Jesper Moller - Böcker

Spatial statistics and Markov Chain Monte Carlo (MCMC) techniques have each undergone major developments in the last decade. Also, these two areas are mutually reinforcing, because MCMC methods are often necessary for the practical implementation of spatial statistical inference, while new spatial stochastic models in turn motivate the development of improved MCMC algorithms. This volume shows how sophisticated spatial statistical and computational methods apply to a range of problems of increasing importance for applications in science and technology. It consists of four chapters: 1. Petros Dellaportas and Gareth O. Roberts give a tutorial on MCMC methods, the computational methodology which is essential for virtually all the complex spatial models to be considered in subsequent chapters. 2. Peter J. Diggle, Paulo J, Ribeiro Jr., and Ole F. Christensen introduce the reader to the model- based approach to geostatistics, i.e. the application of general statistical principles to the formulation of explicit stochastic models for geostatistical data, and to inference within a declared class of models. 3. Merrilee A. Hurn, Oddvar K. Husby, and H?vard Rue discuss various aspects of image analysis, ranging from low to high level tasks, and illustrated with different examples of applications. 4. Jesper Moller and Rasmus P. Waggepetersen collect recent theoretical advances in simulation-based inference for spatial point processes, and discuss some examples of applications. The volume introduces topics of current interest in spatial and computational statistics, which should be accessible to postgraduate students as well as to experienced statistical researchers. It is partly based on the course material for the "TMR and MaPhySto Summer School on Spatial Statistics and Computational Methods," held at Aalborg University, Denmark, August 19-22, 2001.

Tessellations are subdivisions of d-dimensional space into non-overlapping "cells". Voronoi tessellations are produced by first considering a set of points (known as nuclei) in d-space, and then defining cells as the set of points which are closest to each nuclei. A random Voronoi tessellation is produced by supposing that the location of each nuclei is determined by some random process. They provide models for many natural phenomena as diverse as the growth of crystals, the territories of animals, the development of regional market areas, and in subjects such as computational geometry and astrophysics. This volume provides an introduction to random Voronoi tessellations by presenting a survey of the main known results and the directions in which research is proceeding. Throughout the volume, mathematical and rigorous proofs are given making this essentially a self-contained account in which no background knowledge of the subject is assumed.