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Some edge correction methods for marked spatio-temporal point process models

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  • Cronie, Ottmar
  • Särkkä, Aila

Abstract

Three edge correction methods for (marked) spatio-temporal point processes are proposed. They are all based on the idea of placing an approximated expected behaviour of the process at hand (simulated realisations) outside the study region which interacts with the data during the estimation. These methods are applied to the so-called growth-interaction model. The specific choices of growth function and interaction function made are purely motivated by the forestry applications considered. The parameters of the growth and interaction functions, i.e. the parameters related to the development of the marks, are estimated using the least-squares approach together with the proposed edge corrections. Finally, the edge corrected estimation methods are applied to a data set of Swedish Scots pine.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:csdana:v:55:y:2011:i:7:p:2209-2220
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    References listed on IDEAS

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    1. Mandal, A. & Huang, W.T. & Bhandari, S.K. & Basu, A., 2011. "Goodness-of-fit testing in growth curve models: A general approach based on finite differences," Computational Statistics & Data Analysis, Elsevier, vol. 55(2), pages 1086-1098, February.
    2. Lu, Tong-Yu & Poon, Wai-Yin & Tsang, Yim-Fan, 2011. "Latent growth curve modeling for longitudinal ordinal responses with applications," Computational Statistics & Data Analysis, Elsevier, vol. 55(3), pages 1488-1497, March.
    3. Veen, Alejandro & Schoenberg, Frederic P., 2008. "Estimation of SpaceTime Branching Process Models in Seismology Using an EMType Algorithm," Journal of the American Statistical Association, American Statistical Association, vol. 103, pages 614-624, June.
    4. Grabarnik, Pavel & Särkkä, Aila, 2009. "Modelling the spatial structure of forest stands by multivariate point processes with hierarchical interactions," Ecological Modelling, Elsevier, vol. 220(9), pages 1232-1240.
    5. 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.
    6. 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. Ottmar Cronie & Julia Jansson & Konstantinos Konstantinou, 2024. "Discussion of the Paper “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 379-388, June.
    2. Mohammad Ghorbani & Ottmar Cronie & Jorge Mateu & Jun Yu, 2021. "Functional marked point processes: a natural structure to unify spatio-temporal frameworks and to analyse dependent functional data," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 30(3), pages 529-568, September.
    3. Edith Gabriel, 2014. "Estimating Second-Order Characteristics of Inhomogeneous Spatio-Temporal Point Processes," Methodology and Computing in Applied Probability, Springer, vol. 16(2), pages 411-431, June.
    4. 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.
    5. O. Cronie & M. N. M. Van Lieshout, 2015. "A J -function for Inhomogeneous Spatio-temporal Point Processes," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 42(2), pages 562-579, June.
    6. Ottmar Cronie & Mehdi Moradi & Christophe A N Biscio, 2024. "A cross-validation-based statistical theory for point processes," Biometrika, Biometrika Trust, vol. 111(2), pages 625-641.
    7. 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).

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