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Summary statistics for inhomogeneous marked point processes

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Abstract

We propose new summary statistics for intensity-reweighted moment stationary marked point processes with particular emphasis on discrete marks. The new statistics are based on the \(n\)-point correlation functions and reduce to cross \(J\)- and \(D\)-functions when stationarity holds. We explore the relationships between the various functions and discuss their explicit forms under specific model assumptions. We derive ratio-unbiased minus sampling estimators for our statistics and illustrate their use on a data set of wildfires.

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Acknowledgments

The authors are grateful to R. Turner for useful discussions and access to data and to two anonymous referees and the associate editor for useful and constructive feedback.

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Authors and Affiliations

  1. Department of Mathematics and Mathematical Statistics, Umeå university, SE-901 87, Umeå, Sweden

    O. Cronie

  2. CWI, P.O. Box 94079, NL-1090 GB, Amsterdam, The Netherlands

    M. N. M. van Lieshout

  3. Department of Applied Mathematics, University of Twente, P.O. Box 217, 7500 AE, Enschede, The Netherlands

    M. N. M. van Lieshout

Authors
  1. O. Cronie
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  2. M. N. M. van Lieshout
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Corresponding author

Correspondence to M. N. M. van Lieshout.

Additional information

This research was supported by the Netherlands Organisation for Scientific Research NWO (613.000.809) and carried out while Cronie was at CWI.

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Cronie, O., van Lieshout, M.N.M. Summary statistics for inhomogeneous marked point processes. Ann Inst Stat Math 68, 905–928 (2016). https://doi.org/10.1007/s10463-015-0515-z

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  • DOI: https://doi.org/10.1007/s10463-015-0515-z

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