Parameter estimation and model selection for Neyman-Scott point processes

Biometrical Journal

Volumn 50, Issue 1, 2008, Pages 43-57

  Tanaka, Ushio ^a   Ogata, Yosihiko ^a,b   Stoyan, Dietrich ^c  

^a GRADUATE UNIVERSITY FOR ADVANCED STUDIES   (Japan)

^b INSTITUTE OF STATISTICAL MATHEMATICS   (Japan)

^c TU BERGAKADEMIE FREIBERG   (Germany)

Author keywords

AIC; Generalized thomas model; Inverse power type model; K function; Multi type clusters; Pair correlation function; Palm intensity function; Palm likelihood function; Thomas model

Indexed keywords

INVERSE PROBLEMS; MAXIMUM LIKELIHOOD ESTIMATION;

AIC; GENERALIZED THOMAS MODEL; INTENSITY FUNCTIONS; INVERSE-POWER TYPE MODEL; K-FUNCTION; LIKELIHOOD FUNCTIONS; MULTI-TYPE CLUSTER; PAIR CORRELATION FUNCTIONS; PALM INTENSITY FUNCTION; PALM LIKELIHOOD FUNCTION; POWER; THOMAS MODELS;

PARAMETER ESTIMATION;

ARTICLE; CLUSTER ANALYSIS; COMPARATIVE STUDY; COMPUTER SIMULATION; GROWTH, DEVELOPMENT AND AGING; PLANT; STATISTICAL MODEL;

CLUSTER ANALYSIS; COMPUTER SIMULATION; LIKELIHOOD FUNCTIONS; MODELS, STATISTICAL; PLANTS;

EID: 41149133391     PISSN: 03233847     EISSN: 15214036     Source Type: Journal    
DOI: 10.1002/bimj.200610339     Document Type: Article

References (27)

1. Akaike, H. (1974). A new look at the statistical model identification. IEEE Transaction on Automatic Control AC-19, 716-723.
2. Baddeley, A. and van Lieshout, M. N. M. (1995). Area-interaction point processes. Annals of the Institute of Statistical Mathematics 47, 601-619.
3. Baudin, M. (1981). Likelihood and nearest-neighbor distance properties of multidimensional Poisson cluster processes. Journal of Applied Probability 18, 879-888.
4. Cressie, N. (1993). Statistics for Spatial Data. Springer-Verlag, Berlin.
5. Daley, D. J. and Vere-Jones, D. (1988). An Introduction to the Theory of Point Processes. Springer-Verlag, Berlin.
6. Diggle, P. J. (1983). Statistical Analysis of Spatial Point Patterns. Academic Press, London.
7. Diggle, P. J. (2003). Statistical Analysis of Spatial Point Patterns. Second Edition, Arnord, London.
8. Hutchings, M. J. (1979). Standing crop and pattern in pure stands of Mercurialis perennis and Rubus fruticosus in mixed deciduous woodland. Oikos 31, 351-357.
9. Mecke, K. R. and Stoyan, D. (2005). Morphological characterization of point patterns. Biometrical Journal 47, 473-488.
10. Møller, J. and Waagepetersen, R. (2004). Statistical Inference and Simulation for Spatial Point Processes. Monographs on Statistics and Applied Probability 100, Chapman and Hall/CRC, London.
11. Nelder, J. A. and Mead, R. (1965). A simplex method for function minimization. Computer Journal 7, 308.
12. Neyman, J. and Scott, E. (1958). Statistical approach to problems of cosmology. Journal of the Royal Statistical Society, series B 20, 1-43.
13. Ogata, Y. (1978). The asymptotic behaviour of maximum likelihood estimators for stationary point processes. Annals of the Institute of Statistical Mathematics 30, 243-261.
14. Ogata, Y. and Tanemura, M. (1981). Estimation of interaction potentials of spatial point patterns through the maximum likelihood procedure. Annals of the Institute of Statistical Mathematics 33, 315-338.
15. Ogata, Y. and Tanemura, M. (1984). Likelihood analysis of spatial point patterns. Journal of the Royal Statistical Society, series B 46, 496-518.
16. Ogata Y. and Katsura K. (1991). Maximum likelihood estimates of the fractal dimension for random spatial patterns. Biometrika 78, 463-474.
17. Press, W. H., Teukolsky, S. A., Vettering, W. T. and Flannery, B. P. (1992). Numerical Recipes in Fortran 77 2nd Ed., Cambridge University Press, Cambridge.
18. Press, W. H. (2006). Numerical Recipes in Fortran, http://www.library.cornell.edu/nr/cbookfpdf.html
19. Platt, W. J., Evans, G.W. and Rathbun, S. L. (1988). The population dynamics of a long-lived conifer. (Pinus Palustris) American Naturalist 131, 491-525.
20. Rathbun, S. L. and Cressie, N. (1990). A space-time survival point process for a longleaf pine forest in southern Geogea. Journal of the American Statistical Association 89, 1164-1174.
21. Renshaw, E. (2002). Two-dimensional spectral analysis for marked point processes. Biometrical Journal, 44, 718-745.
22. Ripley, B. (1977). Modelling spatial patterns. Journal of the Royal Statistical Society, series B, 39, 172-212.
23. Spendley, W., Hext G. R. and Himsworth F. R. (1962). Application of simplex designs in optimization and evolutionary operation. Technometrics, 4, 441.
24. Stoyan, D. and Stoyan, H. (1994). Fractals, Random Shapes and Point Fields. John Wiley & Sons, London.
25. Stoyan, D. and Stoyan, H. (1996). Estimating pair correlation functions of planar cluster processes. Biometrical Journal, 38, 259-271.
26. Thomas, M. (1949). A generalization of Poissons binomial limit for use in ecology. Biometrika, 36, 18-25.
27. Tanaka, U. and Ogata, Y. (2004). Estimation of parameters for the Neyman-Scott's spatial cluster model (in Japanese). 2004 Proceeding of the Japanese Joint Statistical Meeting. Japanese Federation of Statistical Science Association, 317-318.