Spatial Interaction and the Statistical Analysis of Lattice Systems

作者：Julian Besag · 发表于：Journal of the Royal Statistical Society Series B (Statistical Methodology) · 年份：1974 · DOI：10.1111/j.2517-6161.1974.tb00999.x · 被引用次数：6202 · 研究领域：Ecology and Vegetation Dynamics Studies、Plant and animal studies、Statistical Methods and Bayesian Inference

Summary The formulation of conditional probability models for finite systems of spatially interacting random variables is examined. A simple alternative proof of the Hammersley–Clifford theorem is presented and the theorem is then used to construct specific spatial schemes on and off the lattice. Particular emphasis is placed upon practical applications of the models in plant ecology when the variates are binary or Gaussian. Some aspects of infinite lattice Gaussian processes are discussed. Methods of statistical analysis for lattice schemes are proposed, including a very flexible coding technique. The methods are illustrated by two numerical examples. It is maintained throughout that the conditional probability approach to the specification and analysis of spatial interaction is more attractive than the alternative joint probability approach.