超越自动模型:自相关隋模的重新定义

IF 3.3 3区 地球科学 Q1 GEOGRAPHY Geographical Analysis Pub Date : 2024-08-19 DOI:10.1111/gean.12411
Daniel A. Griffith
{"title":"超越自动模型:自相关隋模的重新定义","authors":"Daniel A. Griffith","doi":"10.1111/gean.12411","DOIUrl":null,"url":null,"abstract":"This year is the 50th anniversary of Besag's classic auto‐models publication, a cornerstone in the development of modern‐day spatial statistics/econometrics. Besag struggled for nearly two decades to make his conceptualization collectively successful across a wide suite of random variables. But only his auto‐normal, and to a lesser degree his auto‐logistic/binomial, were workable. Others, like his auto‐Poisson, were effectively failures, whereas still others, such as potentials like an auto‐Weibull, defied even awkward mathematical incorporations of spatial lag terms. Besag circumvented this impediment by introducing an auto‐normal random effects components (within a Bayesian estimation context), building upon his single total success. This article describes an alternative approach, partly paralleling his reformulation while avoiding inserting spatial lag terms directly into probability density/mass functions, implanting spatial autocorrelation into cumulative distributions functions (CDFs), instead, via a spatially autocorrelated uniform distribution. The already existing probability integral transform and quantile function mathematical statistics theorems enable this mechanism to spatialize any random variable, with these new ones labeled sui‐models.","PeriodicalId":12533,"journal":{"name":"Geographical Analysis","volume":"8 1","pages":""},"PeriodicalIF":3.3000,"publicationDate":"2024-08-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Beyond Auto‐Models: Self‐Correlated Sui‐Model Respecifications\",\"authors\":\"Daniel A. Griffith\",\"doi\":\"10.1111/gean.12411\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"This year is the 50th anniversary of Besag's classic auto‐models publication, a cornerstone in the development of modern‐day spatial statistics/econometrics. Besag struggled for nearly two decades to make his conceptualization collectively successful across a wide suite of random variables. But only his auto‐normal, and to a lesser degree his auto‐logistic/binomial, were workable. Others, like his auto‐Poisson, were effectively failures, whereas still others, such as potentials like an auto‐Weibull, defied even awkward mathematical incorporations of spatial lag terms. Besag circumvented this impediment by introducing an auto‐normal random effects components (within a Bayesian estimation context), building upon his single total success. This article describes an alternative approach, partly paralleling his reformulation while avoiding inserting spatial lag terms directly into probability density/mass functions, implanting spatial autocorrelation into cumulative distributions functions (CDFs), instead, via a spatially autocorrelated uniform distribution. The already existing probability integral transform and quantile function mathematical statistics theorems enable this mechanism to spatialize any random variable, with these new ones labeled sui‐models.\",\"PeriodicalId\":12533,\"journal\":{\"name\":\"Geographical Analysis\",\"volume\":\"8 1\",\"pages\":\"\"},\"PeriodicalIF\":3.3000,\"publicationDate\":\"2024-08-19\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Geographical Analysis\",\"FirstCategoryId\":\"89\",\"ListUrlMain\":\"https://doi.org/10.1111/gean.12411\",\"RegionNum\":3,\"RegionCategory\":\"地球科学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q1\",\"JCRName\":\"GEOGRAPHY\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Geographical Analysis","FirstCategoryId":"89","ListUrlMain":"https://doi.org/10.1111/gean.12411","RegionNum":3,"RegionCategory":"地球科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"GEOGRAPHY","Score":null,"Total":0}
引用次数: 0

摘要

今年是贝萨格经典自动模型出版 50 周年,该模型是现代空间统计学/计量经济学发展的基石。贝萨格奋斗了近二十年,才使他的概念化在广泛的随机变量中取得了集体成功。但是,只有他的自正态分布以及在较小程度上的自逻辑/二项式分布是可行的。其他的随机变量,比如自变泊松(auto-Poisson),实际上是失败的;还有一些随机变量,比如自变韦布尔(auto-Weibull),甚至连空间滞后项的笨拙数学结合都无法实现。贝萨格通过引入自动正态随机效应成分(在贝叶斯估计的背景下)规避了这一障碍,并在其唯一一次成功的基础上更进一步。本文介绍了另一种方法,在部分程度上与贝萨格的重构相似,但避免在概率密度/质量函数中直接插入空间滞后项,而是通过空间自相关均匀分布将空间自相关植入累积分布函数(CDF)。已有的概率积分变换和量子函数数理统计定理使这一机制能够将任何随机变量空间化,这些新的随机变量被称为隋模型。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
查看原文
分享 分享
微信好友 朋友圈 QQ好友 复制链接
本刊更多论文
Beyond Auto‐Models: Self‐Correlated Sui‐Model Respecifications
This year is the 50th anniversary of Besag's classic auto‐models publication, a cornerstone in the development of modern‐day spatial statistics/econometrics. Besag struggled for nearly two decades to make his conceptualization collectively successful across a wide suite of random variables. But only his auto‐normal, and to a lesser degree his auto‐logistic/binomial, were workable. Others, like his auto‐Poisson, were effectively failures, whereas still others, such as potentials like an auto‐Weibull, defied even awkward mathematical incorporations of spatial lag terms. Besag circumvented this impediment by introducing an auto‐normal random effects components (within a Bayesian estimation context), building upon his single total success. This article describes an alternative approach, partly paralleling his reformulation while avoiding inserting spatial lag terms directly into probability density/mass functions, implanting spatial autocorrelation into cumulative distributions functions (CDFs), instead, via a spatially autocorrelated uniform distribution. The already existing probability integral transform and quantile function mathematical statistics theorems enable this mechanism to spatialize any random variable, with these new ones labeled sui‐models.
求助全文
通过发布文献求助,成功后即可免费获取论文全文。 去求助
来源期刊
CiteScore
8.70
自引率
5.60%
发文量
40
期刊介绍: First in its specialty area and one of the most frequently cited publications in geography, Geographical Analysis has, since 1969, presented significant advances in geographical theory, model building, and quantitative methods to geographers and scholars in a wide spectrum of related fields. Traditionally, mathematical and nonmathematical articulations of geographical theory, and statements and discussions of the analytic paradigm are published in the journal. Spatial data analyses and spatial econometrics and statistics are strongly represented.
期刊最新文献
Issue Information Impacts of improved transport on regional market access Testing Hypotheses When You Have More Than a Few* Beyond Auto‐Models: Self‐Correlated Sui‐Model Respecifications Issue Information
×
引用
GB/T 7714-2015
复制
MLA
复制
APA
复制
导出至
BibTeX EndNote RefMan NoteFirst NoteExpress
×
×
提示
您的信息不完整,为了账户安全,请先补充。
现在去补充
×
提示
您因"违规操作"
具体请查看互助需知
我知道了
×
提示
现在去查看 取消
×
提示
确定
0
微信
客服QQ
Book学术公众号 扫码关注我们
反馈
×
意见反馈
请填写您的意见或建议
请填写您的手机或邮箱
已复制链接
已复制链接
快去分享给好友吧!
我知道了
×
扫码分享
扫码分享
Book学术官方微信
Book学术文献互助
Book学术文献互助群
群 号:481959085
Book学术
文献互助 智能选刊 最新文献 互助须知 联系我们:info@booksci.cn
Book学术提供免费学术资源搜索服务,方便国内外学者检索中英文文献。致力于提供最便捷和优质的服务体验。
Copyright © 2023 Book学术 All rights reserved.
ghs 京公网安备 11010802042870号 京ICP备2023020795号-1