{"id":"https://openalex.org/W2107711562","doi":"https://doi.org/10.1155/2002/683164","title":"On Determining the Order of Markov Dependence of an Observed Process Governed by a Hidden Markov Model","display_name":"On Determining the Order of Markov Dependence of an Observed Process Governed by a Hidden Markov Model","publication_year":2002,"publication_date":"2002-01-01","ids":{"openalex":"https://openalex.org/W2107711562","doi":"https://doi.org/10.1155/2002/683164","mag":"2107711562"},"language":"en","primary_location":{"id":"doi:10.1155/2002/683164","is_oa":true,"landing_page_url":"https://doi.org/10.1155/2002/683164","pdf_url":"https://downloads.hindawi.com/journals/sp/2002/683164.pdf","source":{"id":"https://openalex.org/S166774750","display_name":"Scientific Programming","issn_l":"1058-9244","issn":["1058-9244","1875-919X"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319869","host_organization_name":"Hindawi Publishing Corporation","host_organization_lineage":["https://openalex.org/P4310319869"],"host_organization_lineage_names":["Hindawi Publishing Corporation"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Scientific Programming","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"hybrid","oa_url":"https://downloads.hindawi.com/journals/sp/2002/683164.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5109228523","display_name":"R. J. Boys","orcid":null},"institutions":[{"id":"https://openalex.org/I84884186","display_name":"Newcastle University","ror":"https://ror.org/01kj2bm70","country_code":"GB","type":"education","lineage":["https://openalex.org/I84884186"]}],"countries":["GB"],"is_corresponding":true,"raw_author_name":"R.J. Boys","raw_affiliation_strings":["Department of Statistics, University of Newcastle, Newcastle upon Tyne, NE1 7RU","Department of Statistics, University of Newcastle, Newcastle upon Tyne, NE1 7RU, UK. Tel.: +44 (0)191 222 7297; E-mail: Richard.Boys@ncl.ac.uk#TAB#"],"affiliations":[{"raw_affiliation_string":"Department of Statistics, University of Newcastle, Newcastle upon Tyne, NE1 7RU","institution_ids":["https://openalex.org/I84884186"]},{"raw_affiliation_string":"Department of Statistics, University of Newcastle, Newcastle upon Tyne, NE1 7RU, UK. Tel.: +44 (0)191 222 7297; E-mail: Richard.Boys@ncl.ac.uk#TAB#","institution_ids":["https://openalex.org/I84884186"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5058839771","display_name":"Daniel A. Henderson","orcid":"https://orcid.org/0000-0002-4376-4276"},"institutions":[{"id":"https://openalex.org/I204136569","display_name":"The Open University","ror":"https://ror.org/05mzfcs16","country_code":"GB","type":"education","lineage":["https://openalex.org/I204136569"]}],"countries":["GB"],"is_corresponding":false,"raw_author_name":"D.A. Henderson","raw_affiliation_strings":["Department of Statistics, The Open University, Milton Keynes, MK7 6AA","Department of Statistics, The Open University, Milton Keynes, MK7 6AA, UK. Tel.: +44 (0)1908 652 030; E-mail: d.a.henderson@open.ac.uk (Corresponding author)#TAB#"],"affiliations":[{"raw_affiliation_string":"Department of Statistics, The Open University, Milton Keynes, MK7 6AA","institution_ids":["https://openalex.org/I204136569"]},{"raw_affiliation_string":"Department of Statistics, The Open University, Milton Keynes, MK7 6AA, UK. Tel.: +44 (0)1908 652 030; E-mail: d.a.henderson@open.ac.uk (Corresponding author)#TAB#","institution_ids":["https://openalex.org/I204136569"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5109228523"],"corresponding_institution_ids":["https://openalex.org/I84884186"],"apc_list":{"value":1800,"currency":"USD","value_usd":1800},"apc_paid":{"value":1800,"currency":"USD","value_usd":1800},"fwci":0.8337,"has_fulltext":true,"cited_by_count":24,"citation_normalized_percentile":{"value":0.77367465,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":99},"biblio":{"volume":"10","issue":"3","first_page":"241","last_page":"251"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11901","display_name":"Bayesian Methods and Mixture Models","score":0.9998000264167786,"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"}},"topics":[{"id":"https://openalex.org/T11901","display_name":"Bayesian Methods and Mixture Models","score":0.9998000264167786,"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/T11303","display_name":"Bayesian Modeling and Causal Inference","score":0.9952999949455261,"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/T10243","display_name":"Statistical Methods and Bayesian Inference","score":0.9864000082015991,"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/markov-chain","display_name":"Markov chain","score":0.7777469158172607},{"id":"https://openalex.org/keywords/variable-order-markov-model","display_name":"Variable-order Markov model","score":0.6729828715324402},{"id":"https://openalex.org/keywords/markov-chain-monte-carlo","display_name":"Markov chain Monte Carlo","score":0.6674999594688416},{"id":"https://openalex.org/keywords/markov-chain-mixing-time","display_name":"Markov chain mixing time","score":0.6521252393722534},{"id":"https://openalex.org/keywords/markov-model","display_name":"Markov model","score":0.6338642835617065},{"id":"https://openalex.org/keywords/markov-property","display_name":"Markov property","score":0.5971115231513977},{"id":"https://openalex.org/keywords/markov-renewal-process","display_name":"Markov renewal process","score":0.5345636606216431},{"id":"https://openalex.org/keywords/statistical-physics","display_name":"Statistical physics","score":0.5337679386138916},{"id":"https://openalex.org/keywords/markov-kernel","display_name":"Markov kernel","score":0.5316076278686523},{"id":"https://openalex.org/keywords/markov-process","display_name":"Markov process","score":0.5290557146072388},{"id":"https://openalex.org/keywords/balance-equation","display_name":"Balance equation","score":0.5220394134521484},{"id":"https://openalex.org/keywords/continuous-time-markov-chain","display_name":"Continuous-time Markov chain","score":0.4818635880947113},{"id":"https://openalex.org/keywords/examples-of-markov-chains","display_name":"Examples of Markov chains","score":0.4791830778121948},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.47886916995048523},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.468680202960968},{"id":"https://openalex.org/keywords/hidden-markov-model","display_name":"Hidden Markov model","score":0.4686443507671356},{"id":"https://openalex.org/keywords/hidden-semi-markov-model","display_name":"Hidden semi-Markov model","score":0.4197271764278412},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.4132750332355499},{"id":"https://openalex.org/keywords/sequence","display_name":"Sequence (biology)","score":0.41251513361930847},{"id":"https://openalex.org/keywords/variable-order-bayesian-network","display_name":"Variable-order Bayesian network","score":0.41142144799232483},{"id":"https://openalex.org/keywords/bayesian-probability","display_name":"Bayesian probability","score":0.408669650554657},{"id":"https://openalex.org/keywords/bayesian-inference","display_name":"Bayesian inference","score":0.2438259720802307},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.23606398701667786},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.18214350938796997},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.08659946918487549}],"concepts":[{"id":"https://openalex.org/C98763669","wikidata":"https://www.wikidata.org/wiki/Q176645","display_name":"Markov chain","level":2,"score":0.7777469158172607},{"id":"https://openalex.org/C54907487","wikidata":"https://www.wikidata.org/wiki/Q7915688","display_name":"Variable-order Markov model","level":4,"score":0.6729828715324402},{"id":"https://openalex.org/C111350023","wikidata":"https://www.wikidata.org/wiki/Q1191869","display_name":"Markov chain Monte Carlo","level":3,"score":0.6674999594688416},{"id":"https://openalex.org/C97074811","wikidata":"https://www.wikidata.org/wiki/Q6771322","display_name":"Markov chain mixing time","level":5,"score":0.6521252393722534},{"id":"https://openalex.org/C163836022","wikidata":"https://www.wikidata.org/wiki/Q6771326","display_name":"Markov model","level":3,"score":0.6338642835617065},{"id":"https://openalex.org/C189973286","wikidata":"https://www.wikidata.org/wiki/Q176695","display_name":"Markov property","level":4,"score":0.5971115231513977},{"id":"https://openalex.org/C163540672","wikidata":"https://www.wikidata.org/wiki/Q1115431","display_name":"Markov renewal process","level":5,"score":0.5345636606216431},{"id":"https://openalex.org/C121864883","wikidata":"https://www.wikidata.org/wiki/Q677916","display_name":"Statistical physics","level":1,"score":0.5337679386138916},{"id":"https://openalex.org/C106666656","wikidata":"https://www.wikidata.org/wiki/Q6771323","display_name":"Markov kernel","level":5,"score":0.5316076278686523},{"id":"https://openalex.org/C159886148","wikidata":"https://www.wikidata.org/wiki/Q176645","display_name":"Markov process","level":2,"score":0.5290557146072388},{"id":"https://openalex.org/C158917313","wikidata":"https://www.wikidata.org/wiki/Q4849964","display_name":"Balance equation","level":4,"score":0.5220394134521484},{"id":"https://openalex.org/C147080032","wikidata":"https://www.wikidata.org/wiki/Q176720","display_name":"Continuous-time Markov chain","level":5,"score":0.4818635880947113},{"id":"https://openalex.org/C76408418","wikidata":"https://www.wikidata.org/wiki/Q5419314","display_name":"Examples of Markov chains","level":5,"score":0.4791830778121948},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.47886916995048523},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.468680202960968},{"id":"https://openalex.org/C23224414","wikidata":"https://www.wikidata.org/wiki/Q176769","display_name":"Hidden Markov model","level":2,"score":0.4686443507671356},{"id":"https://openalex.org/C64939953","wikidata":"https://www.wikidata.org/wiki/Q3859882","display_name":"Hidden semi-Markov model","level":5,"score":0.4197271764278412},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.4132750332355499},{"id":"https://openalex.org/C2778112365","wikidata":"https://www.wikidata.org/wiki/Q3511065","display_name":"Sequence (biology)","level":2,"score":0.41251513361930847},{"id":"https://openalex.org/C71983512","wikidata":"https://www.wikidata.org/wiki/Q7915687","display_name":"Variable-order Bayesian network","level":4,"score":0.41142144799232483},{"id":"https://openalex.org/C107673813","wikidata":"https://www.wikidata.org/wiki/Q812534","display_name":"Bayesian probability","level":2,"score":0.408669650554657},{"id":"https://openalex.org/C160234255","wikidata":"https://www.wikidata.org/wiki/Q812535","display_name":"Bayesian inference","level":3,"score":0.2438259720802307},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.23606398701667786},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.18214350938796997},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.08659946918487549},{"id":"https://openalex.org/C54355233","wikidata":"https://www.wikidata.org/wiki/Q7162","display_name":"Genetics","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}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1155/2002/683164","is_oa":true,"landing_page_url":"https://doi.org/10.1155/2002/683164","pdf_url":"https://downloads.hindawi.com/journals/sp/2002/683164.pdf","source":{"id":"https://openalex.org/S166774750","display_name":"Scientific Programming","issn_l":"1058-9244","issn":["1058-9244","1875-919X"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319869","host_organization_name":"Hindawi Publishing Corporation","host_organization_lineage":["https://openalex.org/P4310319869"],"host_organization_lineage_names":["Hindawi Publishing Corporation"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Scientific Programming","raw_type":"journal-article"},{"id":"pmh:oai:doaj.org/article:36a57afea31944469f2fae77dd7b588d","is_oa":true,"landing_page_url":"https://doaj.org/article/36a57afea31944469f2fae77dd7b588d","pdf_url":null,"source":{"id":"https://openalex.org/S112646816","display_name":"SHILAP Revista de lepidopterolog\u00eda","issn_l":"0300-5267","issn":["0300-5267","2340-4078"],"is_oa":true,"is_in_doaj":true,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"journal"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Scientific Programming, Vol 10, Iss 3, Pp 241-251 (2002)","raw_type":"article"}],"best_oa_location":{"id":"doi:10.1155/2002/683164","is_oa":true,"landing_page_url":"https://doi.org/10.1155/2002/683164","pdf_url":"https://downloads.hindawi.com/journals/sp/2002/683164.pdf","source":{"id":"https://openalex.org/S166774750","display_name":"Scientific Programming","issn_l":"1058-9244","issn":["1058-9244","1875-919X"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319869","host_organization_name":"Hindawi Publishing Corporation","host_organization_lineage":["https://openalex.org/P4310319869"],"host_organization_lineage_names":["Hindawi Publishing Corporation"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Scientific Programming","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[{"id":"https://openalex.org/F4320320295","display_name":"Newcastle University","ror":"https://ror.org/01kj2bm70"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2107711562.pdf","grobid_xml":"https://content.openalex.org/works/W2107711562.grobid-xml"},"referenced_works_count":36,"referenced_works":["https://openalex.org/W48332454","https://openalex.org/W1582801283","https://openalex.org/W1602466807","https://openalex.org/W1966083328","https://openalex.org/W1969543361","https://openalex.org/W1971912858","https://openalex.org/W1982891217","https://openalex.org/W2006165373","https://openalex.org/W2027255954","https://openalex.org/W2047554048","https://openalex.org/W2054038204","https://openalex.org/W2068502909","https://openalex.org/W2074320545","https://openalex.org/W2076092328","https://openalex.org/W2083875149","https://openalex.org/W2084416457","https://openalex.org/W2085667778","https://openalex.org/W2086699924","https://openalex.org/W2087101057","https://openalex.org/W2106706098","https://openalex.org/W2118728396","https://openalex.org/W2125838338","https://openalex.org/W2166325326","https://openalex.org/W2326956676","https://openalex.org/W2340884735","https://openalex.org/W2797570932","https://openalex.org/W3127380004","https://openalex.org/W4229626626","https://openalex.org/W4231963017","https://openalex.org/W4234467048","https://openalex.org/W4242650025","https://openalex.org/W4247985008","https://openalex.org/W4253573210","https://openalex.org/W4299542564","https://openalex.org/W4301717455","https://openalex.org/W4302434451"],"related_works":["https://openalex.org/W2987631717","https://openalex.org/W4388292411","https://openalex.org/W3099350264","https://openalex.org/W292716529","https://openalex.org/W2189874347","https://openalex.org/W2159877461","https://openalex.org/W2100578510","https://openalex.org/W1560931929","https://openalex.org/W3012090835","https://openalex.org/W3022658609"],"abstract_inverted_index":{"This":[0],"paper":[1],"describes":[2],"a":[3,11,23,50],"Bayesian":[4],"approach":[5],"to":[6,37,56,85,91,104],"determining":[7],"the":[8,60,65,71,75],"order":[9,66],"of":[10,67],"finite":[12,25],"state":[13,26],"Markov":[14,27,35,43,51,68],"chain":[15,52],"whose":[16],"transition":[17],"probabilities":[18],"are":[19,99],"themselves":[20],"governed":[21],"by":[22,101],"homogeneous":[24,34],"chain.":[28],"It":[29],"extends":[30],"previous":[31],"work":[32],"on":[33],"chains":[36],"more":[38],"general":[39],"and":[40,74,107],"applicable":[41],"hidden":[42],"models.":[44],"The":[45,97],"method":[46],"we":[47],"describe":[48],"uses":[49],"Monte":[53],"Carlo":[54],"algorithm":[55],"obtain":[57],"samples":[58,81],"from":[59],"(posterior)":[61],"distribution":[62],"for":[63],"both":[64,105],"dependence":[69],"in":[70,89],"observed":[72],"sequence":[73],"other":[76],"governing":[77],"model":[78],"parameters.":[79],"These":[80],"allow":[82],"coherent":[83],"inferences":[84],"be":[86],"made":[87],"straightforwardly":[88],"contrast":[90],"those":[92],"which":[93],"use":[94],"information":[95],"criteria.":[96],"methods":[98],"illustrated":[100],"their":[102],"application":[103],"simulated":[106],"real":[108],"data":[109],"sets.":[110]},"counts_by_year":[{"year":2023,"cited_by_count":1},{"year":2020,"cited_by_count":2},{"year":2019,"cited_by_count":1},{"year":2018,"cited_by_count":1},{"year":2017,"cited_by_count":3},{"year":2016,"cited_by_count":1},{"year":2015,"cited_by_count":1},{"year":2014,"cited_by_count":2},{"year":2012,"cited_by_count":6}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}