Abstract
Summary Bartlett (1966) and Whittle (1963), respectively, have proposed alternative, non-equivalent definitions of nearest-neighbour systems. The former, conditional probability definition, whilst the more intuitively attractive, presents several basic problems, not least in the identification of available models. In this paper, conditional probability nearest-neighbour systems for interacting random variables on a two-dimensional rectangular lattice are examined. It is shown that, in the case of 0, 1 variables and a homogeneous system, the only possibility is a logistic-type model but in which the explanatory variables at a point are the surrounding array variables themselves. A spatial–temporal approach leading to the same model is also suggested. The final section deals with linear nearest-neighbour systems, especially for continuous variables. The results of the paper may easily be extended to three or more dimensions.
Keywords
Binary dataBinary numberNearest neighbourLogistic regressionComputer scienceStatisticsArtificial intelligenceMathematics
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Publication Info
- Year
- 1972
- Type
- article
- Volume
- 34
- Issue
- 1
- Pages
- 75-83
- Citations
- 284
- Access
- Closed
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Cite This
Julian Besag
(1972).
Nearest-Neighbour Systems and the Auto-Logistic Model for Binary Data.
Journal of the Royal Statistical Society Series B (Statistical Methodology)
, 34
(1)
, 75-83.
https://doi.org/10.1111/j.2517-6161.1972.tb00889.x
Identifiers
- DOI
- 10.1111/j.2517-6161.1972.tb00889.x