Detecting dependence between marks and locations of marked point processes |
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Authors: | Martin Schlather Paulo J Ribeiro Jr and Peter J Diggle |
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Institution: | Universität Bayreuth, Germany; Universidade Federal do Paraná, Brazil; Lancaster University, UK |
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Abstract: | Summary. We introduce two characteristics for stationary and isotropic marked point proces- ses, E ( h ) and V ( h ), and describe their use in investigating mark–point interactions. These quantities are functions of the interpoint distance h and denote the conditional expectation and the conditional variance of a mark respectively, given that there is a further point of the process a distance h away. We present tests based on E and V for the hypothesis that the values of the marks can be modelled by a random field which is independent of the unmarked point process. We apply the methods to two data sets in forestry. |
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Keywords: | Independence test Mark correlation function Mark variogram Nearest neighbour Preferential sampling Random-field model |
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