A J-function for Inhomogeneous Spatio-temporal Point Processes

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We propose a new summary statistic for inhomogeneous intensity-reweighted moment stationarity spatio-temporal point processes. The statistic is defined in terms of the n-point correlation functions of the point process, and it generalizes the J-function when stationarity is assumed. We show that our statistic can be represented in terms of the generating functional and that it is related to the spatio-temporal K-function. We further discuss its explicit form under some specific model assumptions and derive ratio-unbiased estimators. We finally illustrate the use of our statistic in practice.
Original languageEnglish
Pages (from-to)562-579
Number of pages18
JournalScandinavian journal of statistics
Issue number2
Publication statusPublished - Jun 2015


  • EWI-26222
  • $n$-point correlation function
  • Intensity-reweighted moment stationarity
  • Location-dependent thinning of hard core model
  • Log-Gaussian Cox process
  • Papangelou conditional intensity
  • $K$-function
  • inhomogeneous spatio-temporal point process
  • METIS-312696
  • IR-97134
  • (reduced Palm measure) Generating functional
  • $J$-function
  • Poisson process


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