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This book offers a comprehensive overview of statistical methodology for modelling and evaluating spatial variables useful in a variety of applications. These spatial variables fall into three categories: continuous, like terrain elevation; events, like tree locations; and mosaics, like medical images.
Definitions and discussions of random field models are included for each of these three previously mentioned spatial variable types. Moreover, the readers will have access to algorithms suitable for applying this methodology in practical problem solving, and the computational efficiency of these algorithms are discussed.
The presentation is made in a consistent predictive Bayesian framework, which allows separate modelling of the observation acquisition procedure, as a likelihood model, and of the spatial variable characteristics, as a prior spatial model. The likelihood and prior models uniquely define the posterior spatial model, which provides the basis for spatial simulations, spatial predictions with associated precisions, and model parameter inference. The emphasis is on Bayesian spatial modelling with conjugate pairs of likelihood and prior models that are analytically tractable and hence suitable for data abundant spatial studies. Alternative methods frequently used in spatial statistics are presented using a unified notation.
The book is suitable as a textbook for a 'Spatial Statistics' course at the MSc or PhD level, as it also includes algorithm descriptions, project texts, and exercises.
Henning Omre is currently a Professor Emeritus in Statistics (2022--) at the Department of Mathematical Sciences, Norwegian University of Science and Technology (NTNU), Trondheim, Norway. He is a Norwegian citizen born in 1951, and he received an MSc (Siv.ing) in Statistics from NTNU in 1975, and in 1985, a PhD in Geostatistics from Stanford University, Stanford, California. He was employed at the Norwegian Computing Center (1976--1999) and at NTNU (1992--2021) as a professor of statistics. His major research interests are in spatial and spatio-temporal methodology in statistics, with applications primarily to sub-surface modelling. He has been active in establishing university education in statistics in Ethiopia. He has received several awards for his contributions to statistical methodology and to the statistical community.
Torstein Mæland Fjeldstad is currently a Senior Researcher (2020--) at the Norwegian Computing Center, Oslo, Norway. He is a Norwegian citizen born in 1991 and holds a BSc (2013), MSc (2015), and PhD (2020) in statistics, all from the Norwegian University of Science and Technology (NTNU), Trondheim, Norway. His primary research interests lie in spatial and computational statistics, with a particular emphasis on geostatistical applications. Additionally, he has instructed an undergraduate course in statistics at NTNU.
Ole Bernhard Forberg is currently a data scientist (2021--) at NTE Energy, Trondheim, Norway; an electric power company involved in the production, management, and development of electric power. He keeps in touch with the statistical community by being active in the Norwegian Statistical Association. He is a Norwegian citizen born in 1989. He holds an MSc (2017) and PhD (2021) in statistics, both from the Norwegian University of Science and Technology (NTNU), Trondheim, Norway. His primary fields of interests within statistics lie in spatial and computational statistics, with a particular emphasis on geostatistical applications.
- Introduction.- Bayesian Spatial Modelling.- Conjugate Inversion Models.- Random Fields.- Part I Traditional Conjugate Spatial Models.- Likelihood Models.- Prior Models.- Posterior Models.- Model Parameter Inference.- Computational Challenges.
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