Stochastic geometry - inhomogeneity, marking, dynamics and stereology

GAČR P201/10/0472 (2010-14)

The team

Faculty of Mathematics and Physics, Charles University in Prague

Staff

• Viktor Beneš
• Jan Rataj
• Lev Klebanov
• Zbyněk Pawlas
• Michaela Prokešová
• Jakub Staněk

External staff

• Petr Král (Institute of Physics of Materials, Academy of Sciences of the Czech Republic, Brno)
• Petr Ponížil (Faculty of Technology, Tomáš Baťa University in Zlín)
• Kateřina Staňková Helisová (Faculty of Electrical Engineering, Czech Technical University in Prague)
• Blažena Kratochvílová (Faculty of Science, Palacký University in Olomouc)
• Radka Lechnerová (Private University College of Economic Studies, Ltd.)

PhD students

• Markéta Zikmundová
• Jiří Dvořák
• Ondřej Šedivý
• Antonín Koubek
• Pavel Kříž

Faculty of Economics, University of South Bohemia

• Tomáš Mrkvička

Publications

Papers in journals

V. Beneš, M. Zikmundová (2014): Functionals of spatial point processes having a density with respect to the Poisson process. Kybernetika 50, 896-913.

D. Dereudre, F. Lavancier, K. Staňková Helisová (2014): Estimation of the intensity parameter of the germ-grain quermass-interaction model when the number of germs is not observed. Scandinavian Journal of Statistics 41, 809-829.

D. Hug, G. Last, Z. Pawlas, W. Weil (2014): Statistics for Poisson models of overlapping spheres, Advances in Applied Probability 46, 937-962.

T. Mrkvička (2014): Checking type of inhomogeneity in Neyman-Scott point processes. Methodology and Computing in Applied Probability 16, 385-395.

T. Mrkvička, M. Muška, J. Kubečka (2014): Two step estimation for Neyman-Scott point process with inhomogeneous cluster centers. Statistics and Computing 24, 91-100.

T. Mrkvička, S. Souberand, A. Pentinnen (2014): Nonstationary cylinder-based model describing group dispersal in fragmented habitat. Stochastic Models 30, 48-67.

Z. Pawlas (2014): Self-crossing points of a line segment process. Methodology and Computing in Applied Probability 16, 295-309.

M. Prokešová, J. Dvořák (2014): Statistics for inhomogeneous space-time shot-noise Cox processes. Methodology and Computing in Applied Probability 16, 433-449.

J. Staněk, O. Šedivý, V. Beneš (2014): On random marked sets with a smaller integer dimension. Methodology and Computing in Applied Probability 16, 397-410.

K. Staňková Helisová, J. Staněk (2014): Dimension reduction in extended quermass-interaction process. Methodology and Computing in Applied Probability 16, 355-368.

O. Šedivý, A. Penttinen (2014): Intensity estimation for inhomogeneous Gibbs point processes with covariate-dependent chemical activity, Statistica Neerlandica 68, 225-249.

M. Zikmundová, K. Staňková Helisová, V. Beneš (2014): On the use of particle Markov chain Monte Carlo in parameter estimation of space-time interacting discs. Methodology and Computing in Applied Probability 16, 451-463.

J. Dvořák, E. B. Vedel-Jensen (2013): On semiautomatic estimation of surface area. Journal of Microscopy 250, 142-157.

L. Heinrich, Z. Pawlas (2013): Absolute regularity and Brillinger-mixing of stationary point processes. Lithuanian Mathematical Journal 53, 293-310.

R. Lechnerová, T. Lechner (2013): Analýza časových řad formální komunikace obcí (in Czech). Information Bulletin of the Czech Statistical Society 24, 63-70.

M. Prokešová, E. B. Vedel-Jensen (2013): Asymptotic Palm likelihood theory for stationary point processes. Annals of the Institute of Statistical Mathematics 65, 387-412.

O. Šedivý, V. Beneš, P. Ponížil, P. Král, V. Sklenička (2013): Quantitative characterization of microstructure of pure copper processed by ECAP. Image Analysis & Stereology 32, 65-75.

O. Šedivý, J. Staněk, B. Kratochvílová, V. Beneš (2013): Sliced inverse regression and independence in random marked sets with covariates. Advances in Applied Probability 45, 626-644.

J. Dvořák, M. Prokešová (2012): Moment estimation methods for stationary spatial Cox processes - a comparison. Kybernetika 48, 1007-1026.

T. Mrkvička, S. Soubeyrand, J. Chadoeuf (2012): Goodness-of-fit test of the mark distribution in a point process with non-stationary marks. Statistics and Computing 22, 931-943.

Z. Pawlas (2012): Local stereology of extremes. Image Analysis & Stereology 31, 99-108.

M. Zikmundová, K. Staňková Helisová, V. Beneš (2012): Spatio-temporal model for a random set given by a union of interacting discs. Methodology and Computing in Applied Probability 14, 883-894.

P. Král, J. Dvořák, M. Kvapilová, M. Svoboda, V. Beneš, P. Ponížil, O. Šedivý, V. Sklenička (2011): Quantitative characterization of microstructure in copper processed by equal-channel angular pressing. Materials Science Forum 667-669, 235-240.

T. Mikosch, Z. Pawlas, G. Samorodnitsky (2011): A large deviation principle for Minkowski sums of heavy-tailed random compact convex sets with finite expectation. In: New Frontiers in Applied Probability. A Festschrift for Søren Asmussen. P. Glynn, T. Mikosch and T. Rolski (eds.). Journal of Applied Probability 48A, 133-144.

T. Mikosch, Z. Pawlas, G. Samorodnitsky (2011): Large deviations for Minkowski sums of heavy-tailed generally non-convex random compact sets. Vestnik Sankt-Peterburgskogo Universiteta, Ser. 1 Matematika Mekhanika Astronomia, issue 2. Spec. issue in honor of V. V. Petrov, 70-78.

T. Mrkvička, F. Goreaud, J. Chadoeuf (2011): Spatial prediction of the mark of a location-dependent marked point process: How the use of a parametric model may improve prediction. Kybernetika 47, 696-714.

T. Mrkvička, T. Mattfeldt (2011): Testing histological images of mammary tissues on compatibility with the Boolean model of random sets. Image Analysis & Stereology 30, 101-108.

Z. Pawlas (2011): Estimation of summary characteristics from replicated spatial point processes. Kybernetika 47, 880-892.

M. Prchalová, T. Mrkvička, J. Peterka, M. Čech, L. Berec, J. Kubečka (2011): A model of gillnet catch to the catchable biomass, saturation, soak time and camping period. Fisheries Research 107, 201-209.

Chapter in a book

V. Beneš, M. Prokešová, K. Staňková Helisová, M. Zikmundová (2015): Space-Time Models in Stochastic Geometry. In: Stochastic Geometry, Spatial Statistics and Random Fields: Models and Algorithms, Lecture Notes in Mathematics 2120. V. Schmidt (ed.). Springer, Heidelberg, Chapter 7, 205-232.

V. Beneš, J. Staněk, B. Kratochvílová, O. Šedivý (2015): Random Marked Sets and Dimension Reduction. In: Stochastic Geometry, Spatial Statistics and Random Fields: Models and Algorithms, Lecture Notes in Mathematics 2120. V. Schmidt (ed.). Springer, Heidelberg, Chapter 6, 171-204.

V. Beneš, L. Klebanov, R. Lechnerová, P. Sláma (2011): Statistical tests based on the geometry of second phase particles. In: Recent Trends in Processing and Degradation of Aluminium Alloys. Z. Ahmad (ed.). InTech, Rijeka, 459-476.

Papers in Conference Proceedings

P. Král, M. Kvapilová, J. Dvořák, P. Ponížil, O. Šedivý, K. Helisová (2014): Quantitative characteristics of inhomogeneous microstructure in UFG copper. In: 6th International Conference on Nanomaterials by Severe Plastic Deformation 63, 012137.

V. Beneš, O. Šedivý (2011): Random marked sets in R^d with integer dimension <d. In: Proceedings of the 13th International Congress for Stereology. Guoquan Liu et al. (eds.). Chinese Society for Stereology, Beijing, electronic document, 4p.

J. Dvořák (2011): On moment estimation methods for spatial Cox processes. In: WDS'11 Proceedings of Contrib. Papers. Part I: Mathem. Comput. Sci. J.Šafránková, J. Pavlů (eds.). Prague, Matfyzpress, 31-36.

O. Šedivý (2011): Dependencies in stochastic geometry - a simulation study. In: WDS'11 Proceedings of Contrib. Papers. Part I: Mathem. Comput. Sci. J.Šafránková, J. Pavlů (eds.). Prague, Matfyzpress, 37-42.

Miscellaneous

J. Dvořák (2014): Statistical inference for spatial and space-time Cox point processes. Ph.D. thesis, Faculty of Mathematics and Physics, Charles University in Prague.

O. Šedivý (2014): Random marked sets and dimension reduction. Ph.D. thesis, Faculty of Mathematics and Physics, Charles University in Prague.

M. Zikmundová (2014): Interacting spatial particle systems. Ph.D. thesis, Faculty of Mathematics and Physics, Charles University in Prague.

Z. Pawlas (2013): Limit theorems for geometric models. Habilitation thesis, Faculty of Mathematics and Physics, Charles University in Prague.

Accepted papers

J. Rataj (2014): Random sets of finite perimeter, Mathematische Nachrichten, Online First, DOI: 10.1002/mana.201300341.

Events

Conferences and workshops

• January 27 - February 1, 2013: Workshop STOCHASTIKA 2013, Kohútka
• June 25-28, 2012: S4G Conference 2012, Prague
• January 31 - February 4, 2011: Workshop STOCHASTIKA 2011, Kohútka
• June 21-24, 2010: Czech Summer School on Stochastic Geometry, Horská Kvilda
  book of abstracts

Seminars

• April 29, 2014: Eva B. Vedel Jensen (University of Aarhus)
  Stereology of tensors - abstract
• April 22, 2014: Michal Matuszak (Nicolaus Copernicus University in Toruń)
  Image segmentation by locally specified multi-coloured polygonal Markov fields
• January 7, 2014: Jean-Francois Coeurjolly (Grenoble)
  Variational approach for spatial point process intensity estimation - abstract
• December 10, 2013: Christian Hirsch (Ulm University)
  A general framework for consistent estimation of charge transport properties via random walks in random environments
• December 3, 2013: Anna-Kaisa Ylitalo (University of Jyväskylä)
  Looking at a painting: a statistical modeling perspective
• November 26, 2013: Stephan Huckemann (University of Göttingen)
  Scale spaces methods for mode estimation with application to stem cell diversification
• October 8, 2013: Dominic Schuhmacher (University of Göttingen)
  Stein's method for Gibbs process approximation - abstract

• November 20, 2012: Markus Kiderlen (University of Aarhus)
  Estimating specific intrinsic volumes of stationary random sets from digital images
• March 20, 2012: Stephan Huckemann (University of Göttingen)
  On Asymptotics of Means of Non-Euclidean Data - abstract
• November 1, 2011: Tilmann Gneiting (University of Heidelberg)
  Making and evaluating point forecasts - abstract
• April 5, 2011: Volker Schmidt (Ulm University)
  Stochastic 3D modeling of tomographic image data - abstract
• February 15, 2011: Ute Hahn (University of Aarhus)
  Studentized permutation test for the comparison of spatial point patterns - abstract
• October 26, 2010: Markus Kiderlen (University of Aarhus)
  Large parallel volume of compact sets and digitized Boolean models - abstract
• October 19, 2010: Thordis L. Thorarinsdottir (University of Heidelberg)
  Model selection for point process models - abstract
• August 3, 2010: Gennady Samorodnitsky (Cornell University)
  Large deviations for point processes based on stationary sequences with heavy tails - abstract

Seminar on stochastic geometry takes place roughly every second Tuesday (from 15.40 to 17.10) throughout the academic year.