Stochastic Geometry, Spatial Statistics and Random Fields: Models and AlgorithmsVolker Schmidt 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. |
Contents
| 1 | |
Chapter 2 Clustering Comparison of Point Processes with Applications to Random Geometric Models | 31 |
Chapter 3 Random Tessellations and their Application to the Modelling of Cellular Materials | 73 |
Chapter 4 Stochastic 3D Models for the Microstructure of Advanced Functional Materials | 95 |
Chapter 5 Boolean Random Functions | 143 |
Chapter 6 Random Marked Sets and Dimension Reduction | 171 |
Chapter 7 SpaceTime Models in Stochastic Geometry | 205 |
Chapter 8 Rotational Integral Geometry and Local Stereology with a View to Image Analysis | 233 |
Chapter 9 An Introduction to Functional Data Analysis | 257 |
Chapter 10 Some Statistical Methods in Genetics | 293 |
Chapter 11 Extrapolation of Stationary Random Fields | 321 |
Chapter 12 Spatial Process Simulation | 369 |
Chapter 13 Introduction to CouplingfromthePast using | 405 |
| 441 | |
| 459 | |
Other editions - View all
Stochastic Geometry, Spatial Statistics and Random Fields: Models and Algorithms Volker Schmidt No preview available - 2014 |
Stochastic Geometry, Spatial Statistics and Random Fields: Models and Algorithms Volker Schmidt No preview available - 2014 |
Common terms and phrases
algorithm analysis approximation Boolean Borel sets CFTP characteristics cluster compute consider convex corresponding covariance function Cox point Cox point processes Cox process defined Definition denotes density distribution edge estimator example fibers finite Gaussian random field germ-grain model given graph independent innovations integral intensity function intensity measure intrinsic volumes isotropic K-function kriging lattice Lemma Lévy process linear Markov chain Matérn matrix mean method morphology Note obtained parameters percolation point patterns Poisson point process Poisson process predictor properties radius random function random measure random set random tessellation random variables random vector random walk realization regression rotational sample Sect simulated annealing space space-time stochastic geometry stochastic model stochastic process sub-Poisson point processes super-Poisson Theorem tion values variogram void probabilities voxels Wiener process