The DOI matches its Crossref record; 10 of the 10 references it cites were found in a registry or an index.
Nearest-Neighbour Systems and the Auto-Logistic Model for Binary Data
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.
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Cites
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Physical nearest-neighbour models and non-linear time-series
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Inference and stochastic processes
Bartlett, M. S. (1975) · Springer eBooks · doi:10.1007/978-94-009-5889-0_4 · Cited by 38
Inference and Stochastic Processes
Bartlett, M. S. (1967) · Journal of the Royal Statistical Society Series A (General) · doi:10.2307/2982519 · Cited by 33
A Further Note on Nearest Neighbour Models
Bartlett, M. S. (1968) · Journal of the Royal Statistical Society Series A (General) · doi:10.2307/2343725 · Cited by 32
Introduction to Stochastic Processes
Marco Bittelli, A., Olmi, R., & Rosa, R. (2022) · doi:10.1093/oso/9780198862512.003.0003 · Cited by 9
Cited by
Spatial Interaction and the Statistical Analysis of Lattice Systems
Besag, J. (1974) · Journal of the Royal Statistical Society Series B: Statistical Methodology · doi:10.1111/j.2517-6161.1974.tb00999.x · Cited by 6,067
Self-citationStatistical Analysis of Non-Lattice Data
Besag, J. (1975) · The Statistician · doi:10.2307/2987782 · Cited by 1,559
Self-citationLogit models and logistic regressions for social networks: II. Multivariate relations
Pattison, P., & Wasserman, S. (1999) · British Journal of Mathematical and Statistical Psychology · doi:10.1348/000711099159053 · Cited by 327
On a System of Two-Dimensional Recurrence Equations
Besag, J. (1981) · Journal of the Royal Statistical Society Series B: Statistical Methodology · doi:10.1111/j.2517-6161.1981.tb01675.x · Cited by 57
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Metadata
- Authors
- Besag, J. E.
- Venue
- Journal of the Royal Statistical Society Series B: Statistical Methodology
- Publisher
- Oxford University Press (OUP)
- Published
- 1972-09-01
- Volume
- 34
- Issue
- 1
- Pages
- 75-83
- ISSN
- 1369-7412 (ISSN-L)
- 1467-9868
- OpenAlex
- W2905074708
- Cited by
- 298
- References
- 10
- FWCI
- 27.31
- Type
- journal article
- Language
- en
- Open access
- closed
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Contains information from the Semantic Scholar Academic Graph Datasets, made available under the ODC Attribution License (ODC-BY 1.0).
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