Quermass-interaction process with convex compact grains

Kateřina Helisová; Jakub Staněk

Applications of Mathematics (2016)

  • Volume: 61, Issue: 4, page 463-487
  • ISSN: 0862-7940

Abstract

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The paper concerns an extension of random disc Quermass-interaction process, i.e. the model of discs with mutual interactions, to the process of interacting objects of more general shapes. Based on the results for the random disc process and the process with polygonal grains, theoretical results for the generalized process are derived. Further, a simulation method, its advantages and the corresponding complications are described, and some examples are introduced. Finally, a short comparison to the random disc process is given.

How to cite

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Helisová, Kateřina, and Staněk, Jakub. "Quermass-interaction process with convex compact grains." Applications of Mathematics 61.4 (2016): 463-487. <http://eudml.org/doc/283402>.

@article{Helisová2016,
abstract = {The paper concerns an extension of random disc Quermass-interaction process, i.e. the model of discs with mutual interactions, to the process of interacting objects of more general shapes. Based on the results for the random disc process and the process with polygonal grains, theoretical results for the generalized process are derived. Further, a simulation method, its advantages and the corresponding complications are described, and some examples are introduced. Finally, a short comparison to the random disc process is given.},
author = {Helisová, Kateřina, Staněk, Jakub},
journal = {Applications of Mathematics},
keywords = {attractiveness; germ-grain model; Markov Chain Monte Carlo simulation; Quermass-interaction process; random set; repulsiveness; Ruelle stability; attractiveness; germ-grain model; Markov Chain Monte Carlo simulation; Quermass-interaction process; random set; repulsiveness; Ruelle stability},
language = {eng},
number = {4},
pages = {463-487},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Quermass-interaction process with convex compact grains},
url = {http://eudml.org/doc/283402},
volume = {61},
year = {2016},
}

TY - JOUR
AU - Helisová, Kateřina
AU - Staněk, Jakub
TI - Quermass-interaction process with convex compact grains
JO - Applications of Mathematics
PY - 2016
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 61
IS - 4
SP - 463
EP - 487
AB - The paper concerns an extension of random disc Quermass-interaction process, i.e. the model of discs with mutual interactions, to the process of interacting objects of more general shapes. Based on the results for the random disc process and the process with polygonal grains, theoretical results for the generalized process are derived. Further, a simulation method, its advantages and the corresponding complications are described, and some examples are introduced. Finally, a short comparison to the random disc process is given.
LA - eng
KW - attractiveness; germ-grain model; Markov Chain Monte Carlo simulation; Quermass-interaction process; random set; repulsiveness; Ruelle stability; attractiveness; germ-grain model; Markov Chain Monte Carlo simulation; Quermass-interaction process; random set; repulsiveness; Ruelle stability
UR - http://eudml.org/doc/283402
ER -

References

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  1. Altendorf, H., Latourte, F., Jeulin, D., Faessel, M., Saintyant, L., 10.5566/ias.v33.p121-130, Image Anal. Stereol. 33 (2014), 121-130. (2014) DOI10.5566/ias.v33.p121-130
  2. Chiu, S. N., Stoyan, D., Kendall, W. S., Mecke, J., Stochastic Geometry and Its Applications, Wiley Series in Probability and Statistics John Wiley & Sons, Chichester (2013). (2013) Zbl1291.60005MR3236788
  3. Dereudre, D., 10.1017/S0001867800003517, Adv. Appl. Probab. 41 (2009), 664-681. (2009) MR2571312DOI10.1017/S0001867800003517
  4. Dereudre, D., Lavancier, F., Helisová, K. Staňková, 10.1111/sjos.12064, Scand. J. Stat. 41 (2014), 809-829. (2014) MR3249430DOI10.1111/sjos.12064
  5. Diggle, P. J., 10.2307/2530566, Biometrics 37 (1981), 531-539. (1981) DOI10.2307/2530566
  6. Geyer, C. J., Møller, J., Simulation procedures and likelihood inference for spatial point processes, Scand. J. Stat. 21 (1994), 359-373. (1994) Zbl0809.62089MR1310082
  7. Helisová, K., Modeling, statistical analyses and simulations of random items and behavior on material surfaces, Supplemental UE: TMS 2014 Conference Proceedings, San Diego (2014), 461-468. (2014) 
  8. Hermann, P., Mrkvička, T., Mattfeldt, T., Minárová, M., Helisová, K., Nicolis, O., Wartner, F., Stehlík, M., 10.1002/sim.6497, Stat. Med. 34 (2015), 2636-2661. (2015) MR3368407DOI10.1002/sim.6497
  9. Kendall, W. S., Lieshout, M. N. M. van, Baddeley, A. J., 10.1017/S0001867800009137, Adv. Appl. Probab. 31 (1999), 315-342. (1999) MR1724554DOI10.1017/S0001867800009137
  10. Klazar, M., Generalised Davenport-Schinzel sequences: results, problems and applications, Integers: The Electronic Journal of Combinatorial Number Theory 2 (2002), A11. (2002) MR1917956
  11. Molchanov, I., Theory of Random Sets, Probability and Its Applications Springer, London (2005). (2005) Zbl1109.60001MR2132405
  12. Møller, J., Helisová, K., 10.1017/S0001867800002548, Adv. Appl. Probab. 40 (2008), 321-347. (2008) Zbl1146.60322MR2431299DOI10.1017/S0001867800002548
  13. Møller, J., Helisová, K., 10.1111/j.1467-9469.2009.00660.x, Scand. J. Stat. 37 (2010), 365-381. (2010) Zbl1226.60016MR2724503DOI10.1111/j.1467-9469.2009.00660.x
  14. Møller, J., Waagepetersen, R. P., Statistical Inference and Simulation for Spatial Point Processes, Monographs on Statistics and Applied Probability 100 Chapman and Hall/CRC, Boca Raton (2004). (2004) Zbl1044.62101MR2004226
  15. Mrkvička, T., Mattfeldt, T., 10.5566/ias.v30.p11-18, Image Anal. Stereol. 30 (2011), 11-18. (2011) MR2816303DOI10.5566/ias.v30.p11-18
  16. Mrkvička, T., Rataj, J., On the estimation of intrinsic volume densities of stationary random closed sets, Stochastic Processes Appl. 118 (2008), 213-231. (2008) Zbl1148.62023MR2376900
  17. Ohser, J., Mücklich, F., Statistical Analysis of Microstructures in Materials Science, Wiley Series in Statistics in Practice Wiley, Chichester (2000). (2000) 
  18. Pratt, W. K., Digital Image Processing, Wiley & Sons, New York (2001). (2001) 
  19. Team, R Development Core, R: A language and environment for statistical computing, R Found Stat Comp, Vienna. http://www.R-project.org/ (2010). (2010) 
  20. Helisová, K. Staňková, Staněk, J., 10.1007/s11009-013-9343-x, Methodol. Comput. Appl. Probab. 16 (2014), 355-368. (2014) MR3199051DOI10.1007/s11009-013-9343-x
  21. Zikmundová, M., Helisová, K. Staňková, Beneš, V., 10.1007/s11009-012-9287-6, Methodol. Comput. Appl. Probab. 14 (2012), 883-894. (2012) MR2966326DOI10.1007/s11009-012-9287-6
  22. Zikmundová, M., Helisová, K. Staňková, Beneš, V., 10.1007/s11009-013-9367-2, Methodol. Comput. Appl. Probab. 16 (2014), 451-463. (2014) MR3199057DOI10.1007/s11009-013-9367-2

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