This book offers essential, systematic information on the assessment of the spatial association between two processes from a statistical standpoint. Divided into eight chapters, the book begins with preliminary concepts, mainly concerning spatial statistics. The following seven chapters focus on the methodologies needed to assess the correlation between two or more processes; from theory introduced 35 years ago, to techniques that have only recently been published. Furthermore, each chapter contains a section on R computations to explore how the methodology works with real data. References and a list of exercises are included at the end of each chapter.

The assessment of the correlation between two spatial processes has been tackled from several different perspectives in a variety of applications fields. In particular, the problem of testing for the existence of spatial association between two georeferenced variables is relevant for posterior modeling and inference. One evident application in this context is the quantification of the spatial correlation between two images (processes defined on a rectangular grid in a two-dimensional space). From a statistical perspective, this problem can be handled via hypothesis testing, or by using extensions of the correlation coefficient. In an image-processing framework, these extensions can also be used to define similarity indices between images.

The analysis and code shown in the book use the R software and most of the methods are implemented by the contributed packages GeoModels and SpatialPack .

Ronny Vallejos is an Associate Professor of Statistics in the Department of Mathematics at Universidad Técnica Federico Santa María. His research focuses largely on spatial statistics, statistical image processing, time series, and robust modeling. He has contributed with multidisciplinary work on the frontier of statistics and ecology, through collaborations with members of the Harvard Forest.

Felipe Osorio is an Assistant Professor in the Department of Mathematics at Universidad Técnica Federico Santa María. His research interests include models for data with longitudinal structure (mixed-effects models, GEE) and diagnostic methods as well as the computational implementation of such techniques.

Moreno Bevilacqua is an Associate Professor at the Faculty of Engineering and Sciences of Universidad Adolfo Ibañez, Viña del Mar, Chile. His main research interests concern theory, methodology and applications in multivariate spatio-temporal statistics. Specifically inference based on likelihood approximations, construction of covariance models and analysis of atmospheric and environmental data.