{"id":"https://openalex.org/W2953846402","doi":"https://doi.org/10.1080/03610918.2019.1634203","title":"WHIM: function approximation where it matters","display_name":"WHIM: function approximation where it matters","publication_year":2019,"publication_date":"2019-07-05","ids":{"openalex":"https://openalex.org/W2953846402","doi":"https://doi.org/10.1080/03610918.2019.1634203","mag":"2953846402"},"language":"en","primary_location":{"id":"doi:10.1080/03610918.2019.1634203","is_oa":false,"landing_page_url":"https://doi.org/10.1080/03610918.2019.1634203","pdf_url":null,"source":{"id":"https://openalex.org/S153329750","display_name":"Communications in Statistics - Simulation and Computation","issn_l":"0361-0918","issn":["0361-0918","1532-4141"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320547","host_organization_name":"Taylor & Francis","host_organization_lineage":["https://openalex.org/P4310320547"],"host_organization_lineage_names":["Taylor & Francis"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Communications in Statistics - Simulation and Computation","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/A5038341754","display_name":"Michael Lavine","orcid":"https://orcid.org/0000-0002-1798-3619"},"institutions":[{"id":"https://openalex.org/I24603500","display_name":"University of Massachusetts Amherst","ror":"https://ror.org/0072zz521","country_code":"US","type":"education","lineage":["https://openalex.org/I24603500"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Michael Lavine","raw_affiliation_strings":["Department of Mathematics and Statistics, University of Massachusetts, Amherst, Massachusetts, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics and Statistics, University of Massachusetts, Amherst, Massachusetts, USA","institution_ids":["https://openalex.org/I24603500"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5038341754"],"corresponding_institution_ids":["https://openalex.org/I24603500"],"apc_list":null,"apc_paid":null,"fwci":0.2087,"has_fulltext":false,"cited_by_count":2,"citation_normalized_percentile":{"value":0.53268173,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":94},"biblio":{"volume":"50","issue":"12","first_page":"3839","last_page":"3869"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11871","display_name":"Advanced Statistical Methods and Models","score":0.9980999827384949,"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/T11871","display_name":"Advanced Statistical Methods and Models","score":0.9980999827384949,"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/T10136","display_name":"Statistical Methods and Inference","score":0.9976000189781189,"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/T10243","display_name":"Statistical Methods and Bayesian Inference","score":0.9961000084877014,"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/focus","display_name":"Focus (optics)","score":0.6622604131698608},{"id":"https://openalex.org/keywords/function","display_name":"Function (biology)","score":0.6540300846099854},{"id":"https://openalex.org/keywords/maximum-a-posteriori-estimation","display_name":"Maximum a posteriori estimation","score":0.552320659160614},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5347968935966492},{"id":"https://openalex.org/keywords/likelihood-function","display_name":"Likelihood function","score":0.48213908076286316},{"id":"https://openalex.org/keywords/plateau","display_name":"Plateau (mathematics)","score":0.4666929841041565},{"id":"https://openalex.org/keywords/class","display_name":"Class (philosophy)","score":0.46538272500038147},{"id":"https://openalex.org/keywords/space","display_name":"Space (punctuation)","score":0.4598466157913208},{"id":"https://openalex.org/keywords/a-priori-and-a-posteriori","display_name":"A priori and a posteriori","score":0.4526583254337311},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.420474112033844},{"id":"https://openalex.org/keywords/maximum-likelihood","display_name":"Maximum likelihood","score":0.36581504344940186},{"id":"https://openalex.org/keywords/statistical-physics","display_name":"Statistical physics","score":0.3496786952018738},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.33923202753067017},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.2964481711387634},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.2349088191986084},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.17422911524772644},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.1529574990272522},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.15250718593597412},{"id":"https://openalex.org/keywords/epistemology","display_name":"Epistemology","score":0.05966070294380188},{"id":"https://openalex.org/keywords/philosophy","display_name":"Philosophy","score":0.05938851833343506}],"concepts":[{"id":"https://openalex.org/C192209626","wikidata":"https://www.wikidata.org/wiki/Q190909","display_name":"Focus (optics)","level":2,"score":0.6622604131698608},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.6540300846099854},{"id":"https://openalex.org/C9810830","wikidata":"https://www.wikidata.org/wiki/Q635384","display_name":"Maximum a posteriori estimation","level":3,"score":0.552320659160614},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5347968935966492},{"id":"https://openalex.org/C89106044","wikidata":"https://www.wikidata.org/wiki/Q45284","display_name":"Likelihood function","level":3,"score":0.48213908076286316},{"id":"https://openalex.org/C2780030769","wikidata":"https://www.wikidata.org/wiki/Q4968575","display_name":"Plateau (mathematics)","level":2,"score":0.4666929841041565},{"id":"https://openalex.org/C2777212361","wikidata":"https://www.wikidata.org/wiki/Q5127848","display_name":"Class (philosophy)","level":2,"score":0.46538272500038147},{"id":"https://openalex.org/C2778572836","wikidata":"https://www.wikidata.org/wiki/Q380933","display_name":"Space (punctuation)","level":2,"score":0.4598466157913208},{"id":"https://openalex.org/C75553542","wikidata":"https://www.wikidata.org/wiki/Q178161","display_name":"A priori and a posteriori","level":2,"score":0.4526583254337311},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.420474112033844},{"id":"https://openalex.org/C49781872","wikidata":"https://www.wikidata.org/wiki/Q1045555","display_name":"Maximum likelihood","level":2,"score":0.36581504344940186},{"id":"https://openalex.org/C121864883","wikidata":"https://www.wikidata.org/wiki/Q677916","display_name":"Statistical physics","level":1,"score":0.3496786952018738},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.33923202753067017},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.2964481711387634},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.2349088191986084},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.17422911524772644},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.1529574990272522},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.15250718593597412},{"id":"https://openalex.org/C111472728","wikidata":"https://www.wikidata.org/wiki/Q9471","display_name":"Epistemology","level":1,"score":0.05966070294380188},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"score":0.05938851833343506},{"id":"https://openalex.org/C120665830","wikidata":"https://www.wikidata.org/wiki/Q14620","display_name":"Optics","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/C111919701","wikidata":"https://www.wikidata.org/wiki/Q9135","display_name":"Operating system","level":1,"score":0.0},{"id":"https://openalex.org/C78458016","wikidata":"https://www.wikidata.org/wiki/Q840400","display_name":"Evolutionary biology","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1080/03610918.2019.1634203","is_oa":false,"landing_page_url":"https://doi.org/10.1080/03610918.2019.1634203","pdf_url":null,"source":{"id":"https://openalex.org/S153329750","display_name":"Communications in Statistics - Simulation and Computation","issn_l":"0361-0918","issn":["0361-0918","1532-4141"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320547","host_organization_name":"Taylor & Francis","host_organization_lineage":["https://openalex.org/P4310320547"],"host_organization_lineage_names":["Taylor & Francis"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Communications in Statistics - Simulation and Computation","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":11,"referenced_works":["https://openalex.org/W1518167443","https://openalex.org/W1559626027","https://openalex.org/W1905717976","https://openalex.org/W2003173267","https://openalex.org/W2007162267","https://openalex.org/W2104442032","https://openalex.org/W2162040858","https://openalex.org/W2418785680","https://openalex.org/W2787894218","https://openalex.org/W2798141208","https://openalex.org/W4212908912"],"related_works":["https://openalex.org/W1503532423","https://openalex.org/W2150865841","https://openalex.org/W1967494390","https://openalex.org/W2138865713","https://openalex.org/W2013921918","https://openalex.org/W3013496002","https://openalex.org/W2169353922","https://openalex.org/W2465363361","https://openalex.org/W2896820906","https://openalex.org/W4284711868"],"abstract_inverted_index":{"If":[0],"f":[1,73,102],"is":[2,22,50,74,103,107,154,169],"a":[3,9,16,31,78],"function":[4,14,89],"of":[5,37,43,99,119],"interest,":[6],"typically":[7],"either":[8],"likelihood":[10,26],"or":[11,28,47,56,76,129],"posterior":[12],"density":[13],"on":[15,143,155],"parameter":[17],"space":[18],"\u0398,":[19],"and":[20,68,105,137,158],"\u03b8\u0302":[21],"the":[23,41,97,116,140,152,156,165],"MLE":[24],"(maximum":[25,30],"estimate)":[27],"MAP":[29],"posteriori":[32],"estimate),":[33],"it":[34],"can":[35,70,160],"be":[36,161],"interest":[38],"to":[39,110],"find":[40],"region":[42,98,166],"\u0398":[44,100],"where":[45,101,139,167],"f(\u03b8)":[46,49,168],"log":[48,57],"nearly":[51],"as":[52,54,66],"large":[53,104,117],"f(\u03b8\u0302)":[55],"f(\u03b8\u0302).":[58],"Typical":[59],"tools":[60],"for":[61,88,112],"working":[62],"with":[63,147],"f,":[64],"such":[65],"optimizers":[67],"MCMC,":[69],"fail":[71,111],"when":[72,124],"multimodal":[75,128],"has":[77],"plateau.":[79],"This":[80],"paper":[81],"describes":[82],"an":[83],"algorithm":[84,157],"called":[85],"WHIM":[86],"\u2013":[87,94],"approximation":[90],"WHere":[91],"It":[92],"Matters":[93],"that":[95,106],"finds":[96],"guaranteed":[108],"not":[109],"f\u2019s":[113,126],"arising":[114],"from":[115],"class":[118],"models":[120,146],"described":[121],"here,":[122],"even":[123],"those":[125],"are":[127],"have":[130],"plateaus.WHIM":[131],"was":[132,142],"introduced":[133],"in":[134],"Lavine,":[135],"Bray,":[136],"Hodges,":[138],"focus":[141,153],"linear":[144],"mixed":[145],"exactly":[148],"two":[149],"variances.":[150],"Here,":[151],"what":[159],"learned":[162],"by":[163],"finding":[164,173],"large,":[170],"rather":[171],"than":[172],"just":[174],"\u03b8\u0302.":[175]},"counts_by_year":[{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":1}],"updated_date":"2026-07-29T09:40:50.615796","created_date":"2025-10-10T00:00:00"}