{"id":"https://openalex.org/W2044492509","doi":"https://doi.org/10.1137/110832288","title":"On the Optimal Transition Matrix for Markov Chain Monte Carlo Sampling","display_name":"On the Optimal Transition Matrix for Markov Chain Monte Carlo Sampling","publication_year":2012,"publication_date":"2012-01-01","ids":{"openalex":"https://openalex.org/W2044492509","doi":"https://doi.org/10.1137/110832288","mag":"2044492509"},"language":"en","primary_location":{"id":"doi:10.1137/110832288","is_oa":false,"landing_page_url":"https://doi.org/10.1137/110832288","pdf_url":null,"source":{"id":"https://openalex.org/S897311980","display_name":"SIAM Journal on Control and Optimization","issn_l":"0363-0129","issn":["0363-0129","1095-7138"],"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 Control and Optimization","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/A5048996304","display_name":"Ting\u2010Li Chen","orcid":"https://orcid.org/0000-0002-1375-0164"},"institutions":[{"id":"https://openalex.org/I4210141710","display_name":"Institute of Statistical Science, Academia Sinica","ror":"https://ror.org/044gv5910","country_code":"TW","type":"facility","lineage":["https://openalex.org/I4210141710","https://openalex.org/I84653119"]}],"countries":["TW"],"is_corresponding":true,"raw_author_name":"Ting-Li Chen","raw_affiliation_strings":["Institute of Statistical Science, Academia Sinica"],"affiliations":[{"raw_affiliation_string":"Institute of Statistical Science, Academia Sinica","institution_ids":["https://openalex.org/I4210141710"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5110260684","display_name":"Wei-Kuo Chen","orcid":null},"institutions":[{"id":"https://openalex.org/I84653119","display_name":"Academia Sinica","ror":"https://ror.org/05bxb3784","country_code":"TW","type":"facility","lineage":["https://openalex.org/I84653119"]}],"countries":["TW"],"is_corresponding":false,"raw_author_name":"Wei-Kuo Chen","raw_affiliation_strings":["Academia Sinica )"],"affiliations":[{"raw_affiliation_string":"Academia Sinica )","institution_ids":["https://openalex.org/I84653119"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5111737690","display_name":"Chii-Ruey Hwang","orcid":null},"institutions":[{"id":"https://openalex.org/I84653119","display_name":"Academia Sinica","ror":"https://ror.org/05bxb3784","country_code":"TW","type":"facility","lineage":["https://openalex.org/I84653119"]}],"countries":["TW"],"is_corresponding":false,"raw_author_name":"Chii-Ruey Hwang","raw_affiliation_strings":["Academia Sinica )"],"affiliations":[{"raw_affiliation_string":"Academia Sinica )","institution_ids":["https://openalex.org/I84653119"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5089535733","display_name":"Hui-Ming Pai","orcid":null},"institutions":[{"id":"https://openalex.org/I99613584","display_name":"National Taipei University","ror":"https://ror.org/03e29r284","country_code":"TW","type":"education","lineage":["https://openalex.org/I99613584"]}],"countries":["TW"],"is_corresponding":false,"raw_author_name":"Hui-Ming Pai","raw_affiliation_strings":["National Taipei University#TAB#"],"affiliations":[{"raw_affiliation_string":"National Taipei University#TAB#","institution_ids":["https://openalex.org/I99613584"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5048996304"],"corresponding_institution_ids":["https://openalex.org/I4210141710"],"apc_list":null,"apc_paid":null,"fwci":2.8543,"has_fulltext":false,"cited_by_count":22,"citation_normalized_percentile":{"value":0.90324254,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":99},"biblio":{"volume":"50","issue":"5","first_page":"2743","last_page":"2762"},"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":0.9998999834060669,"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":0.9998999834060669,"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/T11716","display_name":"Random Matrices and Applications","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/T11152","display_name":"Stochastic processes and statistical mechanics","score":0.9973999857902527,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.838377833366394},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.7023518681526184},{"id":"https://openalex.org/keywords/markov-chain","display_name":"Markov chain","score":0.6492494344711304},{"id":"https://openalex.org/keywords/stochastic-matrix","display_name":"Stochastic matrix","score":0.585361123085022},{"id":"https://openalex.org/keywords/monte-carlo-method","display_name":"Monte Carlo method","score":0.5099738836288452},{"id":"https://openalex.org/keywords/matrix","display_name":"Matrix (chemical analysis)","score":0.45792967081069946},{"id":"https://openalex.org/keywords/distribution","display_name":"Distribution (mathematics)","score":0.44886577129364014},{"id":"https://openalex.org/keywords/markov-chain-monte-carlo","display_name":"Markov chain Monte Carlo","score":0.4249558448791504},{"id":"https://openalex.org/keywords/chain","display_name":"Chain (unit)","score":0.42213982343673706},{"id":"https://openalex.org/keywords/invariant","display_name":"Invariant (physics)","score":0.41513919830322266},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.3477553427219391},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.22931605577468872},{"id":"https://openalex.org/keywords/mathematical-physics","display_name":"Mathematical physics","score":0.17208486795425415},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.14634820818901062},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.12131786346435547}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.838377833366394},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.7023518681526184},{"id":"https://openalex.org/C98763669","wikidata":"https://www.wikidata.org/wiki/Q176645","display_name":"Markov chain","level":2,"score":0.6492494344711304},{"id":"https://openalex.org/C49555168","wikidata":"https://www.wikidata.org/wiki/Q176583","display_name":"Stochastic matrix","level":3,"score":0.585361123085022},{"id":"https://openalex.org/C19499675","wikidata":"https://www.wikidata.org/wiki/Q232207","display_name":"Monte Carlo method","level":2,"score":0.5099738836288452},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.45792967081069946},{"id":"https://openalex.org/C110121322","wikidata":"https://www.wikidata.org/wiki/Q865811","display_name":"Distribution (mathematics)","level":2,"score":0.44886577129364014},{"id":"https://openalex.org/C111350023","wikidata":"https://www.wikidata.org/wiki/Q1191869","display_name":"Markov chain Monte Carlo","level":3,"score":0.4249558448791504},{"id":"https://openalex.org/C199185054","wikidata":"https://www.wikidata.org/wiki/Q552299","display_name":"Chain (unit)","level":2,"score":0.42213982343673706},{"id":"https://openalex.org/C190470478","wikidata":"https://www.wikidata.org/wiki/Q2370229","display_name":"Invariant (physics)","level":2,"score":0.41513919830322266},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3477553427219391},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.22931605577468872},{"id":"https://openalex.org/C37914503","wikidata":"https://www.wikidata.org/wiki/Q156495","display_name":"Mathematical physics","level":1,"score":0.17208486795425415},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.14634820818901062},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.12131786346435547},{"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/C1276947","wikidata":"https://www.wikidata.org/wiki/Q333","display_name":"Astronomy","level":1,"score":0.0},{"id":"https://openalex.org/C192562407","wikidata":"https://www.wikidata.org/wiki/Q228736","display_name":"Materials science","level":0,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1137/110832288","is_oa":false,"landing_page_url":"https://doi.org/10.1137/110832288","pdf_url":null,"source":{"id":"https://openalex.org/S897311980","display_name":"SIAM Journal on Control and Optimization","issn_l":"0363-0129","issn":["0363-0129","1095-7138"],"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 Control and Optimization","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":11,"referenced_works":["https://openalex.org/W1972309199","https://openalex.org/W2005548917","https://openalex.org/W2020999234","https://openalex.org/W2049590639","https://openalex.org/W2056760934","https://openalex.org/W2066357294","https://openalex.org/W2093197987","https://openalex.org/W2138309709","https://openalex.org/W2505595203","https://openalex.org/W3037124231","https://openalex.org/W3105166259"],"related_works":["https://openalex.org/W2734729804","https://openalex.org/W2186430569","https://openalex.org/W3041997070","https://openalex.org/W1968612088","https://openalex.org/W2364963676","https://openalex.org/W2735388074","https://openalex.org/W2351194865","https://openalex.org/W4388292488","https://openalex.org/W2756643213","https://openalex.org/W1262344082"],"abstract_inverted_index":{"Let":[0,37],"${\\cal":[1,15,24],"X}$":[2],"be":[3,10,39],"a":[4,40,59,83,103],"finite":[5],"space":[6],"and":[7],"let":[8],"$\\pi$":[9],"an":[11],"underlying":[12],"probability":[13],"on":[14,23,79,106],"X}$.":[16],"For":[17],"any":[18],"real-valued":[19],"function":[20],"$f$":[21,34],"defined":[22],"X}$,":[25],"we":[26,86],"are":[27],"interested":[28],"in":[29],"calculating":[30],"the":[31,63,70,89,95],"expectation":[32],"of":[33,73,91],"under":[35],"$\\pi$.":[36,52],"$X_0,X_1,\\ldots,X_n,\\ldots$":[38],"Markov":[41],"chain":[42],"generated":[43],"by":[44],"some":[45],"transition":[46],"matrix":[47,67],"$P$":[48,68],"with":[49,100],"invariant":[50],"distribution":[51,105],"The":[53,76],"time":[54],"average,":[55],"$\\frac{1}{n}\\sum_{k=0}^{n-1}":[56,74],"f(X_k)$,":[57],"is":[58],"reasonable":[60],"approximation":[61],"to":[62,102],"expectation,":[64],"$E_\\pi[f(X)]$.":[65],"Which":[66],"minimizes":[69],"asymptotic":[71,97],"variance":[72],"f(X_k)$?":[75],"answer":[77],"depends":[78],"$f$.":[80,107],"Rather":[81],"than":[82],"worst-case":[84],"analysis,":[85],"will":[87],"identify":[88],"set":[90],"$P$'s":[92],"that":[93],"minimize":[94],"average":[96],"variance,":[98],"averaged":[99],"respect":[101],"uniform":[104]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":1},{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":3},{"year":2021,"cited_by_count":2},{"year":2019,"cited_by_count":2},{"year":2018,"cited_by_count":3},{"year":2015,"cited_by_count":3},{"year":2014,"cited_by_count":2},{"year":2013,"cited_by_count":4}],"updated_date":"2026-03-20T23:20:44.827607","created_date":"2025-10-10T00:00:00"}