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  • Book
  • © 2020

Spatial Relationships Between Two Georeferenced Variables

With Applications in R

Authors:

(view affiliations)
  • Provides theoretical background on spatial statistics

  • Addresses methodological aspects and applications in R

  • Brings together 35 years of research including image similarity

  • Useful for spatial statistics practitioners and researchers alike

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eBook
USD 109.00
Price excludes VAT (USA)
  • ISBN: 978-3-030-56681-4
  • Instant PDF download
  • Readable on all devices
  • Own it forever
  • Exclusive offer for individuals only
  • Tax calculation will be finalised during checkout
Softcover Book
USD 149.99
Price excludes VAT (USA)
Hardcover Book
USD 149.99
Price excludes VAT (USA)

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Table of contents (8 chapters)

  1. Front Matter

    Pages i-xii
  2. Introduction

    • Ronny Vallejos, Felipe Osorio, Moreno Bevilacqua
    Pages 1-25
  3. The Modified t Test

    • Ronny Vallejos, Felipe Osorio, Moreno Bevilacqua
    Pages 27-45
  4. A Parametric Test Based on Maximum Likelihood

    • Ronny Vallejos, Felipe Osorio, Moreno Bevilacqua
    Pages 47-68
  5. Tjøstheim’s Coefficient

    • Ronny Vallejos, Felipe Osorio, Moreno Bevilacqua
    Pages 69-78
  6. The Codispersion Coefficient

    • Ronny Vallejos, Felipe Osorio, Moreno Bevilacqua
    Pages 79-114
  7. A Nonparametric Coefficient

    • Ronny Vallejos, Felipe Osorio, Moreno Bevilacqua
    Pages 115-130
  8. Association for More Than Two Processes

    • Ronny Vallejos, Felipe Osorio, Moreno Bevilacqua
    Pages 131-144
  9. Spatial Association Between Images

    • Ronny Vallejos, Felipe Osorio, Moreno Bevilacqua
    Pages 145-165
  10. Back Matter

    Pages 167-194

About this book

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.

 

Keywords

  • 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

Authors and Affiliations

  • 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

About the authors

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.

Bibliographic Information

Buying options

eBook
USD 109.00
Price excludes VAT (USA)
  • ISBN: 978-3-030-56681-4
  • Instant PDF download
  • Readable on all devices
  • Own it forever
  • Exclusive offer for individuals only
  • Tax calculation will be finalised during checkout
Softcover Book
USD 149.99
Price excludes VAT (USA)
Hardcover Book
USD 149.99
Price excludes VAT (USA)