On the second-order characteristics of marked point processes

Bernoulli

Volumn 7, Issue 1, 2001, Pages 99-117

  Schlather, Martin ^a  

^a LANCASTER UNIVERSITY   (United Kingdom)

Author keywords

Mark correlation function; Mark covariance function; Mark variogram; Marked point process; Moment measure; Second order characteristic

Indexed keywords

EID: 0003016206     PISSN: 13507265     EISSN: None     Source Type: Journal    
DOI: 10.2307/3318604     Document Type: Article

References (25)

1. Baddeley, A.J. (1999) Spatial sampling and censoring. In O.E. Barndorff-Nielsen, W.S. Kendall and M.N.M. van Lieshout (eds), Stochastic Geometry, Likelihood and Computation, pp. 37-78. Boca Raton, FL: Chapman & Hall/CRC.
2. Baddeley, A.J., Møller, J.M. and Waagepetersen, R. (1998) Non- and semi-parametric estimation of interaction in inhomogeneous point patterns. Technical Report 12, Biometry Research Unit, Danish Institute of Agricultural Sciences, Tjele.
3. Capobianco, R. and Renshaw, E. (1998) The autocovariance function for marked point processes: a comparison between two different approaches. Biometrical J., 40, 431-446.
4. Cressie, N.A.C. (1993) Statistics for Spatial Data. New York: Wiley.
5. Diggle, P.J. (1983) Statistical Analysis of Point Processes. London: Chapman & Hall.
6. Diggle, P.J., Lange, N. and Beneš, F. (1991) Analysis of variance for replicated spatial point patterns in clinical neuroanatomy. J. Amer. Staust. Assoc., 86, 618-625.
7. Gavrikov, V.L. and Stoyan, D. (1995) The use of marked point processes in ecological and environmental forest studies. Em-iron. Ecological Statist., 2, 331-344.
8. Goulard, M., Pages, L. and Cananettes, A. (1995) Marked point processes - using correlation functions to explore a spatial data set. Biometrical J., 37, 837-853.
9. Isham, V. (1985) Marked point processes and their correlations. In F. Droesbeke (ed.), Spatial Processes and Spatial Time Series Analysis, pp. 63-75. Brussels: Publications des Facultés Universitaires Saint-Louis.
10. Mase, S. (1996) The threshold method for estimating total rainfall. Ann. Inst. Statist. Math., 48, 201-213.
11. Penttinen, A.K. and Stoyan, D. (1989) Statistical analysis for a class of line segment processes. Scand. J. Statist., 16, 153-168.
12. Penttinen, A.K., Stoyan, D. and Henttonen, H.M. (1992) Marked point processes in forest statistics. Forest Sci., 38, 806-824.
13. Ripley, B.D. (1977) Modelling spatial patterns. J. Roy. Stat. Soc. Ser. B, 39, 172-192.
14. Ripley, B.D. (1981) Spatial Statistics. New York: Wiley.
15. Sasvári, Z. (1994) Positive Definite and Definitizable Functions. Berlin: Akademie Verlag.
16. Stoyan, D. (1984a) Correlations of the marks of marked point processes - statistical inference and simple models. Elektron. Infonnationsverarbeitttng Kybernetik, 20, 285-294.
17. Stoyan, D. (1984b) On correlations of marked point processes. Math. Nachr., 116, 197-207.
18. Stoyan, D. (1990) Stereological formulae for a random system of nonintersecting spheres. Statistics, 21, 131-236.
19. Stoyan, D. and Stoyan, H. (1994) Fractals, Random Shapes and Point Fields. Chichester: Wiley.
20. Stoyan, D., Kendall, W.S. and Mecke, J. (1995) Stochastic Geometry and its Applications, 2nd edition. Chichester: Wiley.
21. Wackernagel, H. (1995) Multivariate Geostatistics. Berlin: Springer-Verlag.
22. Wälder, O. and Stoyan, D. (1996) On variograms in point process statistics. Biometrical J., 38, 895-905.
23. Wälder, O. and Stoyan, D. (1997) Models of marking and thinning of Poisson processes. Statistics, 29, 179-202.
24. Wälder, O. and Stoyan, D. (1998) On variograms in point process statistics: Erratum. Biometrical J., 40, 109.
25. Wen, R. and Sinding-Larsen, R. (1997) Stochastic modelling and simulation of small faults by marked point processes and kriging. In E.Y. Baafi and N.A. Schofield (eds), Geostatistics Wollongong '96, Vol. 1, pp. 398-414. Dordrecht: Kluwer.