We describe practical techniques for fitting stochastic models to spatial point pattern data in the statistical package R. The techniques have been implemented in our package spatstat in R. They are demonstrated on two example datasets.
- EDA for spatial point processes
- Point process model fitting and simulation
- Spatstat package
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L. Anselin. Local indicators of spatial association — LISA. Geographical Analysis, 27:93–115, 1995.
A.C. Atkinson. Plots, Transformations and Regression. Number 1 in Oxford Statistical Science Series. Oxford University Press/ Clarendon, 1985.
A.J. Baddeley, J. Møller, and R.P. Waagepetersen. Non-and semiparametric estimation of interaction in inhomogeneous point patterns. Statistica Neerlandica, 54(3):329–350, 2000.
A.J. Baddeley and R. Turner. spatstat: an R package for analyzing spatial point patterns. Journal of Statistical Software, 12(6):1–42, 2005. URL: http://www.jstatsoft.org.
A.J. Baddeley and R. Turner. Practical maximum pseudolikelihood for spatial point patterns (with discussion). Australian and New Zealand Journal of Statistics, 42(3):283–322, 2000.
A.J. Baddeley and R. Turner. Spatstat: an R package for analyzing spatial point patterns. Research Report 2004/13, School of Mathematics and Statistics, University of Western Australia, September 2004.
A.J. Baddeley, R. Turner, J. Møller and M. Hazelton. Residual analysis for spatial point processes. Journal of the Royal Statistical Society (series B), 67:1–35, 2005.
A.J. Baddeley, M.N.M. van Lieshout and J. Møller. Markov properties of cluster processes. Advances in Applied Probability, 28:346–355, 1996.
M.S. Bartlett. The spectral analysis of two-dimensional point processes. Biometrika, 51:299–311, 1964.
M.S. Bartlett. The statistical analysis of spatial pattern. Chapman and Hall, London, 1975.
M. Berman. Testing for spatial association between a point process and another stochastic process. Applied Statistics, 35:54–62, 1986.
M. Berman and T.R. Turner. Approximating point process likelihoods with GLIM. Applied Statistics, 41:31–38, 1992.
J.E. Besag. Statistical analysis of non-lattice data. The Statistician, 24:179–195, 1975.
J.E. Besag and P.J. Diggle. Simple Monte Carlo tests for spatial pattern. Applied Statistics, 26:327–333, 1977.
C. Chatfield. Problem solving: a statistician’s guide. Chapman and Hall, 1988.
D. Collett. Modelling Binary Data. Chapman and Hall, London, 1991.
D.R. Cox and V. Isham. Point processes. Chapman and Hall, London, 1980.
D.R. Cox and E.J. Snell. Applied Statistics: principles and examples. Chapman and Hall, 1981.
The Comprehensive R Archive Network. URL http://www.cran.r-project.org.
N.A.C. Cressie and L.B. Collins. Analysis of spatial point patterns using bundles of product density LISA functions. Journal of Agricultural, Biological and Environmental Statistics, 6:118–135, 2001.
N.A.C. Cressie and L.B. Collins. Patterns in spatial point locations: local indicators of spatial association in a minefield with clutter. Naval Research Logistics, 48:333–347, 2001.
N.A.C. Cressie. Statistics for Spatial Data. John Wiley and Sons, New York, 1991.
N.A.C. Cressie. Statistics for Spatial Data. John Wiley and Sons, New York, 1993. Revised edition.
A.C. Davison and E.J. Snell. Residuals and diagnostics. In D.V. Hinkley, N. Reid, and E.J. Snell, editors, Statistical theory and modelling (in honour of Sir David Cox FRS), Chap. 4, pp. 83–106. Chapman and Hall, London, 1991.
P.J. Diggle. A kernel method for smoothing point process data. Journal of the Royal Statistical Society, series C (Applied Statistics), 34:138–147, 1985.
P.J. Diggle. Statistical analysis of spatial point patterns. Academic Press, London, 1983.
P.J. Diggle. A point process modelling approach to raised incidence of a rare phenomenon in the vicinity of a prespecified point. Journal of the Royal Statistical Society, series A, 153:349–362, 1990.
P.J. Diggle. Statistical Analysis of Spatial Point Patterns. Arnold, second edition, 2003.
P.J. Diggle, D.J. Gates, and A. Stibbard. A nonparametric estimator for pairwise-interaction point processes. Biometrika, 74:763–770, 1987.
F. Divino, A. Frigessi and P.J. Green. Penalised pseudolikelihood estimation in Markov random field models. Scandinavian Journal of Statistics, 27(3):445–458, 2000.
R. Foxall and A.J. Baddeley. Nonparametric measures of association between a spatial point process and a random set, with geological applications. Applied Statistics, 51(2):165–182, 2002.
C.J. Geyer. Likelihood inference for spatial point processes. In O.E. Barndorff-Nielsen, W.S. Kendall, and M.N.M. van Lieshout, editors, Stochastic Geometry: Likelihood and Computation, number 80 in Monographs on Statistics and Applied Probability, Chap. 3, pp. 79–140. Chapman and Hall / CRC, Boca Raton, Florida, 1999.
C.J. Geyer and J. Møller. Simulation procedures and likelihood inference for spatial point processes. Scandinavian Journal of Statistics, 21(4):359–373, 1994.
K.-H. Hanisch and D. Stoyan. Remarks on statistical inference and prediction for a hard-core clustering model. Statistics, 14:559–567, 1983.
R.D. Harkness and V. Isham. A bivariate spatial point pattern of ants’ nests. Applied Statistics, 32:293–303, 1983.
H. Högmander and A. Särkkä. Multitype spatial point patterns with hierarchical interactions. Biometrics, 55:1051–1058, 1999.
A.C.A. Hope. A simplified Monte Carlo significance test procedure. Journal of the Royal Statistical Society, series B, 30:582–598, 1968.
K. Hornik. The R Faq: Frequently asked questions on R. URL http://www.ci.tuwien.ac.at/~hornik/R/. ISBN 3-901167-51-X.
F. Huang and Y. Ogata. Improvements of the maximum pseudolikelihood estimators in various spatial statistical models. Journal of Computational and Graphical Statistics, 8(3):510–530, 1999.
R. Ihaka and R. Gentleman. R: A language for data analysis and graphics. Journal of Computational and Graphical Statistics, 5(3):299–314, 1996.
V.S. Isham. Multitype Markov point processes: some approximations. Proceedings of the Royal Society of London, Series A, 391:39–53, 1984.
J.L. Jensen and H.R. Künsch. On asymptotic normality of pseudo likelihood estimates for pairwise interaction processes. Annals of the Institute of Statistical Mathematics, 46:475–486, 1994.
J.L. Jensen and J. Møller. Pseudolikelihood for exponential family models of spatial point processes. Annals of Applied Probability, 1:445–461, 1991.
F.P. Kelly and B.D. Ripley. On Strauss’s model for clustering. Biometrika, 63:357–360, 1976.
J.F.C. Kingman. Poisson Processes. Oxford University Press, 1993.
A.B. Lawson. A deviance residual for heterogeneous spatial Poisson processes. Biometrics, 49:889–897, 1993.
M.N.M. van Lieshout. Markov Point Processes and their Applications. Imperial College Press, 2000.
M.N.M. van Lieshout and A.J. Baddeley. A nonparametric measure of spatial interaction in point patterns. Statistica Neerlandica, 50:344–361, 1996.
M.N.M. van Lieshout and A.J. Baddeley. Indices of dependence between types in multivariate point patterns. Scandinavian Journal of Statistics, 26:511–532, 1999.
P. McCullagh and J.A. Nelder. Generalized Linear Models. Chapman and Hall, second edition, 1989.
J. Møller and R.P. Waagepetersen. Statistical Inference and Simulation for Spatial Point Processes. Chapman and Hall/CRC, Boca Raton, 2003.
Y. Ogata and M. Tanemura. Estimation of interaction potentials of spatial point patterns through the maximum likelihood procedure. Annals of the Institute of Statistical Mathematics, B 33:315–338, 1981.
Y. Ogata and M. Tanemura. Likelihood analysis of spatial point patterns. Journal of the Royal Statistical Society, series B, 46:496–518, 1984.
Y. Ogata and M. Tanemura. Likelihood estimation of interaction potentials and external fields of inhomogeneous spatial point patterns. In I.S. Francis, B.J.F. Manly, and F.C. Lam, editors, Pacific Statistical Congress, pp. 150–154. Elsevier, 1986.
A. Penttinen. Modelling Interaction in Spatial Point Patterns: Parameter Estimation by the Maximum Likelihood Method. Number 7 in Jyväskylä Studies in Computer Science, Economics and Statistics. University of Jyväskylä, 1984.
R Development Core Team. R: A language and environment for statistical computing. R Foundation for Statistical Computing, Vienna, Austria, 2004. ISBN 3-900051-00-3.
B.D. Ripley. The second-order analysis of stationary point processes. Journal of Applied Probability, 13:255–266, 1976.
B.D. Ripley. Modelling spatial patterns (with discussion). Journal of the Royal Statistical Society, Series B, 39:172–212, 1977.
B.D. Ripley. Spatial Statistics. John Wiley and Sons, New York, 1981.
B.D. Ripley. Spatial statistics: developments 1980-3. International Statistical Review, 52:141–150, 1984.
B.D. Ripley. Statistical Inference for Spatial Processes. Cambridge University Press, 1988.
B.D. Ripley. Gibbsian interaction models. In D.A. Griffiths, editor, Spatial Statistics: Past, Present and Future, pp. 1–19. Image, New York, 1989.
A. Särkkä. Pseudo-likelihood approach for pair potential estimation of Gibbs processes. Number 22 in Jyväskylä Studies in Computer Science, Economics and Statistics. University of Jyväskylä, 1993.
B.W. Silverman and T.C. Brown. Short distances, flat triangles and poisson limits. Journal of Applied Probability, 15:815–825, 1978.
D. Stoyan and P. Grabarnik. Second-order characteristics for stochastic structures connected with Gibbs point processes. Mathematische Nachrichten, 151:95–100, 1991.
D. Stoyan and P. Grabarnik. Statistics for the stationary Strauss model by the cusp point method. Statistics, 22:283–289, 1991.
D. Stoyan, W.S. Kendall and J. Mecke. Stochastic Geometry and its Applications. John Wiley and Sons, Chichester, second edition, 1995.
D. Stoyan and H. Stoyan. Fractals, random shapes and point fields. Wiley, 1995.
D. Stoyan and H. Stoyan. Non-homogeneous Gibbs process models for forestry — a case study. Biometrical Journal, 40:521–531, 1998.
R. Takacs and T. Fiksel. Interaction pair-potentials for a system of ants’ nests. Biometrical Journal, 28:1007–1013, 1986.
J. Tukey. Exploratory Data Analysis. Addison-Wesley, Reading, Mass., 1977.
W.N. Venables and B.D. Ripley. Modern Applied Statistics with S-Plus. Springer, second edition, 1997.
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Baddeley, A., Turner, R. (2006). Modelling Spatial Point Patterns in R. In: Baddeley, A., Gregori, P., Mateu, J., Stoica, R., Stoyan, D. (eds) Case Studies in Spatial Point Process Modeling. Lecture Notes in Statistics, vol 185. Springer, New York, NY. https://doi.org/10.1007/0-387-31144-0_2
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