Detecting dependence between marks and locations of marked point processes

Journal of the Royal Statistical Society. Series B: Statistical Methodology

Volumn 66, Issue 1, 2004, Pages 79-93

  Schlather, Martin ^a   Ribeiro Jr , Paulo J ^b   Diggle, Peter J ^c  

^a UNIVERSITY OF BAYREUTH   (Germany)

^b FEDERAL UNIVERSITY OF PARANÁ   (Brazil)

^c LANCASTER UNIVERSITY   (United Kingdom)

Author keywords

Independence test; Mark correlation function; Mark variogram; Nearest neighbour; Preferential sampling; Random field model

Indexed keywords

EID: 1042302534     PISSN: 13697412     EISSN: None     Source Type: Journal    
DOI: 10.1046/j.1369-7412.2003.05343.x     Document Type: Review

References (39)

1. Baddeley, A. J. (1999) Spatial sampling and censoring. In Stochastic Geometry: Likelihood and Computation (eds O. E. Barndorff-Nielsen, W. Kendall and M. N. M. van Lieshout), pp. 37-78. London: Chapman and Hall.
2. Besag, J. and Diggle, P. J. (1977) Simple Monte Carlo tests for spatial pattern. Appl. Statist., 26, 327-333.
3. Biondi, F., Myers, D. E. and Avery, C. C. (1994) Geostatistically modeling stem size and increment in an old-growth forest. Can. J. For. Res., 24, 1354-1368.
4. Bogaert, P. and Christakos, G. (1997) Spatiotemporal analysis and processing of thermometric data over Belgium. J. Geophys. Res., 102, 831-846.
5. Chilès, J.-P. and Delfiner, P. (1999) Geostatistics: Modeling Spatial Uncertainty. New York: Wiley.
6. Christakos, G. and Vyas, V. M. (1998) A composite spatiotemporal study of ozone distribution over Eastern United States. Atmosph. Environ., 32, 2845-2857.
7. Cressie, N. A. C. (1993) Statistics for Spatial Data. New York: Wiley.
8. Deutsch, C. V. and Journel, A. G. (1992) GSLIB - Geostatistical Software Library and User's Guide, 1st edn. New York: Oxford University Press.
9. Diggle, P. J. (2000) Discussion on 'Maximum likelihood for spatial point pattern' (by A. Baddeley and R. Turner). Aust. New Zeal. J. Statist., 42, 934-936.
10. Diggle, P. J., Ribeiro, Jr, P. J. and Christensen, O. (2003) An introduction to model-based geostatistics. In Spatial Statistics and Computational Methods (ed. J. Møller), pp. 43-86. New York: Springer.
11. Gneiting, T. (1999) Correlation functions for atmospheric data analysis. Q. J. R. Meteorol. Soc., 125, 2449-2464.
12. Gneiting, T., Sasvári, Z. and Schlather, M. (2001) Analogies and correspondences between variograms and covariance functions. Adv. Appl. Probab., 33, 617-630.
13. Goovaerts, P. (1998) Geostatistics for Natural Resources Evaluation. Oxford: Oxford University Press.
14. Ihaka, R. and Gentleman, R. (1996) R: a language for data analysis and graphics. J. Comput. Graph. Statist., 5, 299-314.
15. Isaaks, E. H. and Srisvastava, R. M. (1989) An Introduction to Applied Geostatistics. New York: Oxford University Press.
16. Isham, V. S. (1985) Marked point processes and their correlations. In Spatial Processes and Spatial Time Series Analysis (ed. F. Droesbeke), pp. 63-75. Brussels: Publications des Facultés universitaires Saint-Louis.
17. Journel, A. G. and Huijbregts, C. J. (1978) Mining Geostatistics. London: Academic Press.
18. König, D. and Schmidt, V. (1992) Zufällige Punktprozesse. Stuttgart: Teubner.
19. Lantuéjoul, C. (2002) Geostatistical Simulation. Berlin: Springer.
20. Mandallaz, D. (2000) Estimation of the spatial covariance in universal kriging: application to forest inventory. Environ. Ecol. Statist., 7, 263-284.
21. Mase, S. (1996) The threshold method for estimating total rainfall. Ann. Inst. Statist. Math., 48, 201-213.
22. Matheron, G. (1970) La théorie des variables régionalisées, et ses applications. Technical Report. Ecole des Mines de Paris, Fontainebleau.
23. Matheron, G. (1987) Suffit-il, pour une covariance, d'être de type positif? Sci. Terre Sér. Inform. Géol., 26, 51-66.
24. Nanos, N., Tadesse, W., Montero, G., Gil, L. and Alia, R. (2001) Spatial stochastic modeling of resin yield from pine stands. Can. J. For. Res., 31, 1140-1147.
25. Picard, N. and Bar-Hen, A. (2002) La corrélation spatiale entre la surface terrière des arbres et leur accroissement est-elle un bon indicateur de la compétition? Ann. For. Sci., 59, 41-51.
26. Ripley, B. D. (1981) Spatial Statistics. New York: Wiley.
27. Sasvári, Z. (1994) Positive Definite and Definitizable Functions. Berlin: Akademie.
28. Schafmeister, M.-T. (1999) Geostatistik für die Hydrologische Praxis. Berlin: Springer.
29. Schlather, M. (2001a) On the second-order characteristics of marked point processes. Bernoulli, 7, 99-117.
30. Schlather, M. (2001b) Simulation and analysis of random fields. R-News, 1, no. 2, 18-20.
31. Schlather, M. (2002) Characterization of point processes with Gaussian marks independent of locations. Math. Nachr., 240, 204-214.
32. Schlather, M. (2003) Simulation of random fields and applications. To be published.
33. Stein, M. L. (1999) Interpolation of Spatial Data. Heidelberg: Springer.
34. Stoyan, D., Kendall, W. S. and Mecke, J. (1995) Stochastic Geometry and Its Applications, 2nd edn. Chichester: Wiley.
35. Stoyan, D. and Stoyan, H. (1994) Fractals, Random Shapes and Point Fields. Chichester: Wiley.
36. Stoyan, D. and Wälder, O. (2000) On variograms in point process statistics, II: Models of markings and ecological interpretation. Biometr. J., 42, 171-187.
37. Takahata, H. (1994) Nonparametric density estimations for a class of marked point processes. Yok. Math. J., 41, 127-152.
38. Wackernagel, H. (1998) Multivariate Geostatistics, 2nd edn. Berlin: Springer.
39. Wälder, O. and Stoyan, D. (1996) On variograms in point process statistics. Biometr. J., 38, 895-905.