Residual analysis for spatial point processes

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

Volumn 67, Issue 5, 2005, Pages 617-666

  Baddeley, A ^a   Turner, R ^b   Moller J ^c   Hazelton, M ^a  

^a UNIVERSITY OF WESTERN AUSTRALIA   (Australia)

^b UNIVERSITY OF NEW BRUNSWICK   (Canada)

^c AALBORG UNIVERSITY   (Denmark)

Author keywords

Berman's diagnostic; Berman Turner device; Estimating equations; Exponential energy marks; Generalized linear models; Georgii Nguyen Zessin formula; K function; Kernel smoothing; Ogata residual; Papangelou conditional intensity; Pearson residuals

Indexed keywords

EID: 28044460504     PISSN: 13697412     EISSN: 14679868     Source Type: Journal    
DOI: 10.1111/j.1467-9868.2005.00519.x     Document Type: Article

References (83)

1. Andersen, P., Borgan, Ø., Gill, R. and Keiding, N. (1993) Statistical Models based on Counting Processes. New York: Springer.
2. Anselin, L. (1995) Local indicators of spatial association - LISA. Geogr. Anal., 27, 93-115.
3. Atkinson, A. (1985) Plots, Transformations and Regression. Oxford: Oxford University Press.
4. Baddeley, A., Møller, J., Hazelton, M. and Turner, R. (2005) Residuals for spatial point processes using the Papangelou conditional intensity. To be published.
5. Baddeley, A., Møller, J. and Waagepetersen, R. (2000) Non- and semiparametric estimation of interaction in inhomogeneous point patterns. Statist. Neerland., 54, 329-350.
6. Baddeley, A., Møller, J. and Waagepetersen, R. (2006) Residual versions of summary functions for spatial point patterns. To be published.
7. Baddeley, A. and Turner, R. (2000) Practical maximum pseudolikelihood for spatial point patterns (with discussion). Aust. New Zeal. J. Statist., 42, 283-322.
8. Baddeley, A. and Turner, R. (2005a) Modelling spatial point patterns in R. Lect. Notes Statist., 185, in the press.
9. Baddeley, A. and Turner, R. (2005b) Spatstat: an R package for analyzing spatial point patterns. J. Statist. Softwr., 12, no. 6, 1-42.
10. Baddeley, A., Turner, R., Møller, J. and Hazelton, M. (2004) Residual analysis for spatial point processes. Research Report 2004/08. School of Mathematics and Statistics, University of Western Australia, Perth.
11. Berman, M. (1986) Testing for spatial association between a point process and another stochastic process. Appl. Statist., 35, 54-62.
12. Berman, M. and Diggle, P. (1989) Estimating weighted integrals of the second-order intensity of a spatial point process. J. R. Statist. Soc. B, 51, 81-92.
13. Berman, M. and Turner, T. R. (1992) Approximating point process likelihoods with GLIM. Appl. Statist., 41, 31-38.
14. Besag, J. (1975) Statistical analysis of non-lattice data. Statistician, 24, 179-195.
15. Besag, J. (1978) Some methods of statistical analysis for spatial data. Bull. Int. Statist. Inst., 44, 77-92.
16. Besag, J. and Diggle, P. J. (1977) Simple Monte Carlo tests for spatial pattern. Appl. Statist., 26, 327-333.
17. Brillinger, D. (1978) Comparative aspects of the study of ordinary time series and of point processes. In Developments in Statistics (ed. P. R. Krishnaiah), pp. 33-133. New York: Academic Press.
18. Brillinger, D. (1988) Maximum likelihood analysis of spike trains of interacting nerve cells. Biol. Cyber., 59, 189-200.
19. Brillinger, D. (1994) Time series, point processes, and hybrids. Can. J. Statist., 22, 177-206.
20. Brillinger, D. and Preisler, H. (1986) Two examples of quantal data analysis: a) multivariate point process, b) pure death process in an experimental design. In Proc. 13th Int. Biometric Conf, Seattle. Seattle: International Biometric Society.
21. Clyde, M. and Strauss, D. (1991) Logistic regression for spatial pair-potential models. In Spatial Statistics and Imaging (ed. A. Possolo), ch. II, pp. 14-30. Hayward: Institute of Mathematical Statistics.
22. Collett, D. (1991) Modelling Binary Data. London: Chapman and Hall.
23. Cox, D. R. and Isham, V. (1980) Point Processes. London: Chapman and Hall.
24. Cox, D. and Lewis, P. (1966) The Statistical Analysis of Series of Events. London: Methuen.
25. Cressie, N. (1991) Statistics for Spatial Data. New York: Wiley.
26. Cressie, N. and Collins, L. (2001a) Analysis of spatial point patterns using bundles of product density LISA functions. J. Agric. Biol. Environ. Statist., 6, 118-135.
27. Cressie, N. and Collins, L. (2001b) Patterns in spatial point locations: local indicators of spatial association in a minefield with clutter. Nov. Res. Logist., 48, 333-347.
28. Daley, D. and Vere-Jones, D. (1988) An Introduction to the Theory of Point Processes. New York: Springer.
29. Davison, A. and Snell, E. (1991) Residuals and diagnostics. In Statistical Theory and Modelling (in Honour of Sir David Cox FRS) (eds D. Hinkley, N. Reid and E. Snell), ch. 4, pp. 83-106. London: Chapman and Hall.
30. Diggle, P. (1978) On parameter estimation for spatial point processes. J. R. Statist. Soc. B, 40, 178-181.
31. Diggle, P. (1985) A kernel method for smoothing point process data. Appl. Statist., 34, 138-147.
32. Diggle, P. J. (1990) A point process modelling approach to raised incidence of a rare phenomenon in the vicinity of a prespecified point. J. R. Statist. Soc. A, 153, 349-362.
33. Diggle, P. (2003) Statistical Analysis of Spatial Point Patterns, 2nd edn. London: Arnold.
34. Diggle, P., Chetwynd, A., Haggkvist, R. and Morris, S. (1995) Second order analysis of space-time clustering. Statist. Meth. Med. Res., 4, 124-136.
35. Diggle, P. J. and Rowlingson, B. S. (1994) A conditional approach to point process modelling of elevated risk. J. R. Statist. Soc. A, 157, 433-440.
36. Fowlkes, E. (1987) Some diagnostics for binary logistic regression via smoothing. Biometrika, 74, 503-515.
37. Foxall, R. and Baddeley, A. (2002) Nonparametric measures of association between a spatial point process and a random set, with geological applications. Appl. Statist., 51, 165-182.
38. Georgii, H.-O. (1976) Canonical and grand canonical Gibbs states for continuum systems. Communs Math. Phys., 48, 31-51.
39. Getis, A. and Franklin, J. (1987) Second-order neighbourhood analysis of mapped point patterns. Ecology, 68, 473-477.
40. Geyer, C. (1999) Likelihood inference for spatial point processes. In Stochastic Geometry: Likelihood and Computation (eds O. Barndorff-Nielsen, W. Kendall and M. van Lieshout), ch. 3, pp. 79-140. Boca Raton: Chapman and Hall-CRC.
41. Geyer, C. and Møller, J. (1994) Simulation procedures and likelihood inference for spatial point processes. Scand. J. Statist., 21, 359-373.
42. Gnanadesikan, R. B. and Wilk, M. (1970) A probability plotting procedure for general analysis of variance. J. R. Statist. Soc. B, 32, 88-101.
43. Horvitz, D. and Thompson, D. (1952) A generalization of sampling without replacement from a finite universe. J. Am. Statist. Ass., 47, 663-685.
44. Jensen, J. and Møller, J. (1991) Pseudolikelihood for exponential family models of spatial point processes. Ann. Appl. Probab., 1, 445-461.
45. Karr, A. (1985) Point Processes and Their Statistical Inference. New York: Dekker.
46. Kulldorff, M. (1999) Spatial scan statistics: models, calculations, and applications. In Recent Advances on Scan Statistics (eds J. Glaz and N. Balakrishnan), pp. 303-322. Boston: Birkhauser.
47. Landwehr, J., Pregibon, D. and Shoemaker, A. (1984) Graphical methods for assessing logistic regression models. J. Am. Statist. Ass., 79, 61-83.
48. Lawson, A. (1992) On fitting non-stationary Markov point process models on GLIM. In Computational Statistics (eds Y Dodge and J. Whittaker), vol. 1, pp. 35-40. Heidelberg: Physica.
49. Lawson, A. (1993) A deviance residual for heterogeneous spatial Poisson processes. Biometrics, 49, 889-897.
50. Lewis, P. (1972) Recent results in the statistical analysis of univariate point processes. In Stochastic Point Processes (ed. P. Lewis), pp. 1-54. New York: Wiley.
51. van Lieshout, M. (2000) Markov Point Processes and Their Applications. London: Imperial College Press.
52. Lindsey, J. (1992) The Analysis of Stochastic Processes using GLIM. Berlin: Springer.
53. Lindsey, J. K. (1995) Fitting parametric counting processes by using log-linear models. Appl. Statist., 44, 201-212.
54. Mase, S., Møller, J., Stoyan, D., Waagepetersen, R. and Döge, G. (2001) Packing densities and simulated tempering for hard core Gibbs point processes. Ann. Inst. Statist. Math., 53, 661-680.
55. Merzbach, E. and Nualart, D. (1986) A characterization of the spatial Poisson process and changing time. Ann. Probab., 14, 1380-1390.
56. Møller, J. (2003) Shot noise Cox processes. Adv. Appl. Probab., 35, 614-640.
57. Møller, J., Syversveen, A.-R. and Waagepetersen, R. (1998) Log Gaussian Cox processes. Scand. J. Statist., 25, 451-482.
58. Møller, J. and Waagepetersen, R. (2003a) Statistical Inference and Simulation for Spatial Point Processes. Boca Raton: Chapman and Hall-CRC.
59. Møller, J. and Waagepetersen, R. P. (2003b) An introduction to simulation-based inference for spatial point processes. Lect. Notes Statist., 173, 143-198.
60. Nair, M. (1990) Random space change for multiparameter point processes. Ann. Probab., 18, 1222-1231.
61. Nguyen, X. and Zessin, H. (1979) Integral and differential characterizations of Gibbs processes. Math. Nacht., 88, 105-115.
62. Numata, M. (1964) Forest vegetation, particularly pine stands in the vicinity of Choshi - flora and vegetation in Choshi, Chiba prefecture, VI (in Japanese). Bull. Choshi Mar. Lab., no. 6, 27-37.
63. Ogata, Y. (1988) Statistical models for earthquake occurrences and residual analysis for point processes. J. Am. Statist. Ass., 83, 9-27.
64. Ogata, Y. and Tanemura, M. (1981) Estimation of interaction potentials of spatial point patterns through the maximum likelihood procedure. Ann. Inst. Statist. Math. B, 33, 315-338.
65. Ogata, Y. and Tanemura, M. (1986) Likelihood estimation of interaction potentials and external fields of inhomogeneous spatial point patterns. In Proc. Pacific Statist. Congr. (eds I. Francis, B. Manly and F. Lam), pp. 150-154. Amsterdam: Elsevier.
66. Papangelou, F. (1974) The conditional intensity of general point processes and an application to line processes. Z. Wahrsch. Ver. Geb., 28, 207-226.
67. Pregibon, D. (1981) Logistic regression diagnostics. Ann. Statist., 9, 705-724.
68. R Development Core Team (2004) R: a Language and Environment for Statistical Computing. Vienna: R Foundation for Statistical Computing.
69. Ripley, B. (1977) Modelling spatial patterns (with discussion). J. R. Statist. Soc. B, 39, 172-212.
70. Ripley, B. (1981) Spatial Statistics. New York: Wiley.
71. Ripley, B. (1988) Statistical Inference for Spatial Processes. Cambridge: Cambridge University Press.
72. Ripley, B. and Kelly, F. (1977) Markov point processes. J. Lond. Math. Soc., 15, 188-192.
73. Särkkä, A. (1993) Pseudo-likelihood Approach for Pair Potential Estimation of Gibbs Processes. Jyväskylä: University of Jyväskylä.
74. Schoenberg, F. (1999) Transforming spatial point processes into Poisson processes. Stochast. Process. Appl., 81, 155-164.
75. Stoyan, D. and Grabarnik, P. (1991) Second-order characteristics for stochastic structures connected with Gibbs point processes. Math. Nacht., 151, 95-100.
76. Stoyan, D., Kendall, W. and Mecke, J. (1995) Stochastic Geometry and Its Applications, 2nd edn. Chichester: Wiley.
77. Stoyan, D. and Stoyan H. (1995) Fractals, Random Shapes and Point Fields. Chichester: Wiley.
78. Venables, W. and Ripley, B. (1997) Modern Applied Statistics with S-Plus, 2nd edn. New York: Springer.
79. Vere-Jones, D. (1970) Stochastic models for earthquake occurrence (with discussion). J. R. Statist. Soc. B, 32, 1-62.
80. Vere-Jones, D. and Schoenberg, F. P. (2004) Rescaling marked point processes. Aust. New Zeal. J. Statist., 46, 133-143.
81. Wand, M. and Jones, M. (1995) Kernel Smoothing. London: Chapman and Hall.
82. Wartenberg, D. (1990) Exploratory spatial analyses: outliers, leverage points, and influence functions. In Spatial Statistics: Past, Present and Future (ed. D. Griffith), pp. 133-162. Ann Arbor: Institute of Mathematical Geography.
83. Zhuang, J., Ogata, Y. and Vere-Jones, D. (2005) Diagnostic analysis of space-time branching processes for earthquakes. Lect. Notes Statist., 185, in the press.