Beyond Auto‐Models: Self‐Correlated Sui‐Model Respecifications

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.