalex.org/S4306400115","display_name":"eScholarship (California Digital Library)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I2801248553","host_organization_name":"California Digital Library","host_organization_lineage":["https://openalex.org/I2801248553"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Haulk, Christopher Kenneth. (2011). Aspects of Exchangeable Partitions and Trees. UC Berkeley: Statistics. Retrieved from: http://www.escholarship.org/uc/item/5419p8xt","raw_type":"dissertation"},{"id":"mag:225101284","doi":null,"is_oa":false,"landing_page_url":"https://escholarship.org/content/qt5419p8xt/qt5419p8xt.pdf?t=mtfcep","pdf_url":null,"source":null,"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":null}],"best_oa_location":{"id":"pmh:oai:escholarship.org/ark:/13030/qt5419p8xt","doi":null,"is_oa":true,"landing_page_url":"https://escholarship.org/uc/item/5419p8xt","pdf_url":"https://escholarship.org/uc/item/5419p8xt","source":{"id":"https://openalex.org/S4306400115","display_name":"eScholarship (California Digital Library)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I2801248553","host_organization_name":"California Digital Library","host_organization_lineage":["https://openalex.org/I2801248553"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"etd"},"sustainable_development_goals":[],"study_designs":[],"awards":[],"funders":[],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W225101284.pdf","grobid_xml":"https://content.openalex.org/works/W225101284.grobid-xml"},"referenced_works_count":79,"referenced_works":["https://openalex.org/W5838217","https://openalex.org/W55269341","https://openalex.org/W58305343","https://openalex.org/W263845233","https://openalex.org/W1527849298","https://openalex.org/W1533473741","https://openalex.org/W1548573677","https://openalex.org/W1551893515","https://openalex.org/W1561114193","https://openalex.org/W1573705578","https://openalex.org/W1576649281","https://openalex.org/W1623834045","https://openalex.org/W1897267496","https://openalex.org/W1964338682","https://openalex.org/W1967929385","https://openalex.org/W1974210916","https://openalex.org/W1974326360","https://openalex.org/W1976289561","https://openalex.org/W1986342834","https://openalex.org/W1992239331","https://openalex.org/W1993462452","https://openalex.org/W1994276501","https://openalex.org/W1995453127","https://openalex.org/W2000650629","https://openalex.org/W2006189674","https://openalex.org/W2006507246","https://openalex.org/W2011342110","https://openalex.org/W2011992729","https://openalex.org/W2014610199","https://openalex.org/W2016588692","https://openalex.org/W2016710671","https://openalex.org/W2018043625","https://openalex.org/W2018415308","https://openalex.org/W2022131627","https://openalex.org/W2033089935","https://openalex.org/W2037774713","https://openalex.org/W2041032921","https://openalex.org/W2043960540","https://openalex.org/W2047042737","https://openalex.org/W2053218206","https://openalex.org/W2054673836","https://openalex.org/W2056513564","https://openalex.org/W2063388380","https://openalex.org/W2067409890","https://openalex.org/W2071103222","https://openalex.org/W2074413713","https://openalex.org/W2079265093","https://openalex.org/W2087309226","https://openalex.org/W2088688045","https://openalex.org/W2095181329","https://openalex.org/W2096274779","https://openalex.org/W2099412267","https://openalex.org/W2114411217","https://openalex.org/W2117059534","https://openalex.org/W2117305637","https://openalex.org/W2117787888","https://openalex.org/W2120450362","https://openalex.org/W2123094878","https://openalex.org/W2125495876","https://openalex.org/W2126105856","https://openalex.org/W2128948564","https://openalex.org/W2128999403","https://openalex.org/W2147398444","https://openalex.org/W2150286230","https://openalex.org/W2158533258","https://openalex.org/W2165969877","https://openalex.org/W2169071224","https://openalex.org/W2181754868","https://openalex.org/W2316414816","https://openalex.org/W2333495832","https://openalex.org/W2335572405","https://openalex.org/W2340541605","https://openalex.org/W2592165824","https://openalex.org/W2596148805","https://openalex.org/W2903830437","https://openalex.org/W3037208153","https://openalex.org/W3098972523","https://openalex.org/W3103788012","https://openalex.org/W3104047422"],"related_works":["https://openalex.org/W2099412267","https://openalex.org/W2962767312","https://openalex.org/W1691511196","https://openalex.org/W2949272977","https://openalex.org/W2076073007","https://openalex.org/W2053218206","https://openalex.org/W4230738705","https://openalex.org/W2323626504","https://openalex.org/W1564875921","https://openalex.org/W7098372726"],"abstract_inverted_index":{"Exchangeability":[0],"--":[1,22],"the":[2,8,11,25,132,138,144,147,152,163,176,205,214,218,228,231,245,249,256,264,267],"probabilistic":[3],"symmetry":[4],"meaning":[5],"``invariance":[6],"under":[7],"action":[9],"of":[10,18,27,39,43,49,54,78,106,108,110,116,137,146,154,186,200,221,230,234,240,251,266],"symmetric":[12],"group,''":[13],"or":[14,20,113],"less":[15],"formally,":[16],"``irrelevance":[17],"labels":[19,140],"indices''":[21],"has":[23],"been":[24],"subject":[26],"continuing":[28],"interest":[29],"to":[30,62,175,195],"probabilists":[31],"and":[32,65,91,159,168,181],"statisticians":[33],"since":[34],"de":[35,72],"Finetti's":[36],"celebrated":[37],"characterization":[38,229],"infinite":[40],"exchangeable":[41,79,111,130,252],"sequences":[42],"Bernoulli":[44],"random":[45,63,119,223],"variables":[46],"as":[47,59,204],"mixtures":[48],"IID":[50],"sequences.":[51],"The":[52,67,95],"topic":[53],"this":[55,187],"dissertation":[56],"is":[57,70,157,171,217,227,248],"exchangeability":[58,191],"it":[60],"pertains":[61],"partitions":[64,112,236,253],"trees.":[66,114],"main":[68],"result":[69,226],"a":[71,76,238],"Finetti-type":[73],"theorem":[74],"characterizing":[75],"class":[77,250],"trees":[80,120,202],"called":[81],"hierarchies":[82],"<\\\\italic>":[83],"which":[84,128,255],"arise":[85],"in":[86,101,131,173,254],"connection":[87],"with":[88,121],"fragmentation":[89],"processes":[90],"hierarchical":[92],"clustering":[93],"problems.":[94],"other":[96],"results":[97],"are":[98,129],"somewhat":[99],"related":[100],"that":[102,134,213],"they":[103],"involve":[104],"consideration":[105],"moments":[107],"statistics":[109],"One":[115],"these":[117],"concerns":[118],"leaves":[122],"labeled":[123],"by":[124,237],"consecutive":[125],"natural":[126],"numbers":[127],"sense":[133],"deterministic":[135],"permutation":[136],"leaf":[139,166,169,179,182],"does":[141],"not":[142],"change":[143],"distribution":[145,174],"tree.":[148],"In":[149],"such":[150,203],"trees,":[151],"set":[153],"interleaf":[155],"distances":[156],"exchangeable,":[158],"so,":[160],"for":[161],"example,":[162],"distance":[164,177],"between":[165,178],"1":[167,259],"2":[170,180],"equal":[172],"3.":[183],"Distributional":[184],"constraints":[185],"type":[188],"arising":[189],"from":[190],"can":[192],"be":[193],"used":[194],"characterize":[196],"finite":[197],"dimensional":[198],"marginals":[199],"well-understood":[201],"Brownian":[206,215],"CRT.":[207],"As":[208],"an":[209],"application":[210],"we":[211],"show":[212],"CRT":[216],"scaling":[219],"limit":[220],"uniform":[222],"hierarchies.":[224],"Another":[225],"two-parameter":[232],"family":[233,247],"Ewens-Pitman":[235,246],"kind":[239],"deletion":[241],"property:":[242],"speaking":[243],"loosely,":[244],"block":[257],"containing":[258],"carries":[260],"no":[261],"information":[262],"about":[263],"rest":[265],"partition.":[268]},"counts_by_year":[{"year":2019,"cited_by_count":1},{"year":2016,"cited_by_count":2}],"updated_date":"2026-11-04T10:54:05.112534","created_date":"2016-06-24T00:00:00"}
