Stochastic Geometry, Spatial Statistics and Random Fields

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.

Stein’s Method for Approximating Complex Distributions, with a View towards Point Processes.- Clustering Comparison of Point Processes, with Applications to Random Geometric Models.- Random Tessellations and their Application to the Modelling of Cellular Materials.- Stochastic 3D Models for the Micro-structure of Advanced Functional Materials.- Boolean Random Functions.- Random Marked Sets and Dimension Reduction.- Space-Time Models in Stochastic Geometry.- Rotational Integral Geometry and Local Stereology - with a View to Image Analysis.- An Introduction to Functional Data Analysis.- Some Statistical Methods in Genetics.- Extrapolation of Stationary Random Fields.- Spatial Process Simulation.- Introduction to Coupling-from-the-Past using R.- References.- Index.