Detecting dependence between marks and locations of marked point processes

Martin Schlather, Paulo J. Ribeiro, Peter J. Diggle

Research output: Contribution to journalArticlepeer-review

72 Scopus citations


We introduce two characteristics for stationary and isotropic marked point processes, 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.

Original languageEnglish (US)
Pages (from-to)79-93
Number of pages15
JournalJournal of the Royal Statistical Society. Series B: Statistical Methodology
Issue number1
StatePublished - 2004
Externally publishedYes


  • Independence test
  • Mark correlation function
  • Mark variogram
  • Nearest neighbour
  • Preferential sampling
  • Random-field model

ASJC Scopus subject areas

  • Mathematics(all)
  • Statistics and Probability


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