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
Daniel A. Griffith
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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。
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.
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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.
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