Spatial Interaction and the Statistical Analysis of Lattice Systems |
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文献名称 | Spatial Interaction and the Statistical Analysis of Lattice Systems | ||||||
文献作者 | Julian Besag | ||||||
作者所在单位 | University of Liverpool | ||||||
文献分类 | 已发表文献 | ||||||
学科一级分类 | 统计 | ||||||
学科二级分类 | 统计学 | ||||||
文献摘要 |
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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参考文献 |
ATKINSONA, . C. (1969). The use of residuals as a concomitant variable. Biometrika, 56, 33-41. BARTLETTM, . S. (1938). The approximate recovery of information from field experiments with large blocks. J. Agric. Sci., 28, 418-427. -(1974). Physical nearest-neighbour models and non-linear time-series, 111. Non-zero means and sub-critical temperatures. J. Appl. Prob. (in press). BESAGJ,. E. and GLEAVEJS., T. (1973). On the detection of spatial pattern in plant communities. BUN. Znt. Statist. Znst., 45, Book 1, 153-158. CLIFFORDP, . and SUDBURYA, . W. (1973). A model for spatial competition. Biometrika, 60, 581-588. DALENIUST,., HAJEKJ, . and ZUBRZYCKSI., (1961). On plane sampling and related geometrical problems. Proc. 4th Berkeley Symp. Math. Prob., 1, 125-150. FAIRFIELD SMITHH, . (1938). An empirical law describing heterogeneity in the yields of agricultural crops. J. Agric. Sci., 28, 1-23. KENDALLD, . G. (1959). Unitary dilations of one-parameter semi-groups of Markov transition operators, and the corresponding integral representations for Markov processes with a countable infinity of states. Proc. London Math. Soc. (3), 9, 417-431. KUEERA, V. (1974). The matrix equation AXSXB = C. SZAM J. Appl. Math., 26, 15-25. QUENOLJILLME., H. (1949). Problems in plane sampling. Ann. Math. Statist., 20, 355-375. WHITTLE,P. (1956). On the variation of yield variance with plot size. Biometrika, 43, 337-343. -(1962). Topographic correlation, power-law covariance functions, and diffusion. Biometrika, 49, 305-314. |
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关键字 | MARKOV FIELDS; SPATIAL INTERACTION;AUTO-MODELS; NEAREST-NEIGHBOUR SCHEMES; STATISTICAL ANALYSIS OF LATTICE SCHEMES ; CODING TECHNIQUES; SIMULTANEOUS BILATERAL AUTOREGRESSIONS; CONDITIONAL PROBABILITY MODELS | ||||||
发表所在刊物(或来源) | Journal of the Royal Statistical Society. Series B (Methodological), Vol. 36, No. 2. (1974), pp.192-236. | ||||||
发表时间 | 1974 | ||||||
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上传时间 | 2011-1-20 15:21 | ||||||
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