This book arises as the natural continuation of the International Spring School "Advances and Challenges in Space-Time modelling of Natural Events," which took place in Toledo (Spain) in March 2010. This Spring School above all focused on young researchers (Master students, PhD students and post-doctoral researchers) in academics, extra-university research and the industry who are interested in learning about recent developments, new methods and applications in spatial statistics and related areas, and in exchanging ideas and findings with colleagues.

Autorentext

Michael Stein is a Professor at the University of Chicago's Department of Statistics. His research interests center on statistical methodology and probability theory, with applications in atmospheric, environmental and geophysical sciences, and on economics, among other disciplines.

Martin Schlather is a Professor at the Institut für Mathematische Stochastik, University of Göttingen, Germany. He has worked on extreme value theory of random fields, random sets and space-time covariance functions, and has published several papers in these fields, all in respected journals such as the Journal of the Royal Statistical Society and Annals of Probability.

Werner Müller is a Professor at the University of Linz. He has done considerable work on spatial design; the majority of the literature coming from this crucial field can essentially be found in his papers. He wrote an excellent book on spatial design which is a reference work in the field.

Marc Genton is a Professor at the Texas A&M. He has done considerable work in several branches of geostatistics, including robust variograms, testing for separability, and nonseparable covariance functions. He is highly experienced in elliptical distributions and skewed normal distributions and has published a book on this subject. He has published more than one hundred papers refereed in international journals. His website is http : //www.stat.tamu.edu/ genton/

Hao Zhang is a Professor at Purdue University. He has done considerable work in the field of geostatistics, equivalence of Gaussian measures and tapering of the covariance function.

Denis Allard is Directeur de Recherche, Directeur de l'unite of the INRA Unite Biostatistiques et Processus Spatiaux. He completed his PhD studies and thesis at the celebrated Ecole des Mines de Paris, centre de Geostatistique, where the discipline of Geostatistics was basically born thanks to theseminal work of George Matheron. He has worked on geostatistical estimation, random sets, detection of abrupt changes and image detection and has considerable international experience in both applied and theoretical projects.

Emilio Porcu is a research fellow at the Universidad de Castilla la Mancha and the University of Göttingen. His main research interest is in positive definite functions and conditionally negative definite ones, with application to space-time data. He has dedicated part of his research to the more theoretical setting of completely monotone functions and the Thorin class of Laplace transforms. He has published more than 30 papers in JCR journals.

Maria Dolores Ruiz Medina is a Professor at the University of Granada. She has published a considerable number of outstanding papers on fractal, long memory, generalized random fields, and wavelet estimation of random fields. She is a recognized scientist in the mathematics, statistics and applied branches of science, where she is considered a trusted expert, such as in genetics.

Finn Lindgren is a Professor at Lund University, Sweden. He obtained his PhD in Mathematical Statistics at the Centre for Mathematical Sciences at Lund University. His main research interests are Bayesian image analysis and shape modelling, their use in particular deformable models, and modelling of spatial processes using Markov random fields, with applications in geostatistics and climate modelling.

Thordis Linda Thorarinsdottir is a Research fellow at Heidelberg University's Department of Mathematics. Her research interest is in space-time point processes and probabilistic forecasts. She collaborates with Peter Guttorp, Eva Jensen and Tilmann Gneiting, among other well known scientists.

Inhalt
Introduction to the Book: Space-Time Random Fields by J.M. Montero, E. Porcu, M. Schlather and G. Fernández-Avilés.- Random Fields Defined on Hilbert Spaces by Hao Zhang.- Some Problems Relating Isotropic Covariance Functions by Michael L. Stein and Emilio Porcu.- Multivariate Random Fields and Robustness in Spatial Statistics by Marc G. Genton.- Spatial and Space-Time Extreme Value Theory for Random Fields by Martin Schlather.- Space-Time Second Order Properties of Random Fields by Emilio Porcu, J.Maria Montero and Gema Fernández-Avilés.- Gaussian Markov Random Fields by Finn Lindgren.- A Journey through non Gaussian Random Fields by Denis Allard.- Space-Time Design for Gaussian Random Fields by Werner Müller.- Simulation of Stochastic Processes and Inference by Maria Dolores Ruiz Medina.- Space Time Point Processes by Thordis Thorarinsdottir.