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Stochastic Geometry, Spatial Statistics and Random Fields

Models and Algorithms

  • Book
  • © 2015

Overview

Editors:
  1. Volker Schmidt

    1. Institute of Stochastic, Ulm University, Ulm, Germany

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  • Frontier theoretical work on point processes, random fields and integral geometry
  • Extensive applications in materials science, biology and genetics
  • Extensive codes in Matlab and R that help the reader with applications
  • Many examples help the reader to deepen their understanding

Part of the book series: Lecture Notes in Mathematics (LNM, volume 2120)

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Table of contents (13 chapters)

  1. Front Matter

    Pages i-xxiv
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  2. Stein’s Method for Approximating Complex Distributions, with a View towards Point Processes

    • Dominic Schuhmacher
    Pages 1-30

  3. Clustering Comparison of Point Processes, with Applications to Random Geometric Models

    • BartÅ‚omiej BÅ‚aszczyszyn, Dhandapani Yogeshwaran
    Pages 31-71

  4. Random Tessellations and their Application to the Modelling of Cellular Materials

    • Claudia Redenbach, André Liebscher
    Pages 73-93

  5. Stochastic 3D Models for the Micro-structure of Advanced Functional Materials

    • Volker Schmidt, Gerd Gaiselmann, Ole Stenzel
    Pages 95-141

  6. Boolean Random Functions

    • Dominique Jeulin
    Pages 143-169

  7. Random Marked Sets and Dimension Reduction

    • Viktor BeneÅ¡, Jakub StanÄ•k, Blažena Kratochvílová, OndÅ™ej Å edivý
    Pages 171-203

  8. Space-Time Models in Stochastic Geometry

    • Viktor BeneÅ¡, Michaela ProkeÅ¡ová, KateÅ™ina Staňková Helisová, Markéta Zikmundová
    Pages 205-232

  9. Rotational Integral Geometry and Local Stereology - with a View to Image Analysis

    • Eva B. Vedel Jensen, Allan Rasmusson
    Pages 233-255

  10. An Introduction to Functional Data Analysis

    • Ulrich Stadtmüller, Marta Zampiceni
    Pages 257-292

  11. Some Statistical Methods in Genetics

    • Alexander Bulinski
    Pages 293-320

  12. Extrapolation of Stationary Random Fields

    • Evgeny Spodarev, Elena Shmileva, Stefan Roth
    Pages 321-368

  13. Spatial Process Simulation

    • Dirk P. Kroese, Zdravko I. Botev
    Pages 369-404

  14. Introduction to Coupling-from-the-Past using R

    • Wilfrid S. Kendall
    Pages 405-439

  15. Back Matter

    Pages 441-466
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Keywords

About this book

This volume is an attempt to provide a graduate level introduction to various aspects of stochastic geometry, spatial statistics and random fields, with special emphasis placed on fundamental classes of models and algorithms as well as on their applications, e.g. in materials science, biology and genetics. This book has a strong focus on simulations and includes extensive codes in Matlab and R which are widely used in the mathematical community. It can be seen as a continuation of the recent volume 2068 of Lecture Notes in Mathematics, where other issues of stochastic geometry, spatial statistics and random fields were considered with a focus on asymptotic methods.

Editors and Affiliations

  • Institute of Stochastic, Ulm University, Ulm, Germany

    Volker Schmidt

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