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Keywords:
non-stationary Poisson point process; estimating the intensity
non-stationary Poisson point process; estimating the intensity
Summary:
The problem of estimating the intensity of a non-stationary Poisson point process arises in many applications. Besides non parametric solutions, e. g. kernel estimators, parametric methods based on maximum likelihood estimation are of interest. In the present paper we have developed an approach in which the parametric function is represented by two-dimensional beta-splines.
References:
[1] Baddeley A., Turner R.: Practical Maximum Pseudolikelihood for Spatial Point Patterns. Research Report No. 1998/16, Department of Mathematics and Statistics, University of Western Australia 1998
[2] Berman M., Turner T. R.: Approximating point process likelihoods with glim. Appl. Statist. 41 (1992), 1, 31–38 DOI 10.2307/2347614 | Zbl 0825.62614
[3] Daley D. J., Vere–Jones D.: An Introduction to the Theory of Point Processes. Springer, New York 1988 MR 0950166 | Zbl 1159.60003
[4] Daniel M., Kolář J., Zeman P., Pavelka K., Sádlo J.: Prediction of sites of enhanced risk of tick Ixodes ricinus attack and developping tick-borne encephalitis in Central Bohemia using satelite data. Epidemiol. Mikrobiol. Imunol. 47 (1998), 1, 3–11
[5] Geyer C. J.: Likelihood inference for spatial point processes. In: Stochastic Geometry, Likelihood and Computation (O. E. Barndorff–Nielsen et al, eds.), Chapman and Hall, London 1999, pp. 79–140 MR 1673118
[6] Machek J.: On statistical models for the mapping of disease-risk. In: International Conference on Stereology, Spatial Statistics and Stochastic Geometry (V. Beneš, J. Janáček and I. Saxl, eds.), Union of the Czech Mathematicians and Physicists, Prague 1999, pp. 191–196
[7] Marčuk G. I.: Methods of Numerical Mathematics. Academia, Prague 1987 MR 0931536
[8] Mašata M.: Assessment of risk infection by means of a bayesian method. In: International Conference on Stereology, Spatial Statistics and Stochastic Geometry (V. Beneš, J. Janáček and I. Saxl, eds.), Union of the Czech Mathematicians and Physicists, Prague 1999, pp. 197–202
[9] Stern S. H., Cressie N.: Inference for extremes in disease mapping. In: Methods of Disease Mapping and Risk Assesment for Public Health Decision Making (A. Lawson et al, eds.), Wiley, New York 1999 Zbl 1072.62671
[10] Zeman P.: Objective assesment of risk maps of tick-borne encephalitis and lyme borreliosis based on spatial patterns of located cases. Internat. J. Epidemiology 26 (1997), 5, 1121–1129 DOI 10.1093/ije/26.5.1121
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