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Parameter estimation for growth interaction processes using spatio-temporal information

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  • Redenbach, Claudia
  • Särkkä, Aila

Abstract

Methods for the parameter estimation for a spatio-temporal marked point process model, the so-called growth-interaction model, are investigated. Least squares estimation methods for this model found in the literature are only concerned with fitting the mark distribution observed in the data. These methods are unable to distinguish between models which have the same birth, death, interaction and growth functions and parameters but different arrival strategies for the points. Hence, they are extended such that the spatial structure of a point pattern is also taken into account. The suggested methods are evaluated in a simulation study and applied to a small data set from forestry.

Suggested Citation

  • Redenbach, Claudia & Särkkä, Aila, 2013. "Parameter estimation for growth interaction processes using spatio-temporal information," Computational Statistics & Data Analysis, Elsevier, vol. 57(1), pages 672-683.
    • Handle: RePEc:eee:csdana:v:57:y:2013:i:1:p:672-683
    DOI: 10.1016/j.csda.2012.08.006
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    References listed on IDEAS

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    1. A. J. Baddeley & J. Møller & R. Waagepetersen, 2000. "Non‐ and semi‐parametric estimation of interaction in inhomogeneous point patterns," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 54(3), pages 329-350, November.
    2. Cronie, Ottmar & Särkkä, Aila, 2011. "Some edge correction methods for marked spatio-temporal point process models," Computational Statistics & Data Analysis, Elsevier, vol. 55(7), pages 2209-2220, July.
    3. Renshaw, Eric & Sarkka, Aila, 2001. "Gibbs point processes for studying the development of spatial-temporal stochastic processes," Computational Statistics & Data Analysis, Elsevier, vol. 36(1), pages 85-105, March.
    4. Sarkka, Aila & Renshaw, Eric, 2006. "The analysis of marked point patterns evolving through space and time," Computational Statistics & Data Analysis, Elsevier, vol. 51(3), pages 1698-1718, December.
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    Cited by:

    1. Eckardt, Matthias & González, Jonatan A. & Mateu, Jorge, 2021. "Graphical modelling and partial characteristics for multitype and multivariate-marked spatio-temporal point processes," Computational Statistics & Data Analysis, Elsevier, vol. 156(C).
    2. Myllymäki, Mari & Kuronen, Mikko & Bianchi, Simone & Pommerening, Arne & Mehtätalo, Lauri, 2024. "A Bayesian approach to projecting forest dynamics and related uncertainty: An application to continuous cover forests," Ecological Modelling, Elsevier, vol. 491(C).
    3. Häbel, Henrike & Myllymäki, Mari & Pommerening, Arne, 2019. "New insights on the behaviour of alternative types of individual-based tree models for natural forests," Ecological Modelling, Elsevier, vol. 406(C), pages 23-32.

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