{"id":"https://openalex.org/W2096039995","doi":"https://doi.org/10.3390/a4020115","title":"Alternatives to the Least Squares Solution to Peelle\u2019s Pertinent Puzzle","display_name":"Alternatives to the Least Squares Solution to Peelle\u2019s Pertinent Puzzle","publication_year":2011,"publication_date":"2011-06-23","ids":{"openalex":"https://openalex.org/W2096039995","doi":"https://doi.org/10.3390/a4020115","mag":"2096039995"},"language":"en","primary_location":{"id":"doi:10.3390/a4020115","is_oa":true,"landing_page_url":"https://doi.org/10.3390/a4020115","pdf_url":"https://www.mdpi.com/1999-4893/4/2/115/pdf?version=1308816426","source":{"id":"https://openalex.org/S190629608","display_name":"Algorithms","issn_l":"1999-4893","issn":["1999-4893"],"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":"Algorithms","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://www.mdpi.com/1999-4893/4/2/115/pdf?version=1308816426","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5038854150","display_name":"Tom Burr","orcid":"https://orcid.org/0000-0002-7298-9706"},"institutions":[{"id":"https://openalex.org/I1343871089","display_name":"Los Alamos National Laboratory","ror":"https://ror.org/01e41cf67","country_code":"US","type":"facility","lineage":["https://openalex.org/I1330989302","https://openalex.org/I1343871089","https://openalex.org/I198811213","https://openalex.org/I4210120050"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Tom Burr","raw_affiliation_strings":["Statistical Sciences, Los Alamos National Laboratory, Los Alamos, NM 87545, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Statistical Sciences, Los Alamos National Laboratory, Los Alamos, NM 87545, USA","institution_ids":["https://openalex.org/I1343871089"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5069448500","display_name":"Todd Graves","orcid":null},"institutions":[{"id":"https://openalex.org/I1343871089","display_name":"Los Alamos National Laboratory","ror":"https://ror.org/01e41cf67","country_code":"US","type":"facility","lineage":["https://openalex.org/I1330989302","https://openalex.org/I1343871089","https://openalex.org/I198811213","https://openalex.org/I4210120050"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Todd Graves","raw_affiliation_strings":["Statistical Sciences, Los Alamos National Laboratory, Los Alamos, NM 87545, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Statistical Sciences, Los Alamos National Laboratory, Los Alamos, NM 87545, USA","institution_ids":["https://openalex.org/I1343871089"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5041470785","display_name":"Nicolas Hengartner","orcid":"https://orcid.org/0000-0002-4157-134X"},"institutions":[{"id":"https://openalex.org/I1343871089","display_name":"Los Alamos National Laboratory","ror":"https://ror.org/01e41cf67","country_code":"US","type":"facility","lineage":["https://openalex.org/I1330989302","https://openalex.org/I1343871089","https://openalex.org/I198811213","https://openalex.org/I4210120050"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Nicolas Hengartner","raw_affiliation_strings":["Information Sciences, Los Alamos National Laboratory, Los Alamos, NM 87545, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Information Sciences, Los Alamos National Laboratory, Los Alamos, NM 87545, USA","institution_ids":["https://openalex.org/I1343871089"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5048344715","display_name":"Toshihiko Kawano","orcid":"https://orcid.org/0000-0001-7463-4899"},"institutions":[{"id":"https://openalex.org/I1343871089","display_name":"Los Alamos National Laboratory","ror":"https://ror.org/01e41cf67","country_code":"US","type":"facility","lineage":["https://openalex.org/I1330989302","https://openalex.org/I1343871089","https://openalex.org/I198811213","https://openalex.org/I4210120050"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Toshihiko Kawano","raw_affiliation_strings":["Nuclear and Particle Physics, Los Alamos National Laboratory, Los Alamos, NM 87545, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Nuclear and Particle Physics, Los Alamos National Laboratory, Los Alamos, NM 87545, USA","institution_ids":["https://openalex.org/I1343871089"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5087146582","display_name":"Feng Pan","orcid":null},"institutions":[{"id":"https://openalex.org/I1343871089","display_name":"Los Alamos National Laboratory","ror":"https://ror.org/01e41cf67","country_code":"US","type":"facility","lineage":["https://openalex.org/I1330989302","https://openalex.org/I1343871089","https://openalex.org/I198811213","https://openalex.org/I4210120050"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Feng Pan","raw_affiliation_strings":["Decision Applications, Los Alamos National Laboratory, Los Alamos, NM 87545, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Decision Applications, Los Alamos National Laboratory, Los Alamos, NM 87545, USA","institution_ids":["https://openalex.org/I1343871089"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5086681973","display_name":"P. Talou","orcid":"https://orcid.org/0000-0002-0536-3615"},"institutions":[{"id":"https://openalex.org/I1343871089","display_name":"Los Alamos National Laboratory","ror":"https://ror.org/01e41cf67","country_code":"US","type":"facility","lineage":["https://openalex.org/I1330989302","https://openalex.org/I1343871089","https://openalex.org/I198811213","https://openalex.org/I4210120050"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Patrick Talou","raw_affiliation_strings":["Nuclear and Particle Physics, Los Alamos National Laboratory, Los Alamos, NM 87545, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Nuclear and Particle Physics, Los Alamos National Laboratory, Los Alamos, NM 87545, USA","institution_ids":["https://openalex.org/I1343871089"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":6,"corresponding_author_ids":["https://openalex.org/A5038854150"],"corresponding_institution_ids":["https://openalex.org/I1343871089"],"apc_list":{"value":1400,"currency":"CHF","value_usd":1515},"apc_paid":{"value":1400,"currency":"CHF","value_usd":1515},"fwci":1.1164,"has_fulltext":false,"cited_by_count":7,"citation_normalized_percentile":{"value":0.80116998,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":96},"biblio":{"volume":"4","issue":"2","first_page":"115","last_page":"130"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12056","display_name":"Markov Chains and Monte Carlo Methods","score":0.9994999766349792,"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/T12056","display_name":"Markov Chains and Monte Carlo Methods","score":0.9994999766349792,"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/T12814","display_name":"Gaussian Processes and Bayesian Inference","score":0.9961000084877014,"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/T10136","display_name":"Statistical Methods and Inference","score":0.9958000183105469,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/estimator","display_name":"Estimator","score":0.7924623489379883},{"id":"https://openalex.org/keywords/approximate-bayesian-computation","display_name":"Approximate Bayesian computation","score":0.7222760915756226},{"id":"https://openalex.org/keywords/least-squares-function-approximation","display_name":"Least-squares function approximation","score":0.5963661074638367},{"id":"https://openalex.org/keywords/context","display_name":"Context (archaeology)","score":0.5912674069404602},{"id":"https://openalex.org/keywords/computation","display_name":"Computation","score":0.5635135173797607},{"id":"https://openalex.org/keywords/covariance-matrix","display_name":"Covariance matrix","score":0.5547545552253723},{"id":"https://openalex.org/keywords/covariance","display_name":"Covariance","score":0.5503737330436707},{"id":"https://openalex.org/keywords/bayesian-probability","display_name":"Bayesian probability","score":0.546795129776001},{"id":"https://openalex.org/keywords/range","display_name":"Range (aeronautics)","score":0.5431460738182068},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.4834945499897003},{"id":"https://openalex.org/keywords/generalized-least-squares","display_name":"Generalized least squares","score":0.46375468373298645},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.459074467420578},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.43771013617515564},{"id":"https://openalex.org/keywords/econometrics","display_name":"Econometrics","score":0.37950077652931213},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.37443971633911133},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.34839028120040894},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.34137898683547974},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.09055137634277344}],"concepts":[{"id":"https://openalex.org/C185429906","wikidata":"https://www.wikidata.org/wiki/Q1130160","display_name":"Estimator","level":2,"score":0.7924623489379883},{"id":"https://openalex.org/C2779377595","wikidata":"https://www.wikidata.org/wiki/Q21045424","display_name":"Approximate Bayesian computation","level":3,"score":0.7222760915756226},{"id":"https://openalex.org/C9936470","wikidata":"https://www.wikidata.org/wiki/Q6510405","display_name":"Least-squares function approximation","level":3,"score":0.5963661074638367},{"id":"https://openalex.org/C2779343474","wikidata":"https://www.wikidata.org/wiki/Q3109175","display_name":"Context (archaeology)","level":2,"score":0.5912674069404602},{"id":"https://openalex.org/C45374587","wikidata":"https://www.wikidata.org/wiki/Q12525525","display_name":"Computation","level":2,"score":0.5635135173797607},{"id":"https://openalex.org/C185142706","wikidata":"https://www.wikidata.org/wiki/Q1134404","display_name":"Covariance matrix","level":2,"score":0.5547545552253723},{"id":"https://openalex.org/C178650346","wikidata":"https://www.wikidata.org/wiki/Q201984","display_name":"Covariance","level":2,"score":0.5503737330436707},{"id":"https://openalex.org/C107673813","wikidata":"https://www.wikidata.org/wiki/Q812534","display_name":"Bayesian probability","level":2,"score":0.546795129776001},{"id":"https://openalex.org/C204323151","wikidata":"https://www.wikidata.org/wiki/Q905424","display_name":"Range (aeronautics)","level":2,"score":0.5431460738182068},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.4834945499897003},{"id":"https://openalex.org/C188649462","wikidata":"https://www.wikidata.org/wiki/Q2246261","display_name":"Generalized least squares","level":3,"score":0.46375468373298645},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.459074467420578},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.43771013617515564},{"id":"https://openalex.org/C149782125","wikidata":"https://www.wikidata.org/wiki/Q160039","display_name":"Econometrics","level":1,"score":0.37950077652931213},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.37443971633911133},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.34839028120040894},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.34137898683547974},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.09055137634277344},{"id":"https://openalex.org/C159985019","wikidata":"https://www.wikidata.org/wiki/Q181790","display_name":"Composite material","level":1,"score":0.0},{"id":"https://openalex.org/C2776214188","wikidata":"https://www.wikidata.org/wiki/Q408386","display_name":"Inference","level":2,"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/C192562407","wikidata":"https://www.wikidata.org/wiki/Q228736","display_name":"Materials science","level":0,"score":0.0},{"id":"https://openalex.org/C151730666","wikidata":"https://www.wikidata.org/wiki/Q7205","display_name":"Paleontology","level":1,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.3390/a4020115","is_oa":true,"landing_page_url":"https://doi.org/10.3390/a4020115","pdf_url":"https://www.mdpi.com/1999-4893/4/2/115/pdf?version=1308816426","source":{"id":"https://openalex.org/S190629608","display_name":"Algorithms","issn_l":"1999-4893","issn":["1999-4893"],"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":"Algorithms","raw_type":"journal-article"},{"id":"pmh:oai:doaj.org/article:c25880afa6454610a5c96ca87aead681","is_oa":true,"landing_page_url":"https://doaj.org/article/c25880afa6454610a5c96ca87aead681","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":"Algorithms, Vol 4, Iss 2, Pp 115-130 (2011)","raw_type":"article"},{"id":"pmh:oai:mdpi.com:/1999-4893/4/2/115/","is_oa":true,"landing_page_url":"https://dx.doi.org/10.3390/a4020115","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":"Algorithms; Volume 4; Issue 2; Pages: 115-130","raw_type":"Text"}],"best_oa_location":{"id":"doi:10.3390/a4020115","is_oa":true,"landing_page_url":"https://doi.org/10.3390/a4020115","pdf_url":"https://www.mdpi.com/1999-4893/4/2/115/pdf?version=1308816426","source":{"id":"https://openalex.org/S190629608","display_name":"Algorithms","issn_l":"1999-4893","issn":["1999-4893"],"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":"Algorithms","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":19,"referenced_works":["https://openalex.org/W114923250","https://openalex.org/W1480376833","https://openalex.org/W1493731025","https://openalex.org/W1548239296","https://openalex.org/W1992456659","https://openalex.org/W1997841560","https://openalex.org/W2020772737","https://openalex.org/W2026594647","https://openalex.org/W2031513770","https://openalex.org/W2045973738","https://openalex.org/W2051351284","https://openalex.org/W2086421081","https://openalex.org/W2112440119","https://openalex.org/W2133195025","https://openalex.org/W2136758725","https://openalex.org/W2462014392","https://openalex.org/W2796865709","https://openalex.org/W4232473718","https://openalex.org/W4249776844"],"related_works":["https://openalex.org/W2886934452","https://openalex.org/W1489099099","https://openalex.org/W2024369332","https://openalex.org/W1974955043","https://openalex.org/W1959514624","https://openalex.org/W2167126078","https://openalex.org/W4319880936","https://openalex.org/W2034819163","https://openalex.org/W2797020683","https://openalex.org/W4250719734"],"abstract_inverted_index":{"Peelle\u2019s":[0],"Pertinent":[1],"Puzzle":[2],"(PPP)":[3],"was":[4],"described":[5],"in":[6,8,17,113],"1987":[7],"the":[9,31,34,100,104,114],"context":[10],"of":[11,33],"estimating":[12],"fundamental":[13],"parameters":[14],"that":[15,40,110],"arise":[16],"nuclear":[18],"interaction":[19],"experiments.":[20],"In":[21],"PPP,":[22],"generalized":[23],"least":[24],"squares":[25],"(GLS)":[26],"parameter":[27],"estimates":[28],"fell":[29],"outside":[30],"range":[32],"data,":[35],"which":[36],"has":[37,46],"raised":[38],"concerns":[39],"GLS":[41,52],"is":[42,72],"somehow":[43],"flawed":[44],"and":[45,64,108],"led":[47],"to":[48,51,91,95,99],"suggested":[49,66],"alternatives":[50],"estimators.":[53],"However,":[54],"there":[55],"have":[56],"been":[57],"no":[58],"corresponding":[59],"performance":[60,78],"comparisons":[61,79],"among":[62,80],"methods,":[63],"one":[65],"approach":[67],"involving":[68],"simulated":[69,92],"data":[70,93],"realizations":[71,94],"statistically":[73],"incomplete.":[74],"Here":[75],"we":[76],"provide":[77],"estimators,":[81],"introduce":[82],"approximate":[83],"Bayesian":[84],"computation":[85],"(ABC)":[86],"using":[87],"density":[88],"estimation":[89,111],"applied":[90],"produce":[96],"an":[97],"alternative":[98],"incomplete":[101],"approach,":[102,107],"complete":[103],"incompletely":[105],"specified":[106],"show":[109],"error":[112],"assumed":[115],"covariance":[116],"matrix":[117],"cannot":[118],"always":[119],"be":[120],"ignored.":[121]},"counts_by_year":[{"year":2019,"cited_by_count":1},{"year":2015,"cited_by_count":2},{"year":2014,"cited_by_count":1},{"year":2013,"cited_by_count":1},{"year":2012,"cited_by_count":1}],"updated_date":"2026-05-21T06:26:12.895304","created_date":"2016-06-24T00:00:00"}