Spatial Interaction and the Statistical Analysis of Lattice Systems
Abstract
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.
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The four-neighbour Gaussian intrinsic autoregression has dual interpretations as a limiting version of a first-order stationary Gaussian conditional autoregression and as locally planar stochastic interpolation.
“and has dual interpretations, both as a limiting version of a ®rst-order stationary Gaussian (conditional) autoregression (Besag, 1974) and as locally planar stochastic interpolation.”
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- Authors
- Besag, J.
- Affiliations
- University of Liverpool (GB)
- Corresponding author
- Besag, Julian
- Venue
- Journal of the Royal Statistical Society Series B: Statistical Methodology
- Publisher
- Oxford University Press (OUP)
- Published
- 1974-01-01
- Volume
- 36
- Issue
- 2
- Pages
- 192-225
- ISSN
- 1369-7412 (ISSN-L)
- 1467-9868
- OpenAlex
- W2114220616
- Cited by
- 6,067
- References
- 0
- Citations by year
- 2026: 132 · 2025: 153 · 2024: 140 · 2023: 160 · 2022: 147 · 2021: 244 · 2020: 195 · 2019: 230 · 2018: 199 · 2017: 189 · 2016: 224 · 2015: 218 · 2014: 262 · 2013: 232 · 2012: 271
- FWCI
- 53.31
- Type
- journal article
- Language
- en
- Open access
- closed
- Licence
- academic.oup.com/journals/pages/open_access/funder_policies/chorus/standard_publication_model (vor)
- Locations
- Journal of the Royal Statistical Society Series B (Statistical Methodology) (publishedVersion)
- Topics
- Social Sciences › Economics, Econometrics and Finance › Economics and Econometrics › Spatial and Panel Data Analysis
- Physical Sciences › Mathematics › Applied Mathematics › Point processes and geometric inequalities
- Physical Sciences › Computer Science › Artificial Intelligence › Bayesian Modeling and Causal Inference
- Keywords
- spatial interaction, lattice systems, Hammersley-Clifford theorem, conditional probability model, Markov random fields, plant ecology
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