Spatial Relationships Between Two Georeferenced Variables

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.

• Spatial process
• Spatial autocorrelation
• t-test
• Cross-variogram
• Image similarity
• Multivariate hypothesis testing
• Spatial Processes
• Spatial correlation
• Relationships between variables
• Georeferenced variables
• Parametric Testing
• Maximum likelihood
• Coefficients of Spatial Association
• Spatial AR process
• Codispersion map
• Image similarity
• SSIM index
• R applications
• quantitative geology

• Department of Mathematics, Federico Santa María Technical University, Valparaíso, Chile

  Ronny Vallejos, Felipe Osorio

• Faculty of Engineering and Sciences, Universidad Adolfo Ibañez, Viña del Mar, Chile

  Moreno Bevilacqua

Ronny Vallejos is an Associate Professor at the Department of Mathematics, Universidad Técnica Federico Santa María in Valparaíso, Chile. Having previously served as Editor-in-Chief of the Chilean Journal of Statistics, his research interests include spatial statistics, robust modeling, time series and statistical image processing.

Felipe Osorio is an Assistant Professor at the Department of Mathematics, Universidad Técnica Federico Santa María, Chile. His research interests include models for data with longitudinal structures (mixed-effects models, GEE) and diagnostic methods, as well as the computational implementation of such techniques. He has created several packages for the R statistical environment.

Moreno Bevilacqua Moreno Bevilacqua is an Associate Professor at the Faculty of Engineering and Sciences of Universidad Adolfo Ibañez, Viña del Mar, Chile. His research interests include spatial random fields, covariance functions, non-Gaussian spatial processes and computational methods. He is the creator and developer of the R package GeoModels.

Policies and ethics