On Fitting Non-Stationary Markov Point Process Models on GLIM

  • A. B. Lawson

Abstract

The possibility of fitting general non-stationary point process models on GLIM is considered. Of primary concern is the possibility of using pseudoliklihood to obtain parameter estimates for a spatial Markov process model applied to the colonisation of plants. Extension of the method to fitting cluster/Cox process models is also considered.

Keywords

Conditional Intensity Mean Integrate Square Error Spatial Point Pattern Interpoint Distance Obtain Parameter Estimate 
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.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. [1]
    Berman, M & Turner, T R (1992). Approximating Point Process Likelihoods using GLIM. App. Stat., 41, 1, 31–38.CrossRefGoogle Scholar
  2. [2]
    Besag, J, York, J & Mollié, A (1991). Bayesian Image Restoration, with Two Applications in Spatial Statistics. Ann Inst Statist Math, 43, 1, 1–59.CrossRefGoogle Scholar
  3. [3]
    Diggle, P J (1983). Statistical Analysis of Spatial Point Patterns. Academic Press.Google Scholar
  4. [4]
    Diggle, P J & Gratton, R J (1984). Monte Carlo Methods of Inference for Implicit Statistical Models. J.R.S.S., B, 46, 193–227.Google Scholar
  5. [5]
    Hall, P (1988). On confidence intervals for spatial parameters estimated from non-replicated data. Biometrics, 44, 271–277.CrossRefGoogle Scholar
  6. [6]
    Koojiman, S.A.L.M. (1979). The description of Point Processes in: Cormack, R M & Ord, J K (eds)’ spatial and Temporal Analysis in Ecology’, Fairland: Int. Cooperative Publishing House., pp 305-332.Google Scholar
  7. [7]
    Lawson, A B (1988). On Tests for Spatial Trend in a Non-Homogeneous Poisson Process. J.A.S., 15, 2, 225–234.Google Scholar
  8. [8]
    Lawson, A B (1991). The Statistical Analysis of Point Events associated with a Fixed point. PhD Thesis, Univ of St Andrews.Google Scholar
  9. [9]
    Lawson, A B (1992). Glim and Normalising Constant Models in Spatial and Directional Data Analysis. Comp Stat and Data Anal, to appear.Google Scholar
  10. [10]
    Moyeed, R A & Baddeley, A J (1991). Stochastic Approximation of the MLE for a Spatial Point Pattern. Scand Jour Stat, 18, 39–50.Google Scholar
  11. [11]
    Palaniappan, VM, Marrs, RH & Bradshaw, AD (1979). The effect of Lupinus Arboreus on the Nitrogen Status of China Clay Wastes. Jour App Ecol, 16, 825–831.CrossRefGoogle Scholar
  12. [12]
    Ripley, B D (1988). Statistical Inference for Spatial Processes. Cambridge Univ Press.Google Scholar
  13. [13]
    Zeger, S L & Karim, M R (1991). Generalised Linear Models with Random Effects; a Gibbs Sampling Approach. J.A.S.A., 86, 413, pp 79–86.CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1992

Authors and Affiliations

  • A. B. Lawson
    • 1
  1. 1.Department of Mathematical and Computer SciencesDundee Institute of TechnologyDundeeUK

Personalised recommendations