{"id":"https://openalex.org/W7220412971","doi":"https://doi.org/10.6084/m9.figshare.34069897","title":"Mixture of Directed Graphical Models for Discrete Spatial Random Fields","display_name":"Mixture of Directed Graphical Models for Discrete Spatial Random Fields","publication_year":2026,"publication_date":"2026-10-05","ids":{"openalex":"https://openalex.org/W7220412971","doi":"https://doi.org/10.6084/m9.figshare.34069897"},"language":"en","primary_location":{"id":"doi:10.6084/m9.figshare.34069897","doi":"https://doi.org/10.6084/m9.figshare.34069897","is_oa":true,"landing_page_url":"https://doi.org/10.6084/m9.figshare.34069897","pdf_url":null,"source":{"id":"https://openalex.org/S4377196282","display_name":"Figshare","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I4210132348","host_organization_name":"Figshare (United Kingdom)","host_organization_lineage":["https://openalex.org/I4210132348"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Dataset"},"volume":null,"type":"dataset","is_traditional":false,"indexed_in":["datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://doi.org/10.6084/m9.figshare.34069897","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5077196365","display_name":"J. Brandon Carter","orcid":"https://orcid.org/0000-0003-1687-0564","observed_orcids":["https://orcid.org/0000-0003-1687-0564"]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"J. Brandon Carter","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5019606876","display_name":"Catherine A. Calder","orcid":"https://orcid.org/0000-0002-4459-1418","observed_orcids":["https://orcid.org/0000-0002-4459-1418"]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Catherine A. Calder","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":null,"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11911","display_name":"Spatial and Panel Data Analysis","score":0.6636000275611877,"subfield":{"id":"https://openalex.org/subfields/2002","display_name":"Economics and Econometrics"},"field":{"id":"https://openalex.org/fields/20","display_name":"Economics, Econometrics and Finance"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}},"topics":[{"id":"https://openalex.org/T11911","display_name":"Spatial and Panel Data Analysis","score":0.6636000275611877,"subfield":{"id":"https://openalex.org/subfields/2002","display_name":"Economics and Econometrics"},"field":{"id":"https://openalex.org/fields/20","display_name":"Economics, Econometrics and Finance"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}},{"id":"https://openalex.org/T11303","display_name":"Bayesian Modeling and Causal Inference","score":0.31520000100135803,"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/T11901","display_name":"Bayesian Methods and Mixture Models","score":0.009999999776482582,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/directed-acyclic-graphs","display_name":"directed acyclic graphs","score":0.8970000147819519},{"id":"https://openalex.org/keywords/areal-units","display_name":"areal units","score":0.8330000042915344},{"id":"https://openalex.org/keywords/spatial-dependence","display_name":"spatial dependence","score":0.7070000171661377},{"id":"https://openalex.org/keywords/markov-random-fields","display_name":"Markov random fields","score":0.828000009059906},{"id":"https://openalex.org/keywords/compatibility","display_name":"compatibility","score":0.3970000147819519},{"id":"https://openalex.org/keywords/posterior-inference","display_name":"posterior inference","score":0.8130000233650208},{"id":"https://openalex.org/keywords/computational-efficiency","display_name":"computational efficiency","score":0.6430000066757202},{"id":"https://openalex.org/keywords/bayesian-inference","display_name":"Bayesian inference","score":0.43299999833106995},{"id":"https://openalex.org/keywords/ecometrics","display_name":"ecometrics","score":0.7379999756813049}],"concepts":[{"id":"https://openalex.org/C155846161","wikidata":"https://www.wikidata.org/wiki/Q1143367","display_name":"Graphical model","level":2,"score":0.876800000667572},{"id":"https://openalex.org/C74197172","wikidata":"https://www.wikidata.org/wiki/Q1195339","display_name":"Directed acyclic graph","level":2,"score":0.7742999792098999},{"id":"https://openalex.org/C2776214188","wikidata":"https://www.wikidata.org/wiki/Q408386","display_name":"Inference","level":2,"score":0.6629999876022339},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.5719000101089478},{"id":"https://openalex.org/C2778045648","wikidata":"https://www.wikidata.org/wiki/Q176827","display_name":"Markov random field","level":4,"score":0.5656999945640564},{"id":"https://openalex.org/C148067565","wikidata":"https://www.wikidata.org/wiki/Q3323718","display_name":"Moral graph","level":5,"score":0.5397999882698059},{"id":"https://openalex.org/C98763669","wikidata":"https://www.wikidata.org/wiki/Q176645","display_name":"Markov chain","level":2,"score":0.5231999754905701},{"id":"https://openalex.org/C160234255","wikidata":"https://www.wikidata.org/wiki/Q812535","display_name":"Bayesian inference","level":3,"score":0.513700008392334},{"id":"https://openalex.org/C2777472644","wikidata":"https://www.wikidata.org/wiki/Q16968992","display_name":"Approximate inference","level":3,"score":0.4921000003814697},{"id":"https://openalex.org/C146380142","wikidata":"https://www.wikidata.org/wiki/Q1137726","display_name":"Directed graph","level":2,"score":0.4666999876499176},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.46630001068115234},{"id":"https://openalex.org/C2776359362","wikidata":"https://www.wikidata.org/wiki/Q2145286","display_name":"Representation (politics)","level":3,"score":0.4641000032424927},{"id":"https://openalex.org/C107673813","wikidata":"https://www.wikidata.org/wiki/Q812534","display_name":"Bayesian probability","level":2,"score":0.45879998803138733},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.4505000114440918},{"id":"https://openalex.org/C3018234147","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Undirected graph","level":3,"score":0.44699999690055847},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.39590001106262207},{"id":"https://openalex.org/C33724603","wikidata":"https://www.wikidata.org/wiki/Q812540","display_name":"Bayesian network","level":2,"score":0.39579999446868896},{"id":"https://openalex.org/C134261354","wikidata":"https://www.wikidata.org/wiki/Q938438","display_name":"Statistical inference","level":2,"score":0.38960000872612},{"id":"https://openalex.org/C159886148","wikidata":"https://www.wikidata.org/wiki/Q176645","display_name":"Markov process","level":2,"score":0.3846000134944916},{"id":"https://openalex.org/C130402806","wikidata":"https://www.wikidata.org/wiki/Q5361768","display_name":"Random field","level":2,"score":0.3643999993801117},{"id":"https://openalex.org/C2779343474","wikidata":"https://www.wikidata.org/wiki/Q3109175","display_name":"Context (archaeology)","level":2,"score":0.3499000072479248},{"id":"https://openalex.org/C163836022","wikidata":"https://www.wikidata.org/wiki/Q6771326","display_name":"Markov model","level":3,"score":0.34610000252723694},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.3416000008583069},{"id":"https://openalex.org/C159246509","wikidata":"https://www.wikidata.org/wiki/Q5428725","display_name":"Factor graph","level":3,"score":0.34049999713897705},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.3303000032901764},{"id":"https://openalex.org/C114289077","wikidata":"https://www.wikidata.org/wiki/Q3284399","display_name":"Statistical model","level":2,"score":0.3192000091075897},{"id":"https://openalex.org/C61224824","wikidata":"https://www.wikidata.org/wiki/Q2260434","display_name":"Mixture model","level":2,"score":0.3098999857902527},{"id":"https://openalex.org/C88230418","wikidata":"https://www.wikidata.org/wiki/Q131476","display_name":"Graph theory","level":2,"score":0.2930999994277954},{"id":"https://openalex.org/C9652623","wikidata":"https://www.wikidata.org/wiki/Q190109","display_name":"Field (mathematics)","level":2,"score":0.290800005197525},{"id":"https://openalex.org/C36464697","wikidata":"https://www.wikidata.org/wiki/Q451553","display_name":"Visualization","level":2,"score":0.2849999964237213},{"id":"https://openalex.org/C2984927552","wikidata":"https://www.wikidata.org/wiki/Q845734","display_name":"Graphical display","level":2,"score":0.28360000252723694},{"id":"https://openalex.org/C169272836","wikidata":"https://www.wikidata.org/wiki/Q5668307","display_name":"Variable elimination","level":3,"score":0.2815999984741211},{"id":"https://openalex.org/C148764684","wikidata":"https://www.wikidata.org/wiki/Q621751","display_name":"Approximation algorithm","level":2,"score":0.2791000008583069},{"id":"https://openalex.org/C111350023","wikidata":"https://www.wikidata.org/wiki/Q1191869","display_name":"Markov chain Monte Carlo","level":3,"score":0.2694999873638153},{"id":"https://openalex.org/C49937458","wikidata":"https://www.wikidata.org/wiki/Q2599292","display_name":"Probabilistic logic","level":2,"score":0.26429998874664307},{"id":"https://openalex.org/C124101348","wikidata":"https://www.wikidata.org/wiki/Q172491","display_name":"Data mining","level":1,"score":0.2632000148296356},{"id":"https://openalex.org/C79772020","wikidata":"https://www.wikidata.org/wiki/Q5159264","display_name":"Conditional independence","level":2,"score":0.2619999945163727}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.6084/m9.figshare.34069897","doi":"https://doi.org/10.6084/m9.figshare.34069897","is_oa":true,"landing_page_url":"https://doi.org/10.6084/m9.figshare.34069897","pdf_url":null,"source":{"id":"https://openalex.org/S4377196282","display_name":"Figshare","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I4210132348","host_organization_name":"Figshare (United Kingdom)","host_organization_lineage":["https://openalex.org/I4210132348"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Dataset"},{"id":"doi:10.6084/m9.figshare.34069897.v1","doi":"https://doi.org/10.6084/m9.figshare.34069897.v1","is_oa":true,"landing_page_url":"https://doi.org/10.6084/m9.figshare.34069897.v1","pdf_url":null,"source":{"id":"https://openalex.org/S4377196282","display_name":"Figshare","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I4210132348","host_organization_name":"Figshare (United Kingdom)","host_organization_lineage":["https://openalex.org/I4210132348"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Dataset"}],"best_oa_location":{"id":"doi:10.6084/m9.figshare.34069897","doi":"https://doi.org/10.6084/m9.figshare.34069897","is_oa":true,"landing_page_url":"https://doi.org/10.6084/m9.figshare.34069897","pdf_url":null,"source":{"id":"https://openalex.org/S4377196282","display_name":"Figshare","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I4210132348","host_organization_name":"Figshare (United Kingdom)","host_organization_lineage":["https://openalex.org/I4210132348"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Dataset"},"sustainable_development_goals":[],"study_designs":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":["https://openalex.org/W6927422434","https://openalex.org/W7098659392","https://openalex.org/W4234548747","https://openalex.org/W7098712235","https://openalex.org/W105718209","https://openalex.org/W1849901425","https://openalex.org/W2468642508","https://openalex.org/W1802230853","https://openalex.org/W2127159115","https://openalex.org/W2061115813"],"abstract_inverted_index":{"Current":[0],"approaches":[1,103],"for":[2,37,104,174],"modeling":[3,35,102],"discrete-valued":[4],"outcomes":[5],"associated":[6],"with":[7],"spatially-dependent":[8],"areal":[9,94,178],"units":[10,179],"incur":[11],"computational":[12],"and":[13,65,144,207,223,236],"theoretical":[14],"challenges,":[15],"especially":[16],"in":[17,154,193,215,218,238],"the":[18,52,74,93,98,115,148,158,175,190,194,233],"Bayesian":[19,210],"setting":[20],"when":[21],"full":[22],"posterior":[23,134],"inference":[24,135,143],"is":[25,117],"desired.":[26],"As":[27],"an":[28,82,87,121,124,129,165,224],"alternative,":[29],"we":[30,199],"propose":[31],"a":[32,42,172,187,208,219],"novel":[33],"statistical":[34],"framework":[36],"this":[38],"data":[39,228],"setting,":[40],"namely":[41],"mixture":[43,75],"of":[44,51,86,92,100,160,183,203,221,226,232],"directed":[45,54,61],"graphical":[46,55,84],"models":[47],"(MDGMs).":[48],"The":[49,71],"components":[50,76],"mixture,":[53],"models,":[56],"can":[57,168],"be":[58,169],"represented":[59,192],"by":[60],"acyclic":[62],"graphs":[63],"(DAGs)":[64],"are":[66,77],"computationally":[67,138],"quick":[68],"to":[69,79,81,123,162,180,205],"evaluate.":[70],"DAGs":[72,184],"representing":[73],"selected":[78],"correspond":[80],"undirected":[83,166,196],"representation":[85],"assumed":[88],"spatial":[89,106],"contiguity/dependence":[90],"structure":[91],"units,":[95],"which":[96],"underlies":[97],"specification":[99],"traditional":[101],"discrete":[105],"processes":[107],"such":[108],"as":[109,120,128,171,186,230],"Markov":[110],"random":[111],"fields":[112],"(MRFs).":[113],"Notably,":[114],"MDGM":[116],"not":[118],"proposed":[119],"approximation":[122,150,213],"MRF,":[125],"but":[126],"rather":[127],"alternative":[130],"that":[131],"provides":[132],"valid":[133],"while":[136],"being":[137],"faster":[139],"than":[140,147],"exact":[141],"MRF":[142,211],"more":[145],"principled":[146],"pseudo-likelihood":[149],"(aMRF)":[151],"commonly":[152],"used":[153,170,214],"practice.":[155],"We":[156],"introduce":[157],"concept":[159],"compatibility":[161],"show":[163],"how":[164],"graph":[167],"template":[173,195],"dependencies":[176,191],"between":[177],"create":[181],"sets":[182],"which,":[185],"collection,":[188],"preserve":[189],"graph.":[197],"Lastly,":[198],"compare":[200],"highlighted":[201],"classes":[202],"MDGMs":[204],"MRFs":[206],"popular":[209],"model":[212],"high-dimensional":[216],"settings":[217],"series":[220],"simulations":[222],"analysis":[225],"ecometrics":[227],"collected":[229],"part":[231],"Adolescent":[234],"Health":[235],"Development":[237],"Context":[239],"Study.":[240]},"counts_by_year":[],"updated_date":"2026-10-28T10:33:24.094632","created_date":"2026-10-06T00:00:00"}