{"title":"在Logistic回归中使用调查抽样算法进行精确推理","authors":"Louis-Paul Rivest, Serigne Abib Gaye","doi":"10.1111/insr.12507","DOIUrl":null,"url":null,"abstract":"<div>\n \n <p>Several exact inference procedures for logistic regression require the simulation of a 0-1 dependent vector according to its conditional distribution, given the sufficient statistics for some nuisance parameters. This is viewed, in this work, as a sampling problem involving a population of \n<math>\n <mi>n</mi></math> units, unequal selection probabilities and balancing constraints. The basis for this reformulation of exact inference is a proposition deriving the limit, as \n<math>\n <mi>n</mi></math> goes to infinity, of the conditional distribution of the dependent vector given the logistic regression sufficient statistics. It is proposed to sample from this distribution using the cube sampling algorithm. The interest of this approach to exact inference is illustrated by tackling new problems. First it allows to carry out exact inference with continuous covariates. It is also useful for the investigation of a partial correlation between several 0-1 vectors. This is illustrated in an example dealing with presence-absence data in ecology.</p>\n </div>","PeriodicalId":14479,"journal":{"name":"International Statistical Review","volume":"91 1","pages":"18-34"},"PeriodicalIF":1.7000,"publicationDate":"2022-05-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"1","resultStr":"{\"title\":\"Using Survey Sampling Algorithms For Exact Inference in Logistic Regression\",\"authors\":\"Louis-Paul Rivest, Serigne Abib Gaye\",\"doi\":\"10.1111/insr.12507\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div>\\n \\n <p>Several exact inference procedures for logistic regression require the simulation of a 0-1 dependent vector according to its conditional distribution, given the sufficient statistics for some nuisance parameters. This is viewed, in this work, as a sampling problem involving a population of \\n<math>\\n <mi>n</mi></math> units, unequal selection probabilities and balancing constraints. The basis for this reformulation of exact inference is a proposition deriving the limit, as \\n<math>\\n <mi>n</mi></math> goes to infinity, of the conditional distribution of the dependent vector given the logistic regression sufficient statistics. It is proposed to sample from this distribution using the cube sampling algorithm. The interest of this approach to exact inference is illustrated by tackling new problems. First it allows to carry out exact inference with continuous covariates. It is also useful for the investigation of a partial correlation between several 0-1 vectors. This is illustrated in an example dealing with presence-absence data in ecology.</p>\\n </div>\",\"PeriodicalId\":14479,\"journal\":{\"name\":\"International Statistical Review\",\"volume\":\"91 1\",\"pages\":\"18-34\"},\"PeriodicalIF\":1.7000,\"publicationDate\":\"2022-05-31\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"1\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"International Statistical Review\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://onlinelibrary.wiley.com/doi/10.1111/insr.12507\",\"RegionNum\":3,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q1\",\"JCRName\":\"STATISTICS & PROBABILITY\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"International Statistical Review","FirstCategoryId":"100","ListUrlMain":"https://onlinelibrary.wiley.com/doi/10.1111/insr.12507","RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"STATISTICS & PROBABILITY","Score":null,"Total":0}
Using Survey Sampling Algorithms For Exact Inference in Logistic Regression
Several exact inference procedures for logistic regression require the simulation of a 0-1 dependent vector according to its conditional distribution, given the sufficient statistics for some nuisance parameters. This is viewed, in this work, as a sampling problem involving a population of
units, unequal selection probabilities and balancing constraints. The basis for this reformulation of exact inference is a proposition deriving the limit, as
goes to infinity, of the conditional distribution of the dependent vector given the logistic regression sufficient statistics. It is proposed to sample from this distribution using the cube sampling algorithm. The interest of this approach to exact inference is illustrated by tackling new problems. First it allows to carry out exact inference with continuous covariates. It is also useful for the investigation of a partial correlation between several 0-1 vectors. This is illustrated in an example dealing with presence-absence data in ecology.
期刊介绍:
International Statistical Review is the flagship journal of the International Statistical Institute (ISI) and of its family of Associations. It publishes papers of broad and general interest in statistics and probability. The term Review is to be interpreted broadly. The types of papers that are suitable for publication include (but are not limited to) the following: reviews/surveys of significant developments in theory, methodology, statistical computing and graphics, statistical education, and application areas; tutorials on important topics; expository papers on emerging areas of research or application; papers describing new developments and/or challenges in relevant areas; papers addressing foundational issues; papers on the history of statistics and probability; white papers on topics of importance to the profession or society; and historical assessment of seminal papers in the field and their impact.