Skip to main content

An Introduction to Simulation-Based Inference for Spatial Point Processes

  • Chapter
Spatial Statistics and Computational Methods

Part of the book series: Lecture Notes in Statistics ((LNS,volume 173))

Abstract

Spatial point processes play a fundamental role in spatial statistics. In the simplest case they model “small” objects that may be identified by a map of points showing stores, towns, plants, nests, or cases of a disease observed in a two dimensional region or galaxies observed in a three dimensional region. The points may be decorated with marks (such as sizes or types) whereby marked point processes are obtained. The areas of applications are manifold: astronomy, geography, ecology, forestry, spatial epidemiology, image analysis, and many more. Currently spatial point processes is an active area of research, which probably will be of increasing importance for many new applications.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 84.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 109.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  • Adler, R. (1981). The Geometry of Random Fields, Wiley, New York.

    MATH  Google Scholar 

  • Baddeley, A. & Gill, R. D. (1997). Kaplan-Meier estimators of distance distributions for spatial point processes, Annals of Statistics 25: 263–292.

    Article  MathSciNet  MATH  Google Scholar 

  • Baddeley, A. J., Moyeed, R. A., Howard, C. V. & Boyde, A. (1993). Analysis of a three-dimensional point patttern with applications, Applied Statistics 42: 641–668.

    Article  MathSciNet  MATH  Google Scholar 

  • Baddeley, A. J. & van Lieshout, M. N. M. (1993). Stochastic geometry models in high-level vision, in K. V. Mardia & G. K. Kanji (eds), Statistics and Images, Advances in Applied Statistics, a supplement to the Journal of Applied Statistics, Vol. 20, Carfax Publishing, Abingdon, chapter 11, pp. 235–256.

    Google Scholar 

  • Baddeley, A. J. & van Lieshout, M. N. M. (1995). Area-interaction point processes, Annals of the Institute of Statistical Mathematics 46: 601–619.

    Article  Google Scholar 

  • Baddeley, A. & Moller, J. (1989). Nearest-neighbour Markov point pro- cesses and random sets, International Statistical Review 2: 89–121.

    Google Scholar 

  • Baddeley, A., Moller, J. & Waagepetersen, R. (2000). Non-and semi-parametric estimation of interaction in inhomogeneous point patterns, Statistica Neerlandica 54: 329–350.

    Article  MathSciNet  MATH  Google Scholar 

  • Baddeley, A. & Silverman, B. W. (1984). A cautionary example for the use of second-order methods for analysing point patterns, Biometrics 40: 1089–1094.

    Article  MathSciNet  Google Scholar 

  • Baddeley, A. & Turner, R. (2000). Practical maximum pseudolikelihood for spatial point patterns, Australian and New Zealand Journal of Statistics 42: 283–322.

    Article  MathSciNet  MATH  Google Scholar 

  • Bartlett, M. S. (1963). The spectral analysis of point processes, Journal of the Royal Statistical Society Series B 29: 264–296.

    MathSciNet  Google Scholar 

  • Bartlett, M. S. (1964). The spectral analysis of two-dimensional point processes, Biometrika 51: 299–311.

    MathSciNet  Google Scholar 

  • Benes, V., Bodlak, K., Moller, J. & Waagepetersen, R. P. (2002). Bayesian analysis of log Gaussian Cox process models for disease mapping, Technical Report R-02–2001, Department of Mathematical Sciences, Aalborg University.

    Google Scholar 

  • Berthelsen, K. K. & Moller, J. (2001a). Perfect simulation and inference for spatial point processes, Technical Report R-01–2009, Department of Mathematical Sciences, Aalborg University. Conditionally accepted for publication in the Scandinavian Journal of Statistics.

    Google Scholar 

  • Berthelsen, K. K. & Moller, J. (2001b). A primer on perfect simulation for spatial point processes, Technical Report R-01–2026, Department of Mathematical Sciences, Aalborg University. To appear in Bulletin of the Brazilian Mathematical Society, 33, 2003.

    Google Scholar 

  • Berman, M. & Turner, T. R. (1992). Approximating point process likelihoods with GLIM, Applied Statistics 41: 31–38.

    Article  MATH  Google Scholar 

  • Berthelsen, K. K. & Moller, J. (2002). Spatial jump processes and perfect simulation, in K. Mecke & D. Stoyan (eds), Morphology of Condensed Matter, Lecture Notes in Physics, Springer-Verlag, Heidelberg. To appear.

    Google Scholar 

  • Besag, J. (1977a). Some methods of statistical analysis for spatial data, Bulletin of the Institute of International Statistics 47: 77–92.

    MathSciNet  Google Scholar 

  • Besag, J. E. (1974). Spatial interaction and the statistical analysis of lattice systems (with discussion), Journal of the Royal Statistical Society Series B 36: 192–236.

    MathSciNet  MATH  Google Scholar 

  • Besag, J. E. (1975). Statistical analysis of non-lattice data, The Statistician 24: 179–195.

    Article  Google Scholar 

  • Besag, J. E. (1977b). Discussion on the paper by Ripley (1977), Journal of the Royal Statistical Society Series B 39: 193–195.

    MathSciNet  Google Scholar 

  • Besag, J. E. (1994). Discussion on the paper by Grenander and Miller, Journal of the Royal Statistical Society Series B 56: 591–592.

    Google Scholar 

  • Besag, J., Milne, R. & Zachary, S. (1982). Point process limits of lattice processes, Journal of Applied Probability 19: 210–216.

    Article  MathSciNet  MATH  Google Scholar 

  • Breyer, L. A. & Roberts, G. O. (2000). From Metropolis to diffusions: Gibbs states and optimal scaling, Stochastic Processes and their Applications 90: 181–206.

    Article  MathSciNet  MATH  Google Scholar 

  • Brix, A. (1999). Generalized gamma measures and shot-noise Cox processes, Advances in Applied Probability 31: 929–953.

    Article  MathSciNet  MATH  Google Scholar 

  • Brix, A. & Chadoeuf, J. (2000). Spatio-temporal modeling of weeds and shot-noise G Cox processes. Submitted.

    Google Scholar 

  • Brix, A. & Kendall, W. S. (2002). Simulation of cluster point processes without edge effects, Advances in Applied Probability 34: 267–280.

    Article  MathSciNet  MATH  Google Scholar 

  • Brix, A. & Moller, J. (2001). Space-time multitype log Gaussian Cox processes with a view to modelling weed data, Scandinavian Journal of Statistics 28: 471–488.

    Article  MathSciNet  MATH  Google Scholar 

  • Chan, K. S. & Geyer, C. J. (1994). Discussion of the paper ‘Markov chains for exploring posterior distributions’ by Luke Tierney, Annals of Statistics 22: 1747–1747.

    Article  Google Scholar 

  • Christensen, O. F., Moller, J. & Waagepetersen, R. P. (2001). Geometric ergodicity of Metropolis-Hastings algorithms for conditional simulation in generalised linear mixed models, Methodology and Computing in Applied Probability 3: 309–327.

    Article  MathSciNet  MATH  Google Scholar 

  • Christensen, O. F. & Waagepetersen, R. (2002). Bayesian prediction of spatial count data using generalised linear mixed models, Biometrics 58: 280–286.

    Article  MathSciNet  MATH  Google Scholar 

  • Coles, P. & Jones, B. (1991). A lognormal model for the cosmological mass distribution, Monthly Notices of the Royal Astronomical Society 248: 1–13.

    Google Scholar 

  • Cressie, N. A. C. (1993). Statistics for Spatial Data, second edn, Wiley, New York.

    Google Scholar 

  • Daley, D. J. & Vere-Jones, D. (1988). An Introduction to the Theory of Point Processes, Springer-Verlag, New York.

    MATH  Google Scholar 

  • Diggle, P. J. (1983). Statistical Analysis of Spatial Point Patterns, Academic Press, London.

    MATH  Google Scholar 

  • Diggle, P. J. (1985). A kernel method for smoothing point process data, Applied Statistics 34: 138–147.

    Article  MATH  Google Scholar 

  • Diggle, P. J., Lange, N. & Benés, F. (1991). Analysis of variance for replicated spatial point patterns in clinical neuroanatomy, Journal of the American Statistical Association 86: 618–625.

    Article  Google Scholar 

  • Diggle, P. J., Mateu, L. & Clough, H. E. (2000). A comparison between parametric and non-parametric approaches to the analysis of replicated spatial point patterns, Advances of Applied Probability 32: 331–343.

    Article  MathSciNet  MATH  Google Scholar 

  • Fernandez, R., Ferrari, P. A. & Garcia, N. L. (1999). Perfect simulation for interacting point processes, loss networks and Ising models. Manuscript.

    Google Scholar 

  • Fiksel, T. (1984). Estimation of parameterized pair potentials of marked and nonmarked Gibbsian point processes, Elektronische Informationsverarbeitung and Kypernetik 20: 270–278.

    MathSciNet  MATH  Google Scholar 

  • Gelfand, A. E. (1996). Model determination using sampling-based methods, in W. R. Gilks, S. Richardson & D. J. Spiegelhalter (eds), Markov chain Monte Carlo in Practice, Chapman and Hall, London, pp. 145–161.

    Google Scholar 

  • Gelman, A. & Meng, X.-L. (1998). Simulating normalizing constants: from importance sampling to bridge sampling to path sampling, Statistical Science 13: 163–185.

    Article  MathSciNet  MATH  Google Scholar 

  • Georgii, H.-O. (1976). Canonical and grand canonical Gibbs states for continuum systems, Communications of Mathematical Physics 48: 31–51.

    Article  MathSciNet  Google Scholar 

  • Georgii, H.-O. (1988). Gibbs Measures and Phase Transition, Walter de Gruyter, Berlin.

    Book  Google Scholar 

  • Geyer, C. J. (1991). Markov chain Monte Carlo maximum likelihood, Computing Science and Statistics: Proceedings of the 23rd Symposium on the Interface, pp. 156–163.

    Google Scholar 

  • Geyer, C. J. (1994). On the convergence of Monte Carlo maximum likelihood calculations, Journal of the Royal Society of Statistics Series B 56: 261–274.

    MathSciNet  MATH  Google Scholar 

  • Geyer, C. J. (1999). Likelihood inference for spatial point processes, in O. E. Barndorff-Nielsen, W. S. Kendall & M. N. M. van Lieshout (eds), Stochastic Geometry: Likelihood and Computation, Chapman and Hall/CRC, London, Boca Raton, pp. 79–140.

    Google Scholar 

  • Geyer, C. J. & Moller, J. (1994). Simulation procedures and likelihood inference for spatial point processes, Scandinavian Journal of Statistics 21: 359–373.

    MathSciNet  MATH  Google Scholar 

  • Geyer, C. J. & Thompson, E. A. (1992). Constrained Monte Carlo maximum likelihood for dependent data, Journal of the Royal Society of Statistics Series B 54: 657–699.

    MathSciNet  Google Scholar 

  • Goulard, M., Särkkä, A. & Grabarnik, P. (1996). Parameter estimation for marked Gibbs point processes through the maximum pseudo-likelihood method, Scandinavian Journal of Statistics 23: 365–379.

    MATH  Google Scholar 

  • Green, P. J. (1995). Reversible jump MCMC computation and Bayesian model determination, Biometrika 82: 711–732.

    Article  MathSciNet  MATH  Google Scholar 

  • Gu, M. G. & Zhu, H.-T. (2001). Maximum likelihood estimation for spatial models by Markov chain Monte Carlo stochastic approximation, Journal of the Royal Statistical Society Series B 63: 339–355.

    Article  MathSciNet  MATH  Google Scholar 

  • Häggström, O., van Lieshout, M. N. M. & Moller, J. (1999). Characterization results and Markov chain Monte Carlo algorithms including exact simulation for some spatial point processes, Bernoulli 5: 641–659.

    Article  MathSciNet  MATH  Google Scholar 

  • Heikkinen, J. & Arjas, E. (1998). Non-parametric Bayesian estimation of a spatial Poisson intensity, Scandinavian Journal of Statistics 25: 435–450.

    Google Scholar 

  • Heikkinen, J. & Penttinen, A. (1999). Bayesian smoothing in the estimation of the pair potential function of Gibbs point processes, Bernoulli 5: 1119–1136.

    Article  MathSciNet  MATH  Google Scholar 

  • Jensen, E. B. V. & Nielsen, L. S. (2001). A review on inhomogeneous spatial point processes, in I. V. Basawa, C. C. Heyde & R. L. Taylor (eds), Selected Proceedings of the Symposium on Inference for Stochastic Processes, Vol. 37, IMS Lecture Notes & Monographs Series, Beachwood, Ohio, pp. 297–318.

    Google Scholar 

  • Jensen, J. L. & Künsch, H. R. (1994). On asymptotic normality of pseudo likelihood estimates for pairwise interaction processes, Annals of the Institute of Statistical Mathematics 46: 475–486.

    MathSciNet  MATH  Google Scholar 

  • Jensen, J. L. & Moller, J. (1991). Pseudolikelihood for exponential family models of spatial point processes, Annals of Applied Probability 3: 445–461.

    Google Scholar 

  • Kallenberg, O. (1975). Random Measures, Akadamie-Verlag, Berlin.

    MATH  Google Scholar 

  • Kallenberg, O. (1984). An informal guide to the theory of conditioning in point processes, International Statistical Review 52: 151–164.

    Article  MathSciNet  MATH  Google Scholar 

  • Karr, A. F. (1991). Point Processes and Their Statistical Inference, Marcel Dekker, New York.

    MATH  Google Scholar 

  • Kelly, F. P. & Ripley, B. D. (1976). A note on Strauss’ model for clustering, Biometrika 63: 357–360.

    Article  MathSciNet  MATH  Google Scholar 

  • Kendall, W. S. (1998). Perfect simulation for the area-interaction point process, in L. Accardi & C. Heyde (eds), Probability Towards 2000, Springer, pp. 218–234.

    Google Scholar 

  • Kendall, W. S. & Moller, J. (2000). Perfect simulation using dominating processes on ordered spaces, with application to locally stable point processes, Advances in Applied Probability 32: 844–865.

    Article  MathSciNet  MATH  Google Scholar 

  • Kerscher, M. (2000). Statistical analysis of large-scale structure in the Universe, in K. R. Mecke & D. Stoyan (eds), Statistical Physics and Spatial Statistics, Lecture Notes in Physics, Springer, Berlin, pp. 36–71.

    Chapter  Google Scholar 

  • Kerstan, J., Matthes, K. & Mecke, J. (1974). Unbegrenzt teilbare Punktprozesse, Akademie-Verlag, Berlin.

    MATH  Google Scholar 

  • Kingman, J. F. C. (1993). Poisson Processes, Clarendon Press, Oxford.

    MATH  Google Scholar 

  • Lieshout, M. N. M. van (2000). Markov Point Processes and Their Applications, Imperial College Press, London.

    Book  MATH  Google Scholar 

  • Lieshout, M. N. M. van & Baddeley, A. J. (1996). A nonparametric measure of spatial interaction in point patterns, Statistica Neerlandica 50: 344–361.

    Article  MathSciNet  MATH  Google Scholar 

  • Loizeaux, M. A. & McKeague, I. W. (2001). Perfect sampling for posterior landmark distributions with an application to the detection of disease clusters, in I. V. Basawa, C. C. Heyde & R. L. Taylor (eds), Selected Proceedings of the Symposium on Inference for Stochastic Processes, Vol. 37, IMS Lecture Notes & Monographs Series, Beachwood, Ohio, pp. 321–331.

    Google Scholar 

  • Lund, J., Penttinen, A. & Rudemo, M. (1999). Bayesian analysis of spatial point patterns from noisy observations. Available at http://www.math.chalmers.se/Stat/ Research/Preprints/.

  • Lund, J. & Rudemo, M. (2000). Models for point processes observed with noise, Biometrika 87: 235–249.

    Article  MathSciNet  MATH  Google Scholar 

  • Lund, J. & Thönnes, E. (2000). Perfect simulation for point processes given noisy observations. Research Report 366, Department of Statistics, University of Warwick.

    Google Scholar 

  • Mase, S. (1995). Consistency of the maximum pseudo-likelihood estimator of continuous state space Gibbs processes, Annals of Applied Probability 5: 603–612.

    Article  MathSciNet  MATH  Google Scholar 

  • Mase, S. (1999). Marked Gibbs processes and asymptotic normality of maximum pseudo-likelihood estimators, Mathematische Nachrichten 209: 151–169.

    Article  MathSciNet  Google Scholar 

  • Mase, S., Moller, J., Stoyan, D., Waagepetersen, R. P. & Döge, G. (2001). Packing densities and simulated tempering for hard core Gibbs point processes, Annals of the Institute of Statistical Mathematics 53: 661–680.

    Article  MathSciNet  MATH  Google Scholar 

  • Matérn, B. (1960). Spatial Variation. Meddelanden frân Statens Skogforskningsinstitut, Band 49, No. 5.

    Google Scholar 

  • Matérn, B. (1986). Spatial Variation, Lecture Notes in Statistics. Springer-Verlag, Berlin.

    MATH  Google Scholar 

  • Matheron, G. (1975). Random Sets and Integral Geometry, Wiley, New York.

    MATH  Google Scholar 

  • Mecke, J. (1967). Stationäre zufällige Maße auf lokalkompakten Abelschen Gruppen, Zeitschrift für Wahrscheinlichkeitstheorie und verwandte Gebiete 9: 36–58.

    Article  MathSciNet  MATH  Google Scholar 

  • Mecke, J., Schneider, R. G., Stoyan, D. & Weil, W. R. R. (1990). Stochastische Geometrie, Birkhäuser Verlag, Basel.

    MATH  Google Scholar 

  • Metropolis, N., Rosenbluth, A. W., Rosenbluth, M. N., Teller, A. H. & Teller, E. (1953). Equations of state calculations by fast computing machines, Journal of Chemical Physics 21: 1087–1092.

    Article  Google Scholar 

  • Moller, J. (1989). On the rate of convergence of spatial birth-and-death processes, Annals of the Institute of Statistical Mathematics 3: 565–581.

    Article  Google Scholar 

  • Moller, J. (1999). Markov chain Monte Carlo and spatial point processes, in O. E. Barndorff-Nielsen, W. S. Kendall & M. N. M. van Lieshout (eds), Stochastic Geometry: Likelihood and Computation, Monographs on Statistics and Applied Probability 80, Chapman and Hall/CRC, Boca Raton, pp. 141–172.

    Google Scholar 

  • Moller, J. (2001). A review of perfect simulation in stochastic geometry, in I. V. Basawa, C. C. Heyde & R. L. Taylor (eds), Selected Proceedings of the Symposium on Inference for Stochastic Processes, Vol. 37, IMS Lecture Notes & Monographs Series, Beachwood, Ohio, pp. 333–355.

    Chapter  Google Scholar 

  • Moller, J. (2002a). A comparison of spatial point process models in epidemiological applications, in P. J. Green, N. L. Hjort & S. Richardson (eds), Highly Structured Stochastic Systems, Oxford University Press, Oxford. To appear.

    Google Scholar 

  • Moller, J. (2002b). Shot noise Cox processes, Technical Report R-02–2009, Department of Mathematical Sciences, Aalborg University.

    Google Scholar 

  • Moller, J., Syversveen, A. R. & Waagepetersen, R. P. (1998). Log Gaussian Cox processes, Scandinavian Journal of Statistics 25: 451–482.

    Article  MathSciNet  Google Scholar 

  • Moller, J. & Waagepetersen, R. P. (2002). Statistical inference for Cox processes, in A. B. Lawson & D. Denison (eds), Spatial Cluster Modelling, Chapman and Hall/CRC, Boca Raton.

    Google Scholar 

  • Moller, J. & Waagepetersen, R. P. (2003). Statistical Inference and Simulation for Spatial Point Processes, Chapman and Hall/CRC, Boca Raton. In preparation.

    Google Scholar 

  • Neyman, J. & Scott, E. L. (1958). Statistical approach to problems of cosmology, Journal of the Royal Statistical Society Series B 20: 1–43.

    MathSciNet  MATH  Google Scholar 

  • Nguyen, X. X. & Zessin, H. (1979). Integral and differential characteriza- tions of Gibbs processes, Mathematische Nachrichten 88: 105–115.

    Article  MathSciNet  MATH  Google Scholar 

  • Ohser, J. & Mücklich, F. (2000). Statistical Analysis of Microstructures in Materials Science, Wiley, New York.

    MATH  Google Scholar 

  • Peebles, P. J. E. (1974). The nature of the distribution of galaxies, Astronomy and Astrophysics 32: 197–202.

    Google Scholar 

  • Peebles, P. J. E. & Groth, E. J. (1975). Statistical analysis of extragalactic objects. V. Three-point correlation function for the galaxy distribution in the Zwicky catalog, Astrophysical Journal 196: 1–11.

    Article  Google Scholar 

  • Penttinen, A. (1984). Modelling Interaction in Spatial Point Patterns: Parameter Estimation by the Maximum Likelihood Method, Number 7 in Jyväskylä Studies in Computer Science, Economics, and Statistics.

    Google Scholar 

  • Penttinen, A., Stoyan, D. & Henttonen, H. M. (1992). Marked point processes in forest statistics, Forest Science 38: 806–824.

    Google Scholar 

  • Preston, C. (1976). Random Fields, Lecture Notes in Mathematics, 534. Springer-Verlag, Berlin-Heidelberg.

    Google Scholar 

  • Preston, C. J. (1977). Spatial birth-and-death processes, Bulletin of the International Statistical Institute 46: 371–391.

    MathSciNet  Google Scholar 

  • Propp, J. G. & Wilson, D. B. (1996). Exact sampling with coupled Markov chains and applications to statistical mechanics, Random Structures and Algorithms 9: 223–252.

    Article  MathSciNet  MATH  Google Scholar 

  • Quine, M. P. & Watson, D. F. (1984). Radial simulation of n-dimensional Poisson processes, Journal of Applied Probability 21: 548–557.

    Article  MathSciNet  MATH  Google Scholar 

  • Rathbun, S. L. (1996). Estimation of Poisson intensity using partially observed concomitant variables, Biometrics 52: 226–242.

    Article  MATH  Google Scholar 

  • Reiss, R.-D. (1993). A Course on Point Processes, Springer Verlag, New York.

    Book  MATH  Google Scholar 

  • Ripley, B. D. (1977). Modelling spatial patterns (with discussion), Journal of the Royal Statistical Society Series B 39: 172–212.

    MathSciNet  Google Scholar 

  • Ripley, B. D. (1979). Simulating spatial patterns: dependent samples from a multivariate density. Algorithm AS 137, Applied Statistics 28: 109–112.

    Article  Google Scholar 

  • Ripley, B. D. (1981). Spatial Statistics, Wiley, New York.

    Book  MATH  Google Scholar 

  • Ripley, B. D. (1988). Statistical Inference for Spatial Processes, Cambridge University Press, Cambridge.

    Book  Google Scholar 

  • Ripley, B. D. & Kelly, F. P. (1977). Markov point processes, Journal of the London Mathematical Society 15: 188–192.

    Article  MathSciNet  MATH  Google Scholar 

  • Roberts, G. O., Gelman, A. & Gilks, W. R. (1997). Weak convergence and optimal scaling of random walk Metropolis algorithms, Annals of Applied Probability 7: 110–120.

    Article  MathSciNet  MATH  Google Scholar 

  • Roberts, G. O. & Rosenthal, J. S. (1997). Geometric ergodicity and hybrid Markov chains, Electronic Communications in Probability 2: 13–25.

    Article  MathSciNet  MATH  Google Scholar 

  • Roberts, G. O. & Rosenthal, J. S. (1998). Optimal scaling of discrete approximations to Langevin diffusions, Journal of the Royal Statistical Society Series B 60: 255–268.

    Article  MathSciNet  MATH  Google Scholar 

  • Roberts, G. O. & Tweedie, R. L. (1996). Exponential convergence of Langevin diffusions and their discrete approximations, Bernoulli 2: 341–363.

    Article  MathSciNet  MATH  Google Scholar 

  • Rossky, P. J., Doll, J. D. & Friedman, H. L. (1978). Brownian dynamics as smart Monte Carlo simulation, Journal of Chemical Physics 69: 4628–4633.

    Article  Google Scholar 

  • Ruelle, D. (1969). Statistical Mechanics: Rigorous Results, W.A. Benjamin, Reading, Massachusetts.

    MATH  Google Scholar 

  • Schladitz, K. & Baddeley, A. J. (2000). A third-order point process characteristic, Scandinavian Journal of Statistics 27: 657–671.

    Article  MathSciNet  MATH  Google Scholar 

  • Schlather, M. (2001). On the second-order characteristics of marked point processes, Bernoulli 7: 99–117.

    Article  MathSciNet  MATH  Google Scholar 

  • Stoyan, D., Kendall, W. S. & Mecke, J. (1995). Stochastic Geometry and Its Applications, second edn, Wiley, Chichester.

    MATH  Google Scholar 

  • Stoyan, D. & Stoyan, H. (1994). Fractals, Random Shapes and Point Fields, Wiley, Chichester.

    MATH  Google Scholar 

  • Stoyan, D. & Stoyan, H. (2000). Improving ratio estimators of second order point process characteristics, Scandinavian Journal of Statistics 27: 641–656.

    Article  MathSciNet  MATH  Google Scholar 

  • Strauss, D. J. (1975). A model for clustering, Biometrika 63: 467–475.

    Article  Google Scholar 

  • Thönnes, E. (1999). Perfect simulation of some point processes for the impatient user, Advances in Applied Probability 31: 69–87.

    Article  MathSciNet  MATH  Google Scholar 

  • Waagepetersen, R. & Sorensen, S. (2001). A tutorial on reversible jump MCMC with a view toward applications in QTL-mapping, International Statistical Review 69 (1): 49–61.

    Article  MATH  Google Scholar 

  • Wolpert, R. L. & Ickstadt, K. (1998). Poisson/gamma random field models for spatial statistics, Biometrika 85: 251–267.

    Article  MathSciNet  MATH  Google Scholar 

  • Wood, A. T. A. & Chan, G. (1994). Simulation of stationary Gaussian processes in [0,1)d, Journal of Computational and Graphical Statistics 3: 409–432.

    MathSciNet  Google Scholar 

Download references

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2003 Springer Science+Business Media New York

About this chapter

Cite this chapter

Møller, J., Waagepetersen, R.P. (2003). An Introduction to Simulation-Based Inference for Spatial Point Processes. In: Møller, J. (eds) Spatial Statistics and Computational Methods. Lecture Notes in Statistics, vol 173. Springer, New York, NY. https://doi.org/10.1007/978-0-387-21811-3_4

Download citation

  • DOI: https://doi.org/10.1007/978-0-387-21811-3_4

  • Publisher Name: Springer, New York, NY

  • Print ISBN: 978-0-387-00136-4

  • Online ISBN: 978-0-387-21811-3

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics