%0 Journal Article %1 besag1972nearestneighbour %A Besag, J. E. %D 1972 %I Wiley for the Royal Statistical Society %J Journal of the Royal Statistical Society. Series B (Methodological) %K Ising_model Markov_random_field statistics %N 1 %P pp. 75-83 %T Nearest-Neighbour Systems and the Auto-Logistic Model for Binary Data %U http://www.jstor.org/stable/2985051 %V 34 %X 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.

@article{besag1972nearestneighbour, abstract = {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.}, added-at = {2014-05-28T16:35:35.000+0200}, author = {Besag, J. E.}, biburl = {https://www.bibsonomy.org/bibtex/2486d451c6a21dc640b6290f704cae7f6/peter.ralph}, description = {Often cited, for the "autologistic" model.}, interhash = {9ecf3a2282e086f8d2db7e0edf0a8f02}, intrahash = {486d451c6a21dc640b6290f704cae7f6}, issn = {00359246}, journal = {Journal of the Royal Statistical Society. Series B (Methodological)}, keywords = {Ising_model Markov_random_field statistics}, language = {English}, number = 1, pages = {pp. 75-83}, publisher = {Wiley for the Royal Statistical Society}, timestamp = {2014-05-28T16:35:35.000+0200}, title = {Nearest-Neighbour Systems and the Auto-Logistic Model for Binary Data}, url = {http://www.jstor.org/stable/2985051}, volume = 34, year = 1972 }