Spatial statistics is concerned with statistical analysis of data collected over a spatial region, possibly including the study of a development over time. Research in spatial statistics mainly deals with geostatistics, lattice processes, and spatial point processes. The focus in geostatistics is modelling of spatial correlation and prediction for variables at a continuum of spatial sites. Lattice processes are models for variables at a discrete set of spatial sites, where Markov random fields play a particular role. Spatial point processes are models for random collections of spatial sites, where Poisson, Cox and Gibbs point process models are of main importance. Statistical analysis for spatial data is a complex task which is often carried out using computational statistical methods.
The modern field of "Computational Statistics'' is concerned with statistical methodologies where intensive computing is an integral component. Computational statistics plays an important role in spatial statistics where Monte Carlo methods are often a prerequisite for implementation of likelihood-based inference. Evaluation of posteriors in Bayesian analysis for complex statistical models is a major challenge. Often it is only possible using the iterative simulation technique of Markov chain Monte Carlo (MCMC). An alternative in relation to Markov models is message passing algorithms. The field of computational statistics is a very active field where current hot research topics include adaptive MCMC strategies, particle filtering, and perfect simulation.
Members of this group and their research interests:
Jesper Møller, Jakob G. Rasmussen, Ege Rubak and Rasmus Waagepetersen have a general interest in statistical methodology for spatial and spatio-temporal processes exhibiting interaction. They have also contributed with computational methods for Bayesian and frequentist-based inference for spatial processes, as well as methodological and applied aspects of various general MCMC algorithms. They are often working with problems related to agricultural research, archaeology, computer science, communication technology, plant and animal ecology, medical image analysis and physics. They are associated to The Center for Stochastic Geometry and Advanced Bioimaging. They are at the forefront in the spatial and computational statistics community, and collaborate with the very leading experts in these fields. Poul Svante Eriksen has a primary interest in message passing algorithms.
Jesper Møller and Rasmus Waagepetersen are the authors of the monograph "Statistical inference and simulation for spatial point processes" and Jesper Møller is the editor of the volume "Spatial and computational statistics".