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Cox Processes Associated with Spatial Copula Observed through Stratified Sampling

Author

Listed:
  • Walguen Oscar

    (Department of Mathematics and Computer Sciences, Université des Antilles, 97157 Pointe-à-Pitre, France
    Université d’Etat d’Haiti, HT6110 Port-au-Prince, Haiti)

  • Jean Vaillant

    (Department of Mathematics and Computer Sciences, Université des Antilles, 97157 Pointe-à-Pitre, France)

Abstract

Cox processes, also called doubly stochastic Poisson processes, are used for describing phenomena for which overdispersion exists, as well as Poisson properties conditional on environmental effects. In this paper, we consider situations where spatial count data are not available for the whole study area but only for sampling units within identified strata. Moreover, we introduce a model of spatial dependency for environmental effects based on a Gaussian copula and gamma-distributed margins. The strength of dependency between spatial effects is related with the distance between stratum centers. Sampling properties are presented taking into account the spatial random field of covariates. Likelihood and Bayesian inference approaches are proposed to estimate the effect parameters and the covariate link function parameters. These techniques are illustrated using Black Leaf Streak Disease (BLSD) data collected in Martinique island.

Suggested Citation

  • Walguen Oscar & Jean Vaillant, 2021. "Cox Processes Associated with Spatial Copula Observed through Stratified Sampling," Mathematics, MDPI, vol. 9(5), pages 1-13, March.
    • Handle: RePEc:gam:jmathe:v:9:y:2021:i:5:p:524-:d:509452
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    References listed on IDEAS

    as
    1. Karlis, Dimitris, 2005. "EM Algorithm for Mixed Poisson and Other Discrete Distributions," ASTIN Bulletin, Cambridge University Press, vol. 35(1), pages 3-24, May.
    2. Peter Xue‐Kun Song, 2000. "Multivariate Dispersion Models Generated From Gaussian Copula," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 27(2), pages 305-320, June.
    3. De Oliveira, Victor, 2013. "Hierarchical Poisson models for spatial count data," Journal of Multivariate Analysis, Elsevier, vol. 122(C), pages 393-408.
    4. Li, Zhongping & Cui, Lirong & Chen, Jianhui, 2018. "Traffic accident modelling via self-exciting point processes," Reliability Engineering and System Safety, Elsevier, vol. 180(C), pages 312-320.
    5. Roger D. Peng & Frederic Paik Schoenberg & James A. Woods, 2005. "A Space-Time Conditional Intensity Model for Evaluating a Wildfire Hazard Index," Journal of the American Statistical Association, American Statistical Association, vol. 100, pages 26-35, March.
    6. Sain, Stephan R. & Cressie, Noel, 2007. "A spatial model for multivariate lattice data," Journal of Econometrics, Elsevier, vol. 140(1), pages 226-259, September.
    7. Jean Vaillant & Gavino Puggioni & Lance A. Waller & Jean Daugrois, 2011. "A spatio‐temporal analysis of the spread of sugarcane yellow leaf virus," Journal of Time Series Analysis, Wiley Blackwell, vol. 32, pages 396-406, July.
    8. Lee, Duncan, 2013. "CARBayes: An R Package for Bayesian Spatial Modeling with Conditional Autoregressive Priors," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 55(i13).
    9. Jesper Møller & Mohammad Ghorbani & Ege Rubak, 2016. "Mechanistic spatio-temporal point process models for marked point processes, with a view to forest stand data," Biometrics, The International Biometric Society, vol. 72(3), pages 687-696, September.
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