Multiresolution Assessment of Forest Inhomogeneity

  • Katja Ickstadt
  • Robert L. Wolpert
Part of the Lecture Notes in Statistics book series (LNS, volume 121)


The spatial distribution of dominant tree species in an undisturbed mature stand tends to be regular and even, often exhibiting less variation than a simple Poisson model would suggest; in contrast the spatial distribution of species in a recovering or transitional stand would be expected to display considerable spatial variation. This paper studies the spatial distribution of hickory trees within the Bormann research plot of Duke Forest in an attempt to assess the degree of variation, as an indicator for forest maturation, using models recently introduced in Wolpert and Ickstadt (1995). A data augmentation scheme and Markov chain Monte Carlo methods are employed to evaluate Bayesian posterior distributions.


Markov Chain Monte Carlo Forest Maturation Markov Chain Monte Carlo Method Gaussian Random Field Random Field Model 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. Bartlett, M.S. (1964) The spectral analysis of two-dimensional point processes. Biometrika, 51: 299–311.MathSciNetGoogle Scholar
  2. Breslow, N.E. and Clayton, D.G. (1993) Approximate inference in generalized linear mixed models. Journal of the American Statistical Association, 88 (421): 9–25.zbMATHGoogle Scholar
  3. Besag, J. (1974) Spatial interaction and the statistical analysis of lattice systems. Journal of the Royal Statistical Society, Series B (Methodological), 35 (2): 192–236.MathSciNetGoogle Scholar
  4. Bormann, F.H. (1953) The statistical eficiency of sample plot size and shape in forest ecology. Ecology, 34: 474–487.CrossRefGoogle Scholar
  5. Bernardinelli, L., Pascutto, C., Best, N.G. and Gilks, W.R. (1996) Disease mapping with errors in covariates. To appear in Statistics in Medicine.Google Scholar
  6. Besag, J., York, J. and Mollie, A. (1991) Bayesian image restoration, with two applications in spatial statistics. Annals of the Institute of Statistical Mathematics, 43: 1–59, (with discussion).MathSciNetGoogle Scholar
  7. Cresie, N.A.C. and Chan, N.H. (1989) Spatial modeling of regional variables. Journal of the American Statistical Association,84(406):393–401.MathSciNetCrossRefGoogle Scholar
  8. Christensen, N.L. (1977) Changes in structure, pattern and diversity assoicated with climax forest maturation in Piedmont, North Carolina. American Midland Naturalist, 97: 176–188.CrossRefGoogle Scholar
  9. Clayton, D.G. and Kaldor, J. (1987) Empirical Bayes estimates of age-standardized relative risks for use in disease mapping. Biometrics, 43 (3): 671–681.CrossRefGoogle Scholar
  10. Cressie, N.A.C. (1993) Statistics for Spatial Data. John Wiley & Sons, New York, NY, USA.Google Scholar
  11. David, F.N. and Moore, P.G. (1954) Notes on contagious distributions in plant populations. Annals of Botany, 18: 47–53.Google Scholar
  12. Gilks, W.R., Richardson, S. and Spiegelhalter, D.J. (editors) (1996) Markov Chain Monte Carlo in Practice. Chapman & Hall, New York, NY, USA.zbMATHGoogle Scholar
  13. Gelfand, A.E. and Smith, A.F.M. (1990) Sampling-based approaches to calculating marginal densities. Journal of the American Statistical Association, 85 (410): 398–409.MathSciNetzbMATHCrossRefGoogle Scholar
  14. Matheron, G. (1963) Principles of geostatistics. Economic Geology, 58: 1246–1266.CrossRefGoogle Scholar
  15. Ripley, B.D. (1981) Spatial Statistics. John Wiley & Sons, New York, NY, USA.Google Scholar
  16. Richardson, S., Monfort, C., Green, M., Draper, G. and Muirhead, C. (1995). Spatial variation of natural radiation and childhood leukaemia incidence in Great Britain. Statistics in Medicine, 14: 2487–2501.CrossRefGoogle Scholar
  17. Reed, R.A., Peet, R.K., Palmer, M.W. and White, P.S. (1993) Scale dependence of vegetation-environment correlations: A case study of a North Carolina piedmont woodland. Journal of Vegetation Science, 4: 329–340.CrossRefGoogle Scholar
  18. Strauss, D.J. (1975) A model for clustering. Biometrika,62(2):467–476.MathSciNetzbMATHCrossRefGoogle Scholar
  19. Tierney, L. (1994) Markov chains for exploring posterior distirbutions. Annals of Statistics, 22(4):1701–1762,(with discussion).MathSciNetzbMATHCrossRefGoogle Scholar
  20. Tanner, M.A. and Wong, W.H. (1987) The calculation of posterior distributions by data augmentation. Journal of the American Statistical Association, 82(398):528–550.MathSciNetzbMATHCrossRefGoogle Scholar
  21. Wolpert, R.L. and Ickstadt, K. (1995) Gamma/Poisson random field models for spatial statistics. Discussion Ppaer 95–43,Duke Univeristy ISDS, USA.Google Scholar

Copyright information

© Springer-Verlag New York, Inc. 1997

Authors and Affiliations

  • Katja Ickstadt
  • Robert L. Wolpert

There are no affiliations available

Personalised recommendations