{"id":"https://openalex.org/W2001136571","doi":"https://doi.org/10.1137/060652105","title":"Asymptotic Sampling Distribution for Polynomial Chaos Representation from Data: A Maximum Entropy and Fisher Information Approach","display_name":"Asymptotic Sampling Distribution for Polynomial Chaos Representation from Data: A Maximum Entropy and Fisher Information Approach","publication_year":2008,"publication_date":"2008-01-01","ids":{"openalex":"https://openalex.org/W2001136571","doi":"https://doi.org/10.1137/060652105","mag":"2001136571"},"language":"en","primary_location":{"id":"doi:10.1137/060652105","is_oa":false,"landing_page_url":"https://doi.org/10.1137/060652105","pdf_url":null,"source":{"id":"https://openalex.org/S165512578","display_name":"SIAM Journal on Scientific Computing","issn_l":"1064-8275","issn":["1064-8275","1095-7197"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Scientific Computing","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/A5102829313","display_name":"Sonjoy Das","orcid":"https://orcid.org/0000-0001-9711-8272"},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Sonjoy Das","raw_affiliation_strings":["[email\u00a0protected] and [email\u00a0protected]#TAB#"],"affiliations":[{"raw_affiliation_string":"[email\u00a0protected] and [email\u00a0protected]#TAB#","institution_ids":[]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5006138292","display_name":"Roger Ghanem","orcid":"https://orcid.org/0000-0002-1890-920X"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Roger Ghanem","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5066890566","display_name":"James C. Spall","orcid":"https://orcid.org/0000-0001-8034-8864"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"James C. Spall","raw_affiliation_strings":["james.spall@jhuapl.edu#TAB#"],"affiliations":[{"raw_affiliation_string":"james.spall@jhuapl.edu#TAB#","institution_ids":[]}]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5102829313"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":8.6254,"has_fulltext":false,"cited_by_count":80,"citation_normalized_percentile":{"value":0.97960784,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":99},"biblio":{"volume":"30","issue":"5","first_page":"2207","last_page":"2234"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10928","display_name":"Probabilistic and Robust Engineering Design","score":0.9998000264167786,"subfield":{"id":"https://openalex.org/subfields/1804","display_name":"Statistics, Probability and Uncertainty"},"field":{"id":"https://openalex.org/fields/18","display_name":"Decision Sciences"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}},"topics":[{"id":"https://openalex.org/T10928","display_name":"Probabilistic and Robust Engineering Design","score":0.9998000264167786,"subfield":{"id":"https://openalex.org/subfields/1804","display_name":"Statistics, Probability and Uncertainty"},"field":{"id":"https://openalex.org/fields/18","display_name":"Decision Sciences"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}},{"id":"https://openalex.org/T11371","display_name":"Wind and Air Flow Studies","score":0.9860000014305115,"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/T13126","display_name":"Scientific Research and Discoveries","score":0.9510999917984009,"subfield":{"id":"https://openalex.org/subfields/3109","display_name":"Statistical and Nonlinear Physics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.8565313220024109},{"id":"https://openalex.org/keywords/estimator","display_name":"Estimator","score":0.5760154724121094},{"id":"https://openalex.org/keywords/asymptotic-distribution","display_name":"Asymptotic distribution","score":0.4829120337963104},{"id":"https://openalex.org/keywords/principle-of-maximum-entropy","display_name":"Principle of maximum entropy","score":0.436767041683197},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.43635299801826477},{"id":"https://openalex.org/keywords/fisher-information","display_name":"Fisher information","score":0.4304477572441101},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.35519522428512573},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.33781981468200684},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.2522197961807251}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8565313220024109},{"id":"https://openalex.org/C185429906","wikidata":"https://www.wikidata.org/wiki/Q1130160","display_name":"Estimator","level":2,"score":0.5760154724121094},{"id":"https://openalex.org/C65778772","wikidata":"https://www.wikidata.org/wiki/Q12345341","display_name":"Asymptotic distribution","level":3,"score":0.4829120337963104},{"id":"https://openalex.org/C9679016","wikidata":"https://www.wikidata.org/wiki/Q1417473","display_name":"Principle of maximum entropy","level":2,"score":0.436767041683197},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.43635299801826477},{"id":"https://openalex.org/C29406490","wikidata":"https://www.wikidata.org/wiki/Q1420659","display_name":"Fisher information","level":2,"score":0.4304477572441101},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.35519522428512573},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.33781981468200684},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.2522197961807251}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1137/060652105","is_oa":false,"landing_page_url":"https://doi.org/10.1137/060652105","pdf_url":null,"source":{"id":"https://openalex.org/S165512578","display_name":"SIAM Journal on Scientific Computing","issn_l":"1064-8275","issn":["1064-8275","1095-7197"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Scientific Computing","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":34,"referenced_works":["https://openalex.org/W1964056897","https://openalex.org/W1975426737","https://openalex.org/W1982769461","https://openalex.org/W1986286822","https://openalex.org/W1995565517","https://openalex.org/W1995875735","https://openalex.org/W2003191951","https://openalex.org/W2006681603","https://openalex.org/W2010737928","https://openalex.org/W2018159038","https://openalex.org/W2032558547","https://openalex.org/W2034544282","https://openalex.org/W2055081012","https://openalex.org/W2058362163","https://openalex.org/W2061604462","https://openalex.org/W2063021587","https://openalex.org/W2067804657","https://openalex.org/W2080928812","https://openalex.org/W2085676736","https://openalex.org/W2086077633","https://openalex.org/W2086140935","https://openalex.org/W2089770162","https://openalex.org/W2095617387","https://openalex.org/W2103621341","https://openalex.org/W2105596596","https://openalex.org/W2107376597","https://openalex.org/W2124289529","https://openalex.org/W2170880683","https://openalex.org/W2321957512","https://openalex.org/W2332771484","https://openalex.org/W3123878694","https://openalex.org/W4252028749","https://openalex.org/W4254218257","https://openalex.org/W4362227092"],"related_works":["https://openalex.org/W3012088032","https://openalex.org/W2238904537","https://openalex.org/W2776312158","https://openalex.org/W4287880334","https://openalex.org/W4366700029","https://openalex.org/W4285230481","https://openalex.org/W1965458961","https://openalex.org/W4385769873","https://openalex.org/W1511751337","https://openalex.org/W2899018032"],"abstract_inverted_index":{"A":[0],"procedure":[1],"is":[2,101,204,249],"presented":[3],"for":[4,260],"characterizing":[5],"the":[6,13,42,51,55,76,108,111,119,130,134,141,146,151,177,181,189,197,224,230,240,243,262],"asymptotic":[7,183,247],"sampling":[8,217],"distribution":[9,185,248],"of":[10,12,18,30,39,50,54,64,66,75,94,99,133,150,154,159,176,180,186,188,192,196,232,242],"estimators":[11,149,167,187,227],"polynomial":[14],"chaos":[15],"(PC)":[16],"coefficients":[17,136,153,191],"a":[19,28,36,46,62,67,72,83,90,209,216],"second-order":[20],"nonstationary":[21],"and":[22,41,82,118,172],"non-Gaussian":[23],"random":[24,33,56,68,77,127,131],"process":[25,34,57,264],"by":[26,104,207],"using":[27,208],"collection":[29],"observations.":[31],"The":[32,79,96,122,148,202,219],"represents":[35],"physical":[37],"quantity":[38],"interest,":[40],"observations":[43],"made":[44],"over":[45],"finite":[47],"denumerable":[48],"subset":[49],"indexing":[52],"set":[53,63],"are":[58,86,161],"considered":[59],"to":[60,88,107,140,163,236],"form":[61],"realizations":[65],"vector":[69],"$\\mathcal{Y}$":[70,155,193],"representing":[71],"finite-dimensional":[73],"projection":[74],"process.":[78,245],"Karhunen\u2013Lo\u00e8ve":[80],"decomposition":[81],"scaling":[84],"transformation":[85],"employed":[87],"produce":[89],"reduced-order":[91],"model":[92],"$\\mathcal{Z}$":[93,100,160],"$\\mathcal{Y}$.":[95],"PC":[97,124,135,152,190,225],"expansion":[98,125],"next":[102],"determined":[103],"having":[105],"recourse":[106],"maximum-entropy":[109],"principle,":[110],"Metropolis\u2013Hastings":[112],"Markov":[113],"chain":[114],"Monte":[115],"Carlo":[116],"algorithm,":[117],"Rosenblatt":[120],"transformation.":[121],"resulting":[123,220],"has":[126],"coefficients,":[128],"where":[129],"characteristics":[132,253],"can":[137,254],"be":[138,164,255],"attributed":[139],"limited":[142],"data":[143,237],"available":[144],"from":[145,157],"experiment.":[147],"obtained":[156],"that":[158],"found":[162],"maximum":[165],"likelihood":[166],"as":[168,170,213,215,251],"well":[169,214],"consistent":[171],"asymptotically":[173],"efficient.":[174],"Computation":[175],"covariance":[178],"matrix":[179,200],"associated":[182],"normal":[184],"requires":[194],"knowledge":[195],"Fisher":[198],"information":[199,234],"(FIM).":[201],"FIM":[203],"evaluated":[205],"here":[206],"numerical":[210],"integration":[211],"scheme":[212],"technique.":[218],"confidence":[221],"interval":[222],"on":[223,239,269],"coefficient":[226],"essentially":[228],"reflects":[229],"effect":[231],"incomplete":[233],"(due":[235],"limitation)":[238],"characterization":[241],"stochastic":[244,263],"This":[246],"significant":[250],"its":[252],"propagated":[256],"through":[257],"predictive":[258],"models":[259],"which":[261],"in":[265],"question":[266],"describes":[267],"uncertainty":[268],"some":[270],"input":[271],"parameters.":[272]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":2},{"year":2023,"cited_by_count":5},{"year":2022,"cited_by_count":6},{"year":2021,"cited_by_count":2},{"year":2020,"cited_by_count":2},{"year":2019,"cited_by_count":1},{"year":2017,"cited_by_count":9},{"year":2016,"cited_by_count":1},{"year":2015,"cited_by_count":7},{"year":2014,"cited_by_count":6},{"year":2013,"cited_by_count":1},{"year":2012,"cited_by_count":4}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
