%0 Journal Article %1 besag1974spatial %A Besag, Julian %D 1974 %I Wiley for the Royal Statistical Society %J Journal of the Royal Statistical Society. Series B (Methodological) %K Markov_random_field spatial_statistics statistics %N 2 %P pp. 192-236 %T Spatial Interaction and the Statistical Analysis of Lattice Systems %U http://www.jstor.org/stable/2984812 %V 36 %X 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.

@article{besag1974spatial, abstract = {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.}, added-at = {2014-05-28T16:19:45.000+0200}, author = {Besag, Julian}, biburl = {https://www.bibsonomy.org/bibtex/281dbd0f16a615ea4744d70ecb3224527/peter.ralph}, description = {Original paper describing "Besag's coding method", i.e. using the likelihood conditioned on a set of sites that makes the remaining sites independent.}, interhash = {a4d3049c33e1706f952f7f30cdff47ef}, intrahash = {81dbd0f16a615ea4744d70ecb3224527}, issn = {00359246}, journal = {Journal of the Royal Statistical Society. Series B (Methodological)}, keywords = {Markov_random_field spatial_statistics statistics}, language = {English}, number = 2, pages = {pp. 192-236}, publisher = {Wiley for the Royal Statistical Society}, timestamp = {2014-05-28T16:19:45.000+0200}, title = {Spatial Interaction and the Statistical Analysis of Lattice Systems}, url = {http://www.jstor.org/stable/2984812}, volume = 36, year = 1974 }