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Biometrika 1979 66(3):495-503; doi:10.1093/biomet/66.3.495
© 1979 by Biometrika Trust
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On the use of bounds in the statistical analysis of spatial processes

PETER CLIFFORD and AIDAN W. SUDBURY

Mathematical Institute, University of Oxford
Department of Mathematics, Monash University Clayton, Victoria

Explicit solutions for the equilibrium distributions of competitive spatial processes in which the rate of invasion is directly proportional to the number of neighbours of a certain type exist only in special cases. Nevertheless these models may be more realistic than those required to produce Markov random fields. As an alternative to Monte Carlo simulation we use local balance equations to find bounds for important properties of the limiting configuration such as the population density. When a sufficient number of statistics of the local pattern are available, estimates of the parameters may be made by solving certain balance equations. When only a few statistics are available a numerical method will determine whether these are consistent with a particular set of parameter values.

Key Words: Contact process • Linear invasion • Spatial process


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