{"title":"A perfect sampling method for exponential family random graph models","authors":"C. Butts","doi":"10.1080/0022250X.2017.1396985","DOIUrl":null,"url":null,"abstract":"ABSTRACT Generation of deviates from random graph models with nontrivial edge dependence is an increasingly important problem. Here, we introduce a method which allows perfect sampling from random graph models in exponential family form (“exponential family random graph” models), using a variant of Coupling From The Past. We illustrate the use of the method via an application to the Markov graphs, a family that has been the subject of considerable research. We also show how the method can be applied to a variant of the biased net models, which are not exponentially parameterized.","PeriodicalId":50139,"journal":{"name":"Journal of Mathematical Sociology","volume":"42 1","pages":"17 - 36"},"PeriodicalIF":1.3000,"publicationDate":"2017-10-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1080/0022250X.2017.1396985","citationCount":"17","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Mathematical Sociology","FirstCategoryId":"90","ListUrlMain":"https://doi.org/10.1080/0022250X.2017.1396985","RegionNum":4,"RegionCategory":"社会学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"MATHEMATICS, INTERDISCIPLINARY APPLICATIONS","Score":null,"Total":0}
引用次数: 17
Abstract
ABSTRACT Generation of deviates from random graph models with nontrivial edge dependence is an increasingly important problem. Here, we introduce a method which allows perfect sampling from random graph models in exponential family form (“exponential family random graph” models), using a variant of Coupling From The Past. We illustrate the use of the method via an application to the Markov graphs, a family that has been the subject of considerable research. We also show how the method can be applied to a variant of the biased net models, which are not exponentially parameterized.
期刊介绍：
The goal of the Journal of Mathematical Sociology is to publish models and mathematical techniques that would likely be useful to professional sociologists. The Journal also welcomes papers of mutual interest to social scientists and other social and behavioral scientists, as well as papers by non-social scientists that may encourage fruitful connections between sociology and other disciplines. Reviews of new or developing areas of mathematics and mathematical modeling that may have significant applications in sociology will also be considered.
The Journal of Mathematical Sociology is published in association with the International Network for Social Network Analysis, the Japanese Association for Mathematical Sociology, the Mathematical Sociology Section of the American Sociological Association, and the Methodology Section of the American Sociological Association.
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