Statistics and Computing

, Volume 24, Issue 1, pp 91–100 | Cite as

Two step estimation for Neyman-Scott point process with inhomogeneous cluster centers



This paper is concerned with parameter estimation for the Neyman-Scott point process with inhomogeneous cluster centers. Inhomogeneity depends on spatial covariates. The regression parameters are estimated at the first step using a Poisson likelihood score function. Three estimation procedures (minimum contrast method based on a modified K function, composite likelihood and Bayesian methods) are introduced for estimation of clustering parameters at the second step. The performance of the estimation methods are studied and compared via a simulation study. This work has been motivated and illustrated by ecological studies of fish spatial distribution in an inland reservoir.


Bayesian method Composite likelihood Clustering Inhomogeneous cluster centers Inhomogeneous point process Minimum contrast method Modified K function Neyman-Scott point process 



We would like to thank to three referees and Samuel Soubeyrand for their helpful comments and Samuel Soubeyrand for checking the program codes.


  1. Baddeley, A., Møller, J., Waagepetersen, R.P.: Non- and semiparametric estimation of interaction in inhomogeneous point patterns. Stat. Neerl. 54, 329–350 (2000) CrossRefMATHGoogle Scholar
  2. Bertram, B.C.R.: Living in groups: predators and prey. In: Krebs, J.R., Davies, N.B. (eds.) Behavioural Ecology, 1st edn., pp. 64–96. Blackwell, Oxford (1978) Google Scholar
  3. Brix, A., Senoussi, R., Couteron, P., Chadouf, J.: Assessing goodness of fit of spatially inhomogeneous Poisson processes. Biometrika 88(2), 487–497 (2001) CrossRefMATHMathSciNetGoogle Scholar
  4. Diggle, P.J.: Statistical Analysis of Spatial Point Patterns, 2nd edn. Oxford University Press, Oxford (2003) MATHGoogle Scholar
  5. Dvořák, J., Prokešová, M.: Moment estimation methods for stationary spatial cox processes—a comparison. Kybernetika (2012, submitted) Google Scholar
  6. Guan, Y.: A composite likelihood approach in fitting spatial point process models. J. Am. Stat. Soc. 101, 1502–1512 (2006) CrossRefMATHGoogle Scholar
  7. Guttorp, P., Thorarinsdottir, T.L.: Bayesian inference for non-Markovian point processes. In: Porcu, E., Montero, J.M., Schlather, M. (eds.) Advances and Challenges in Space-Time Modelling of Natural Events. Springer, Berlin (2012) Google Scholar
  8. Illian, J., Penttinen, A., Stoyan, H., Stoyan, D.: Statistical Analysis and Modelling of Spatial Point Patterns. Wiley, New York (2008) MATHGoogle Scholar
  9. Jarolim, O., Kubecka, J., Cech, M., Vasek, M., Peterka, J., Matena, J.: Sinusoidal swimming in fishes: the role of season, density of large zooplankton, fish length, time of the day, weather condition and solar radiation. Hydrobiologia 654, 253–265 (2010) CrossRefGoogle Scholar
  10. Møller, J., Waagepetersen, R.P.: Statistical Inference and Simulation for Spatial Point Processes. Chapman & Hall/CRC, London (2004) Google Scholar
  11. Møller, J., Waagepetersen, R.P.: Modern statistics for spatial point processes. Scand. J. Stat. 34(4), 643–684 (2007) Google Scholar
  12. Peterka, J., Cech, M., Vasek, M., Juza, T., Drastik, M., Prchalova, M., Kubecka, J., Matena, J.: Fish occurrence in the open water habitat of the eutrophic canyon shaped rimov reservoir (Southern Bohemia): comparing indirect and direct methods of investigation. In: Kubecka, J. (ed.) Fish Stock Assessment Methods for Lakes and Reservoirs. HBI BC AS CR, Ceske Budejovice (2007), 42 pp. Google Scholar
  13. Pitcher, T.J.: Sensory information and the organisation of behaviour of shoaling cyprinid. Anim. Behav. 27, 126–149 (1979) CrossRefGoogle Scholar
  14. Prokešová, M.: Inhomogeneity in spatial point processes—geometry versus tractable estimation. Image Anal. Stereol. 29(3), 133–141 (2010) CrossRefMATHMathSciNetGoogle Scholar
  15. Schoenberg, F.P.: Consistent parametric estimation of the intensity of a spatial-temporal point processes. J. Stat. Plan. Inference 128, 79–93 (2005) CrossRefMATHMathSciNetGoogle Scholar
  16. Simmonds, E.J., MacLennan, D.N.: Fisheries Acoustics, 2nd edn. Wiley-Blackwell, Oxford (2005) CrossRefGoogle Scholar
  17. Stoyan, D., Kendall, W.S., Mecke, J.: Stochastic Geometry and Its Applications, 2nd edn. Wiley, Chichester (1995) MATHGoogle Scholar
  18. Waagepetersen, R.P.: An estimating function approach to inference for inhomogeneous Neyman-Scott processes. Biometrics 63(1), 252–258 (2007) CrossRefMATHMathSciNetGoogle Scholar
  19. Waagepetersen, R.P., Guan, Y.: Two-step estimation for inhomogeneous spatial point processes. J. R. Stat. Soc. B 71(3), 685–702 (2009) CrossRefMATHMathSciNetGoogle Scholar

Copyright information

© Springer Science+Business Media New York 2012

Authors and Affiliations

  1. 1.Department of Applied Mathematics and Informatics, Faculty of EconomicsUniversity of South BohemiaČeské BudějoviceCzech Republic
  2. 2.Biology center of the AS CRInstitute of HydrobiologyČeské BudějoviceCzech Republic
  3. 3.Faculty of ScienceUniversity of South BohemiaČeské BudějoviceCzech Republic

Personalised recommendations