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Bayesian Inference on a Cox Process Associated with a Dirichlet Process

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International Journal of Computer Applications
© 2014 by IJCA Journal
Volume 95 - Number 18
Year of Publication: 2014
Authors:
Larissa Valmy
Jean Vaillant
10.5120/16691-6825

Larissa Valmy and Jean Vaillant. Article: Bayesian Inference on a Cox Process Associated with a Dirichlet Process. International Journal of Computer Applications 95(18):1-7, June 2014. Full text available. BibTeX

@article{key:article,
	author = {Larissa Valmy and Jean Vaillant},
	title = {Article: Bayesian Inference on a Cox Process Associated with a Dirichlet Process},
	journal = {International Journal of Computer Applications},
	year = {2014},
	volume = {95},
	number = {18},
	pages = {1-7},
	month = {June},
	note = {Full text available}
}

Abstract

In ecology and epidemiology, spatio-temporal distributions of events can be described by Cox processes. Situations for which there exists a hidden process which contributes to random effects on the intensity of the observed Cox process are considered. The observed process is a generalized shot noise Cox process and the hidden process is a Poisson process associated with a Dirichlet process. The distributional properties of quadrat counts are presented and bayesian inference is proposed for estimating and predicting parameters of interest in the model. Illustrations are given from weed spatial count data and disease mortality data.

References

  • D. Blackwell and J. B. Macqueen. Ferguson distributions via polya urn schemes. Annals of Statistics, 1(2):353–355, 1973.
  • P. Bremaud. Point Processes and Queues: Martingale Dynamics. 1981.
  • P. Bremaud. Point Processes and Their Statistical Inference. 1991.
  • A. Brix and J. Chadoeuf. Spatio-temporal modeling of weeds and shotnoise cox processes. Biometrical Journal, 44:83–99, 2002.
  • Comas C. , Mateu J. , and Delicado P. On tree intensity estimation for forest inventories: Some statistical issues. Biometrical Journal, 23(6):994–1010, 2011.
  • A. D. Cliff and K. Ord. Spatial Processes: Models & Applications. 1981.
  • J. Cuzick and R. Edwards. Spatial clustering for inhomogeneous populations. Journal of the Royal Statistical Society: Series B, 52:73–104, 1990.
  • D. J. Daley and D. Vere-Jones. Introduction to the Theory of Point Processes. Vol 1: Elementary Theory and Methods (second edition). 2003.
  • P. Diaconis and D. Freedman. Prior distributions on spaces of probability measures. The Annals of Statistics, 2:615–629, 1974.
  • P. Diaconis and D. Freedman. De finetti's theorem for markov chains. The Annals of Probability, 8(1):115–130, 1980.
  • P. Diggle, B. Rowlingson, and T. Su. Point process methodology for on-line spatio-temporal disease surveillance. Environmetrics, 16:423–434, 2005.
  • P. J. Diggle. Statistical Analysis of Spatial Point Patterns. 1983.
  • T. S. Ferguson. A bayesian analysis of some nonparametric problems. The Annals of Statistics, 1:209–230, 1973.
  • A. Kottas, J. A. Duan, and A. E. Gelfand. Modeling disease incidence data with spatial and spatio-temporal dirichlet process mixtures. Biometrical Journal, 49:1–14, 2007.
  • A. B. Lawson. Bayesian disease mapping: hierarchical modeling in spatial epidemiology. 2009.
  • G. J. Melville and A. H. Welsh. Line transect sampling in small regions. Biometrics, 4(5):1130–1137, 2001.
  • J. Møller. Shot noise cox processes. Advanced in Applied Probability, 35:614–640, 2003.
  • J. Møller and G. L. Torrisi. Generalised shot noise cox processes. Advances in Applied Probability, 37:48–74, 2005.
  • J. Møller and R. Waagepetersen. Modern statistics for spatial point processes. Scandinavian Journal of Statistics, 34:643– 684, 2007.
  • G. L. W Perry, B. P. Miller, and N. J. Enright. A comparison of methods for the statistical analysis of spatial point patterns in plant ecology. Plant Ecology, 187(1):59–82, 2006.
  • S. L Poggio, E. H. Satorre, and E. B. de la Fuente. Structure of weed communities occuring in pea and wheat crops in the rolling pampa (argentina). Agriculture, Ecosystems and Environment, 103:225–235, 2004.
  • B. D. Ripley. Spatial Statistics. 1981.
  • S. D. Spiegelhalter, N. G. Best, B. P. Carlin, and A. van der Linde. Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B, 4:583–639, 2002.
  • J. Vaillant. Negative binomal distributions of individuals and spatio-temporal cox processes. Scandinavian Journal of Statistics, 18:235–248, 1991.
  • J. Vaillant, Puggioni G. , Waller L. , and Daugrois J. -H. A spatio-temporal analysis of the spread of sugar cane yellow leaf virus. Journal of Time Series Analysis, 32:396–406, 2011.
  • T. Zhang and S. C. Kou. Non parametric inference of doubly stochastic poisson process data via the kernel method. The Annals of Applied Statistics, 4(4):1913–1941, 2010.
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