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The Interpretation of Process from Pattern Using Two‐Dimensional Spectral Analysis: Methods and Problems of Interpretation

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  • E. Renshaw
  • E. D. Ford

Abstract

Two‐dimensional spectral analysis provides a comprehensive description of both the structure and scales of pattern in a spatial data set. It assumes no structural characteristics in the data prior to analysis. We demonstrate the advantage of this in an ecological situation where pattern may exist over a range of scales, be anisotropic and non‐stationary. All these may be important features relating to the underlying biological and environmental pattern generating mechanisms and should be explained prior to model building. We discuss general problems of estimation, discrimination and interpretation of spectra and illustrate them through the analysis of a forest canopy data set.

Suggested Citation

  • E. Renshaw & E. D. Ford, 1983. "The Interpretation of Process from Pattern Using Two‐Dimensional Spectral Analysis: Methods and Problems of Interpretation," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 32(1), pages 51-63, March.
    • Handle: RePEc:bla:jorssc:v:32:y:1983:i:1:p:51-63
    DOI: 10.2307/2348042
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    Cited by:

    1. 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.
    2. 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).
    3. Renshaw, Eric & Mateu, Jorge & Saura, Fuensanta, 2007. "Disentangling mark/point interaction in marked-point processes," Computational Statistics & Data Analysis, Elsevier, vol. 51(6), pages 3123-3144, March.
    4. Jose Vidal-Sanz, 2009. "Automatic spectral density estimation for random fields on a lattice via bootstrap," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 18(1), pages 96-114, May.
    5. Mugglestone, Moira A. & Renshaw, Eric, 1996. "A practical guide to the spectral analysis of spatial point processes," Computational Statistics & Data Analysis, Elsevier, vol. 21(1), pages 43-65, January.

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