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Analysing binary lattice data with the nearest-neighbor property

Published online by Cambridge University Press:  14 July 2016

David J. Strauss
David J. Strauss*
Affiliation:
University of California, Riverside
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Abstract

The probability density of binary variables on a lattice with the nearest-neighbor condition is given by the Gibbs Random Field formula. This paper examines some consequences of the result. Approximate formulae for the maximum likelihood estimator of the persistence parameter are derived and discussed, with an example. A comparison is made between two test statistics for independence.

Keywords

NEAREST NEIGHBOR SYSTEMMARKOV RANDOM FIELDPERSISTENCE

Information

Type
Research Papers
Information
Journal of Applied Probability , Volume 12 , Issue 4 , December 1975, pp. 702 - 712
Copyright
Copyright © Applied Probability Trust 1975 

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References

Bartlett, M. S. (1971a) Physical nearest neighbor systems and non-linear time series. J. Appl. Prob. 8, 222–232.Google Scholar
Bartlett, M. S. (1971b) Two-dimensional nearest neighbor systems and their ecological application. In Statistical Ecology I, 179–194. Pennsylvania State University Press.Google Scholar
Besag, J. E. (1972a) Nearest neighbor systems and the auto-logistic model for binary data. J. R. Statist. Soc., B 34, 75–83.Google Scholar
Besag, J. E. (1972b) On the statistical analysis of nearest-neighbor systems. European meeting of statisticians, Budapest 1972. Google Scholar
Besag, J. E. (1974) Spatial interaction and the statistical analysis of lattice systems. J. R. Statist. Soc. B 36, 192–235.Google Scholar
Cliff, A. D. and Ord, J. K. (1973) Spatial Autocorrelation. Pion, London.Google Scholar
Barton, D. E. and David, F. N. (1958) Non randomness in a sequence of two alternatives, II. Runs test. Biometrika 45, 253–255.Google Scholar
Barton, D. E. (1962) Combinatorial Chance. Griffin, London.Google Scholar
David, F. N. (1970) Measurement of diversity, I. Sixth Berkeley Symp. Math. Statist. Prob. 631–648.Google Scholar
David, F. N. (1971) Measurement of diversity, II. Sixth Berkeley Symp. Math. Statist. Prob. 4, 109–136.Google Scholar
Grimmett, G. R. (1973) A theorem about random fields. Bull. Lond. Math. Soc. 5, 81–84.Google Scholar
Hammersley, J. M. and Clifford, P. (1971) Markov fields on finite graphs and lattices (unpublished).Google Scholar
Kendall, M. G. and Stuart, A. (1961) Advanced Theory of Statistics, Vol. II, Griffin, London.Google Scholar
Iyer, P. V. A. Krishnah (1949) The first and second moments of some distributions arising from points on a lattice, and their application. Biometrika 36, 135–141.Google Scholar
Iyer, P. V. A. Krishnah (1952) Factorial moments and cumulants of distributions arising in Markov chains. J. Ind. Soc. Agr. Statist. 4, 113–123.Google Scholar
Moran, P. A. P. (1948) The interpretation of statistical maps. J. R. Statist. Sot. B 10, 243–251.Google Scholar
Preston, C. J. (1973) Generalised Gibbs states and Markov random fields. Adv. Appl. Prob. 5, 242–261.Google Scholar
Spitzer, F. (1971) Markov Random Fields and Gibbs ensembles. Amer. Math. Monthly 78, 142–154.Google Scholar