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The statistical analysis of spatial pattern

Published online by Cambridge University Press:  01 July 2016

M. S. Bartlett
M. S. Bartlett*
Affiliation:
University of Oxford
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Abstract

A brief survey is made of the range of models and statistical techniques relevant to the analysis of spatial pattern, and more detailed discussion given to three specific classes of stochastic process in two dimensions viz. (i) continuous processes X(r), (ii) point processes N(r), (iii) lattice processes Xi . The appropriate theory for these classes of processes is indicated in Part I; and in Part II some examples of data are classified under these same three headings, and their statistical analysis discussed.

Keywords

SPATIAL PATTERNTWO-DIMENSIONAL CORRELATION ANALYSISNEAREST NEIGHBOUR SYSTEMSLATTICE PROCESSESINHIBITORY POINT PROCESSES

Information

Type
Research Article
Information
Advances in Applied Probability , Volume 6 , Issue 2 , June 1974 , pp. 336 - 358
Copyright
Copyright © Applied Probability Trust 1974 

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References

(Starred items contain useful further bibliographies.) Google Scholar
Bartlett, M. S. (1964a) A note on spatial pattern. Biometrics 20, 891–892.Google Scholar
Bartlett, M. S. (1964b) The spectral analysis of two-dimensional point processes. Biometrika 51, 299–311.Google Scholar
Bartlett, M. S. (1966) Stochastic Processes. 2nd ed. Cambridge University Press.Google Scholar
Bartlett, M. S. (1967) Inference and stochastic processes. J. R. Statist. Soc. A 130, 457–477.Google Scholar
Bartlett, M. S. (1968) A further note on nearest neighbour models. J. R. Statist. Soc. A 131, 579–580.Google Scholar
Bartlett, M. S. (1971a) Two-dimensional nearest-neighbour systems and their ecological applications. Statistical Ecology. Vol. 1. Pennsylvania State University Press. 179–194.Google Scholar
Bartlett, M. S. (1971b) Physical nearest-neighbour models and non-linear time-series. J. Appl. Prob. 8, 222–232.Google Scholar
Bartlett, M. S. (1972) Physical nearest-neighbour models and non-linear time-series II. J. Appl. Prob. 9, 76–86.Google Scholar
Bartlett, M. S. and Besag, J. E. (1969) Correlation properties of some nearest neighbour systems. Bull. Int. Statist. (Book 2) 43, 191–193.Google Scholar
Besag, J. E. (1972a) On the correlation structure of some two-dimensional stationary processes. Biometrika 59, 43–48.CrossRefGoogle Scholar
Besag, J. E. (1972b) Nearest-neighbour systems and the auto-logistic model for binary data. J. R. Statist. Soc. B 34, 75–83.Google Scholar
Besag, J. E. (1972c) Nearest neighbour systems: a lemma with application to Bartlett's global solutions. J. Appl. Prob. 9, 418–421.Google Scholar
* Besag, J. E. (1974) Spatial interaction and the statistical analysis of lattice systems. J. R. Statist. Soc. B 36. To appear.CrossRefGoogle Scholar
Besag, J. E. and Gleaves, J. T. (1973) On the detection of spatial pattern in plant communities. To appear.Google Scholar
Brook, D. (1964) On the distinction between the conditional probability and the joint probability approaches in the specification of nearest-neighbour systems. Biometrika 51, 481–483.Google Scholar
Cox, D. R. and Lewis, P. A. W. (1966) The Statistical Analysis of Series of Events. Methuen, London.CrossRefGoogle Scholar
Crisp, D. J. (1961) Territorial behaviour in barnacle settlement. J. Exp. Biol. 38, 429–446.CrossRefGoogle Scholar
* Diggle, P. (1973) Contagion and allied processes. M. Sc. Thesis, University of Oxford.Google Scholar
Dobrushin, R. L. (1968) The description of a random field by means of its conditional probabilities. Theor. Probability Appl. 13, 197–224.Google Scholar
Eberhardt, L. L. (1967) Some developments in ‘distance sampling’. Biometrics 23, 207–216.Google Scholar
Freeman, G. H. (1953) Spread of diseases in a rectangular plantation with vacancies. Biometrika 40, 287–305.Google Scholar
* Greig-Smith, P. (1957) Quantitative Plant Ecology. Butterworths, London.Google Scholar
Hammersley, J. (1972) Stochastic models for the distribution of particles in space. Proceedings of Symposium on Statistical and Probabilistic Problems in Metallurgy. Seattle, August 1971 (Ed. Nicholson, W. L.). Adv. Appl. Prob. Special Supplement, 47–68.CrossRefGoogle Scholar
Heine, V. (1955) Models for two-dimensional stationary stochastic processes. Biometrika 42, 170–178.Google Scholar
* Holgate, P. (1972) The use of distance methods for the analysis of spatial distribution of points. Stochastic Point Processes. Wiley, New York, 122–135.Google Scholar
* Kendall, M. G. and Moran, P. A. P. (1963) Geometrical Probability. Griffin, London.Google Scholar
Matérn, B. (1960) Spatial Variation. Medd. Skogsforskn. Inst. 49, No. 5. Stockholm.Google Scholar
Matérn, B. (1971) Doubly stochastic Poisson processes in the plane. Statistical Ecology. Vol. 1. Pennsylvania State University Press. 195–213.Google Scholar
Mead, R. (1967) A mathematical model for the estimation of interplant competition. Biometrics 23, 189–205.Google Scholar
Mead, R. (1971) Models for interplant competition in irregularly spaced populations. Statistical Ecology. Vol. 2. Pennsylvania State University Press. 13–30.Google Scholar
* Moran, P. A. P. (1966) A note on recent research in geometrical probability J. Appl. Prob. 3, 453–463.Google Scholar
Moran, P. A. P. (1973) A Gaussian Markovian process on a square lattice. J. Appl. Prob 10, 54–62.Google Scholar
Onsager, L. (1944) Crystal statistics I. A two-dimensional model with an order-disorder transition. Phys. Rev. 65, 117–149.Google Scholar
Ord, K. (1972) Estimation methods for models of spatial interaction. Presented at ASA conference, Montreal.Google Scholar
Pielou, E. C. (1964) The spatial pattern of two phase patchworks of vegetation. Biometrics 20, 156–167.Google Scholar
* Pielou, E. C. (1969) An Introduction to Mathematical Ecology. Wiley, New York.Google Scholar
Skellam, J. G. (1952) Studies in statistical ecology. I Spatial pattern. Biometrika 39, 346–362.Google Scholar
Spitzer, F. (1971) Markov random fields and Gibbs ensembles. Amer. Math. Monthly 78, 142–154.CrossRefGoogle Scholar
Switzer, P. (1971) Mapping a geographically correlated environment. Statistical Ecology. Vol. 1. Pennsylvania State University Press. 235–269.Google Scholar
Thompson, H. R. (1955) Spatial point processes, with application to ecology. Biometrika 42, 102–115.Google Scholar
Whittle, P. (1954) On stationary processes in the plane. Biometrika 41, 434–449.Google Scholar
Whittle, P. (1962) Topographic correlation, power-law covariance functions and diffusion. Biometrika 49, 305–314.CrossRefGoogle Scholar