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Some models for multitype spatial point processes, with remarks on analysing multitype patterns

Published online by Cambridge University Press:  14 July 2016

H. W. Lotwick*
Affiliation:
University of Bath
*
Postal address: 15 Victoria Terrace, Bath BA2 3QZ, U.K.

Abstract

Two classes of ergodic stationary multitype spatial point processes are constructed. These processes have the property that interactions between the types exist, but cannot be detected using standard second-order methods of analysis. Simulations indicate that the interactions can, however, be detected by using ‘empty space' techniques.

Type
Research Papers
Copyright
Copyright © Applied Probability Trust 1984 

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References

Diggle, P. J. (1979) On parameter estimation and goodness-of-fit testing for spatial point patterns. Biometrics 35, 87101.Google Scholar
Hanisch, K.-H. and Stoyan, D. (1979) Formulas for the second-order analysis of marked point processes. Math. Operat. Statist. Ser. Statist. 10, 555560.Google Scholar
Kallenberg, O. (1977) A counterexample to R. Davidson's conjecture on line processes. Math. Proc. Camb. Phil. Soc. 82, 301307.Google Scholar
Kingman, J. F. C. (1977) Contribution to the discussion of Ripley (1977).Google Scholar
Lotwick, H. W. and Silverman, B. W. (1982) Methods for analysing spatial processes of several types of points. J. R. Statist. Soc. B 44, 406413.Google Scholar
Matheron, G. (1975) Random Sets and Integral Geometry. Wiley, New York.Google Scholar
Ripley, B. D. (1977) Modelling spatial patterns (with discussion). J. R. Statist. Soc. B 39, 172212.Google Scholar
Ripley, B. D. (1979) Tests of ‘randomness’ for spatial point patterns. J. R. Statist. Soc. B 41, 368374.Google Scholar
Ripley, B. D. (1981) Spatial Statistics. Wiley, New York.Google Scholar
Stoyan, D. (1979) Interrupted point processes. Biom. J. 21, 607610.Google Scholar