A method of modelling log Gaussian Cox processes
Authors:
Yu. V. Kozachenko and O. O. Pogorilyak
Translated by:
Oleg Klesov
Journal:
Theor. Probability and Math. Statist. 77 (2008), 91-105
MSC (2000):
Primary 68U20; Secondary 60G10
DOI:
https://doi.org/10.1090/S0094-9000-09-00749-2
Published electronically:
January 16, 2009
MathSciNet review:
2432774
Full-text PDF Free Access
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Additional Information
Abstract: We consider a method for constructing models of log Gaussian Cox processes with random intensity. Namely, we consider Cox processes whose intensities are generated by a log Gaussian process. The models are constructed with a given accuracy and reliability.
References
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- Yu. V. Kozachenko and O. O. Pogorīlyak, Modeling logarithmic Gaussian Cox processes with given reliability and accuracy, Teor. Ĭmovīr. Mat. Stat. 76 (2007), 70–83 (Ukrainian, with Ukrainian summary); English transl., Theory Probab. Math. Statist. 76 (2008), 77–91. MR 2368741, DOI https://doi.org/10.1090/S0094-9000-08-00733-3
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References
- P. J. Diggle, Statistical Analysis of Spatial Point Patterns, Academic Press, London, 1983. MR 743593 (85m:62205)
- N. Cressie, Statistics for Spatial Data, Wiley, New York, 1991. MR 1127423 (92k:62166)
- J. Møller, A. R. Syversveen, and R. P. Waagepetersen, Log Gaussian Cox processes, Scand. J. Statist. 25 (1998), no. 4, 451–482. MR 1650019 (2000k:62156)
- J. Møller and R. P. Waagepetersen, Statistical Inference and Simulation for Spatial Point Processes, Chapman & Hall/CRC, Boca Raton, FL, 2004. MR 2004226 (2004h:62003)
- J. Møller, Spatial Statistics and Computational Methods, Springer-Verlag, New York, 2003. MR 2001383 (2004f:62012)
- O. O. Pogorilyak, Modeling log Gaussian Cox processes, Visnyk Kyiv Taras Shevchenko National University, Ser. Matem. Mekh. 2006, no. 15–16, 94–100. (Ukrainian)
- Yu. V. Kozachenko and O. O. Pogorilyak, Modeling log Gaussian Cox processes with given reliability and accuracy, Teor. Ĭmovir. Matem. Statyst. 76 (2007), 70–83; English transl. in Theory Probab. Math. Statist. 76 (2008), 77–91. MR 2368741
- Yu. V. Kozachenko and O. O. Pogorilyak, Modeling log Cox processes governed by a random field, Dopovidi NAN Ukrainy 2006, no. 10, 20–23. (Ukrainian)
- V. V. Buldygin and Yu. V. Kozachenko, Metric Characterization of Random Variables and Random Processes, Amer. Math. Soc., Providence, Rhode Island, 2000. MR 1743716 (2001g:60089)
- H. Cramér and M. R. Leadbetter, Stationary and Related Stochastic Processes. Sample Function Properties and their Applications, John Wiley & Sons, New York–London–Sydney, 1967. MR 0217860 (36:949)
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Additional Information
Yu. V. Kozachenko
Affiliation:
Department of Probability Theory and Mathematical Statistics, Faculty for Mechanics and Mathematics, National Taras Shevchenko University, Academician Glushkov Avenue 6, Kyiv 03127, Ukraine
Email:
yvk@univ.kiev.ua
O. O. Pogorilyak
Affiliation:
Department of Probability Theory and Mathematical Statistics, Faculty for Mechanics and Mathematics, National Taras Shevchenko University, Academician Glushkov Avenue 6, Kyiv 03127, Ukraine
Email:
alex_pogorilyak@ukr.net
Keywords:
Log Gaussian Cox processes,
random intensity,
models of stochastic processes,
accuracy,
reliability
Received by editor(s):
December 26, 2006
Published electronically:
January 16, 2009
Article copyright:
© Copyright 2009
American Mathematical Society
