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The Multi‐scale Marked Area‐interaction Point Process: A Model for the Spatial Pattern of Trees

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  • NICOLAS PICARD
  • AVNER BAR‐HEN
  • FRÉDÉRIC MORTIER
  • JOËL CHADŒUF

Abstract

. The spatial pattern of trees in forests often combines different types of structure (regularity, clustering or randomness) at different scales. Taking species or size into account leads to marked patterns. The question addressed is to model such multi‐scale marked patterns using a single process. Within the category of Markov processes, the area‐interaction process has the advantage of being locally stable, whether it is attractive or repulsive. This process was originally defined as a one‐scale non‐marked process. We propose an extension as a multi‐scale marked process. Three examples are presented to show the adequacy of this process to model tree patterns: 1. A pine pattern showing anisotropic regularity and clustering at different scales. 2. A bivariate (adult/juvenile) kimboto pattern in French Guiana, showing regularity for one type, clustering for the other and repulsion between the two. 3. A marked pattern in Gabon where the mark is tree diameter.

Suggested Citation

  • Nicolas Picard & Avner Bar‐Hen & Frédéric Mortier & Joël Chadœuf, 2009. "The Multi‐scale Marked Area‐interaction Point Process: A Model for the Spatial Pattern of Trees," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 36(1), pages 23-41, March.
    • Handle: RePEc:bla:scjsta:v:36:y:2009:i:1:p:23-41
    DOI: 10.1111/j.1467-9469.2008.00612.x
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    References listed on IDEAS

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    1. Gregori, P. & van Lieshout, M. N. M. & Mateu, J., 2004. "Mixture formulae for shot noise weighted point processes," Statistics & Probability Letters, Elsevier, vol. 67(4), pages 311-320, May.
    2. Rasmus Plenge Waagepetersen, 2007. "An Estimating Function Approach to Inference for Inhomogeneous Neyman–Scott Processes," Biometrics, The International Biometric Society, vol. 63(1), pages 252-258, March.
    3. Ferrari, Pablo A. & Fernández, Roberto & Garcia, Nancy L., 2002. "Perfect simulation for interacting point processes, loss networks and Ising models," Stochastic Processes and their Applications, Elsevier, vol. 102(1), pages 63-88, November.
    4. van Lieshout, M.N.M. & Stoica, R.S., 2006. "Perfect simulation for marked point processes," Computational Statistics & Data Analysis, Elsevier, vol. 51(2), pages 679-698, November.
    5. A. Baddeley & M. Lieshout, 1995. "Area-interaction point processes," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 47(4), pages 601-619, December.
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    1. Mari Myllymäki & Tuomas Rajala & Aila Särkkä, 2024. "Discussion of “Marked Spatial Point Processes: Current State and Extensions to Point Processes on Linear Networks”," Journal of Agricultural, Biological and Environmental Statistics, Springer;The International Biometric Society;American Statistical Association, vol. 29(2), pages 399-404, June.
    2. Chen, Jiaxun & Micheas, Athanasios C. & Holan, Scott H., 2022. "Hierarchical Bayesian modeling of spatio-temporal area-interaction processes," Computational Statistics & Data Analysis, Elsevier, vol. 167(C).
    3. David Dereudre & Frédéric Lavancier & Kateřina Staňková Helisová, 2014. "Estimation of the Intensity Parameter of the Germ-Grain Quermass-Interaction Model when the Number of Germs is not Observed," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 41(3), pages 809-829, September.
    4. Genet, Astrid & Grabarnik, Pavel & Sekretenko, Olga & Pothier, David, 2014. "Incorporating the mechanisms underlying inter-tree competition into a random point process model to improve spatial tree pattern analysis in forestry," Ecological Modelling, Elsevier, vol. 288(C), pages 143-154.
    5. Baddeley, Adrian & Turner, Rolf & Mateu, Jorge & Bevan, Andrew, 2013. "Hybrids of Gibbs Point Process Models and Their Implementation," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 55(i11).

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