A toolbox for fitting complex spatial point process models using integrated nested Laplace approximation (INLA)

Annals of Applied Statistics

Volumn 6, Issue 4, 2012, Pages 1499-1530

  Illian, Janine B ^a   Sørbye, Sigrunn H ^b   Rue, Håvard ^c  

^a UNIVERSITY OF ST ANDREWS   (United Kingdom)

^b UNIVERSITY OF TROMSØ   (Norway)

^c NORWEGIAN UNIVERSITY OF SCIENCE AND TECHNOLOGY   (Norway)

Author keywords

Cox processes; Marked point patterns; Model assessment; Model comparison

Indexed keywords

EID: 84874552697     PISSN: 19326157     EISSN: 19417330     Source Type: Journal    
DOI: 10.1214/11-AOAS530     Document Type: Article

References (59)

1. Baddeley, A., Møller, J. andWaagepetersen, R. (2000). Non-and semi-parametric estimation of interaction in inhomogeneous point patterns. Stat. Neerl. 54 329-350.
2. Baddeley, A. and Turner, R. (2000). Practical maximum pseudolikelihood for spatial point patterns (with discussion). Aust. N. Z. J. Stat. 42 283-322. MR1794056
3. Baddeley, A. J. and Turner, R. (2005). Spatstat: An R package for analyzing spatial point patterns. Journal of Statistical Software 12 1-42.
4. Baddeley, A., Turner, R., Møller, J. andHazelton, M. (2005). Residual analysis for spatial point processes. J. R. Stat. Soc. Ser. B Stat. Methodol. 67 617-666. MR2210685
5. Berman, M. and Turner, R. (1992). Approximating point process likelihoods with GLIM. Applied Statistics 41 31-38.
6. Besag, J. E. (1977). Contribution to the discussion of Dr. Ripley's paper. J. Roy. Statist. Soc. Ser. B 39 193-195.
7. Burslem, D. F. R. P., Garwood, N. C. and Thomas, S. C. (2001). Tropical forest diversity-the plot thickens. Science 291 606-607.
8. Condit, R. (1998). Tropical Forest Census Plots. Springer and R. G. Landes Company, Berlin and Georgetown, TX.
9. Diggle, P. J. (2003). Statistical Analysis of Spatial Point Patterns, 2nd ed. Hodder Arnold, London.
10. Diggle, P. J., Menezes, R. and Su, T.-l. (2010). Geostatistical inference under preferential sampling. J. R. Stat. Soc. Ser. C. Appl. Stat. 59 191-232. MR2744471
11. Forchhammer, M. C. and Boomsma, J. (1995). Foraging strategies and seasonal diet optimization of muskoxen in West Greenland. Oecologia 104 169-180.
12. Forchhammer, M. C. and Boomsma, J. (1998). Optimal mating strategies in nonterritorial ungulates: A general model tested on muskoxen. Behavioural Ecology 9 136-143.
13. Guan, Y. (2008). On consistent nonparametric intensity estimation for inhomogeneous spatial point processes. J. Amer. Statist. Assoc. 103 1238-1247. MR2528839
14. Hanski, I. A. and Gilpin, M. E. (1997). Metapopulation Biology: Ecology, Genetics and Evolution. Academic Press, San Diego.
15. Hardy, O. J. and Vekemans, X. (2002). SPAGEDi: A versatile computer program to analyse spatial genetic structure at the individual or population levels. Molecular Ecology Notes 2 618-620.
16. Ho, L. P. and Stoyan, D. (2008). Modelling marked point patterns by intensity-marked Cox processes. Statist. Probab. Lett. 78 1194-1199. MR2441462
17. Huang, F. and Ogata, Y. (1999). Improvements of the maximum pseudo-likelihood estimators in various spatial statistical models. J. Comput. Graph. Statist. 8 519-530.
18. Hubbell, S. P., Condit, R. and Foster, R. B. (2005). Barro Colorado forest census plot data. Available at http://www.ctfs.si.edu/datasets/bci.
19. Hubbell, S. P., Foster, R. B., O'Brien, S. T., Harms, K. E., Condit, R., Wechsler, B., Wright, S. J. and Loo de Lao, S. (1999). Light gap disturbances, recruitment limitation, and tree diversity in a neotropical forest. Science 283 554-557.
20. Illian, J. B. and Hendrichsen, D. K. (2010). Gibbs point process models with mixed effects. Environmetrics 21 341-353. MR2842247
21. Illian, J. B. and Rue, H. (2010). A toolbox for fitting complex spatial point process models using integrated Laplace transformation (INLA). Technical report, Trondheim Univ.
22. Illian, J. B. and Simpson, D. (2011). Comment on Lindgren et al., an explicit link between Gaussian fields and Gaussian Markov random fields: The SPDE approach. J. Roy. Statist. Soc. Ser. B 73 423-498.
23. Illian, J., Penttinen, A., Stoyan, H. and Stoyan, D. (2008). Statistical Analysis and Modelling of Spatial Point Patterns. Wiley, Chichester. MR2384630
24. Illian, J. B., Sørbye, S. H., Rue, H. and Hendrichsen, D. K. (2012). Fitting a log Gaussian Cox process with temporally varying effects-a case study. Journal of Environmental Statistics. To appear.
25. John, R. C., Dalling, J.W., Harms, K. E., Yavitt, J. B., Stallard, R. F., Mirabello, M., Hubbell, S. P., Valencia, R., Navarrete, H., Vallejo, M. and Foster, R. B. (2007). Soil nutrients influence spatial distributions of tropical tree species. Proc. Natl. Acad. Sci. USA 104 864-869.
26. Johnson, C. R. and Boerlijst, M. C. (2002). Selection at the level of the community: The importance of spatial structure. Trends in Ecology & Evolution 17 83-90.
27. Killingback, T. and Doebeli, M. (1996). Spatial evolutionary game theory: Hawks and doves revisited. Proc. R. Soc. Lond. Ser. B 263 1135-1144.
28. Latimer, A. M., Banerjee, S., Sang, S., Mosher, E. S. and SilanderJr., J. A. (2009). Hierarchical models facilitate spatial analysis of large data sets: A case study on invasive plant species in the northeastern United States. Ecology Letters 12 144-154.
29. Law, R., Purves, D. W., Murrell, D. J. and Dieckmann, U. (2001). Causes and effects of small scale spatial structure in plant populations. In Integrating Ecology and Evolution in a Spatial Context (J. Silvertown and J. Antonovics, eds.) 21-44. Blackwell, Oxford.
30. Law, R., Illian, J. B., Burslem, D. F. R. P., Gratzer, G., Gunatilleke, C. V. S. and Gunatilleke, I. A. U. N. (2009). Ecological information from spatial patterns of plants: Insights from point process theory. Journal of Ecology 97 616-628.
31. Lawson, A. (1992). On fitting non-stationary Markov point process models on GLIM. In Computational Statistics, Volume 1 (Y. Dodge and J. Whittaker, eds.) 35-40. Physica Verlag, Heidelberg.
32. Lindgren, F., Rue, H. and Lindström, J. (2011). An explicit link between Gaussian fields and Gaussian Markov random fields: The SPDE approach. J. Roy. Statist. Soc. Ser. B 73 423-498.
33. Lunn, D. J., Thomas, A., Best, N. and Spiegelhalter, D. (2000). WinBUGS-a Bayesian modelling framework: Concepts, structure, and extensibility. Stat. Comput. 10 325-337.
34. Menezes, R. (2005). Assessing spatial dependency under non-standard sampling. Ph.D. thesis, Universidad de Santiago de Compostela, Santiago de Compostela, Spain.
35. Metropolis, N., Rosenbluth, A.W., Rosenbluth, M. N., Teller, A. H. and Teller, E. (1953). Equations of state calculations by fast computing machines. Journal of Chemical Physics 6 1087-1092.
36. Møller, J., Syversveen, A. R. and Waagepetersen, R. P. (1998). Log Gaussian Cox processes. Scand. J. Stat. 25 451-482. MR1650019
37. Møller, J. andWaagepetersen, R. P. (2004). Statistical Inference and Simulation for Spatial Point Processes. Monographs on Statistics and Applied Probability 100. Chapman & Hall/CRC, Boca Raton, FL. MR2004226
38. Møller, J. and Waagepetersen, R. P. (2007). Modern statistics for spatial point processes. Scand. J. Stat. 34 643-711. MR2392447
39. Moore, B. D., Lawler, I. R., Wallis, I. R., Beale, C. M. and Foley, W. J. (2010). Palatability mapping: A koala's eye view of spatial variation in habitat quality. Ecology 91 3165-3176.
40. Myllymäki, M. and Penttinen, A. (2009). Conditionally heteroscedastic intensity-dependent marking of log Gaussian Cox processes. Stat. Neerl. 63 450-473. MR2598981
41. Naylor, M., Greenhough, J., McCloskey, J., Bell, A. F. andMain, I. G. (2009). Statistical evaluation of characteristic earthquakes in the frequency-magnitude distributions of sumatra and other subduction zone regions. Geophysical Research Letters 36 DOI:10.1029/2009GL040460.
42. Neyman, J. and Scott, E. L. (1952). A theory of the spatial distribution of galaxies. Astrophys. J. 116 144-163. MR0053640
43. Ogata, Y. (1999). Seismicity analysis through point-process modeling: A review. Pure and Applied Geophysics 155 471-507.
44. R Development Core Team. (2009). R: A Language and Environment for Statistical Computing. R Foundation for Statistical Computing, Vienna, Austria. Available at http://www.R-project.org. ISBN 3-900051-07-0.
45. Rajala, T. A. and Illian, J. B. (2012). A family of spatial biodiversity measures based on graphs. Environ. Ecol. Stat. To appear.
46. Ripley, B. D. (1976). The second-order analysis of stationary point processes. J. Appl. Probab. 13 255-266. MR0402918
47. Rue, H. and Held, L. (2005). Gaussian Markov Random Fields: Theory and Applications. Monographs on Statistics and Applied Probability 104. Chapman & Hall/CRC, Boca Raton, FL. MR2130347
48. Rue, H., Martino, S. and Chopin, N. (2009). Approximate Bayesian inference for latent Gaussian models by using integrated nested Laplace approximations. J. R. Stat. Soc. Ser. B Stat. Methodol. 71 319-392. MR2649602
49. Schoenberg, F. P. (2005). Consistent parametric estimation of the intensity of a spatial-temporal point process. J. Statist. Plann. Inference 128 79-93. MR2110179
50. Spiegelhalter, D. J., Best, N. G., Carlin, B. P. and van der Linde, A. (2002). Bayesian measures of model complexity and fit. J. R. Stat. Soc. Ser. B Stat. Methodol. 64 583-639. MR1979380
51. Steffan-Dewenter, I., Münzenberg, U., Thies, C. and Tscharntke, T. (2002). Scale dependent effects of landscape context on three pollinator guilds. Ecology 83 1421-1432.
52. Stoyan, D. and Grabarnik, P. (1991). Second-order characteristics for stochastic structures connected with Gibbs point processes. Math. Nachr. 151 95-100. MR1121200
53. Stoyan, D., Kendall, W. S. and Mecke, J. (1995). Stochastic Geometry and Its Applications, 2nd ed. Wiley, London.
54. Strauss, D. J. (1975). A model for clustering. Biometrika 62 467-475. MR0383493
55. van Lieshout, M. N. M. (2000). Markov Point Processes and Their Applications. Imperial College Press, London. MR1789230
56. Waagepetersen, R. P. (2007). An estimating function approach to inference for inhomogeneous Neyman-Scott processes. Biometrics 63 252-258, 315. MR2345595
57. Waagepetersen, R. and Guan, Y. (2009). Two-step estimation for inhomogeneous spatial point processes. J. R. Stat. Soc. Ser. B Stat. Methodol. 71 685-702. MR2749914
58. Wiegand, T., Gunatilleke, S., Gunatilleke, N. andOkuda, T. (2007). Analysing the spatial structure of a Sri Lankan tree species with multiple scales of clustering. Ecology 88 3088-3012.
59. Yue, Y. and Loh, J. M. (2011). Bayesian semiparametric intensity estimation for inhomogeneous spatial point processes. Biometrics 67 937-946.