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.

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

Autorentext
Prof. Dr. Volker Schmidt lehrt seit 1988 an der Hochschule für Finanzen in Hamburg, deren Leiter er gegenwärtig auch ist. Seine Professur hat ihren Schwerpunkt im Umsatzsteuerrecht, zu dem er zahlreiche Beiträge verfasst hat. Neben seiner Lehrtätigkeit in der Ausbildung für den gehobenen Dienst der Finanzverwaltung ist Prof. Dr. Schmidt seit vielen Jahren als Dozent in Kursen zur Vorbereitung auf die Steuerberaterprüfung tätig. Er ist darüber hinaus Referent auf unterschiedlichen Fortbildungsveranstaltungen zum Steuerrecht.

Klappentext

Providing a graduate level introduction to various aspects of stochastic geometry, spatial statistics and random fields, this volume places a special emphasis on fundamental classes of models and algorithms as well as on their applications, for example 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 regarded 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.

Inhalt

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.