# A maximum likelihood estimator of an inhomogeneous Poisson point processes intensity using beta splines

Kybernetika (2000)

- Volume: 36, Issue: 4, page [455]-464
- ISSN: 0023-5954

## Access Full Article

top## Abstract

top## How to cite

topKrejčíř, Pavel. "A maximum likelihood estimator of an inhomogeneous Poisson point processes intensity using beta splines." Kybernetika 36.4 (2000): [455]-464. <http://eudml.org/doc/33495>.

@article{Krejčíř2000,

abstract = {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.},

author = {Krejčíř, Pavel},

journal = {Kybernetika},

keywords = {non-stationary Poisson point process; estimating the intensity; non-stationary Poisson point process; estimating the intensity},

language = {eng},

number = {4},

pages = {[455]-464},

publisher = {Institute of Information Theory and Automation AS CR},

title = {A maximum likelihood estimator of an inhomogeneous Poisson point processes intensity using beta splines},

url = {http://eudml.org/doc/33495},

volume = {36},

year = {2000},

}

TY - JOUR

AU - Krejčíř, Pavel

TI - A maximum likelihood estimator of an inhomogeneous Poisson point processes intensity using beta splines

JO - Kybernetika

PY - 2000

PB - Institute of Information Theory and Automation AS CR

VL - 36

IS - 4

SP - [455]

EP - 464

AB - 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.

LA - eng

KW - non-stationary Poisson point process; estimating the intensity; non-stationary Poisson point process; estimating the intensity

UR - http://eudml.org/doc/33495

ER -

## References

top- 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 (1998)
- Berman M., Turner T. R., 10.2307/2347614, Appl. Statist. 41 (1992), 1, 31–38 (1992) Zbl0825.62614DOI10.2307/2347614
- Daley D. J., Vere–Jones D., An Introduction to the Theory of Point Processes, Springer, New York 1988 Zbl1159.60003MR0950166
- 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 (1998)
- 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 (1999) MR1673118
- 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 (1999)
- Marčuk G. I., Methods of Numerical Mathematics, Academia, Prague 1987 MR0931536
- 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 (1999)
- 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 Zbl1072.62671
- Zeman P., 10.1093/ije/26.5.1121, Internat. J. Epidemiology 26 (1997), 5, 1121–1129 (1997) DOI10.1093/ije/26.5.1121

## NotesEmbed ?

topTo embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.