In Spatial Analysis, two distinguished authors deliver a practical and insightful exploration of the statistical investigation of the interdependence of random variables as a function of their spatial proximity. The book expertly blends theory and application, offering numerous worked examples and exercises at the end of each chapter.

Increasingly relevant to fields as diverse as epidemiology, geography, geology, image analysis, and machine learning, spatial statistics is becoming more important to a wide range of specialists and professionals. The book includes:

Thorough introduction to stationary random fields, intrinsic and generalized random fields, and stochastic models
Comprehensive exploration of the estimation of spatial structure
Practical discussion of kriging and the spatial linear model Spatial Analysis is an invaluable resource for advanced undergraduate and postgraduate students in statistics, data science, digital imaging, geostatistics, and agriculture. It's also an accessible reference for professionals who are required to use spatial models in their work.

John T. Kent is a Professor in the Department of Statistics at the University of Leeds, UK. He began his career as a research fellow at Sidney Sussex College, Cambridge before moving to the University of Leeds. He has published extensively on various aspects of statistics, including infinite divisibility, directional data analysis, multivariate analysis, inference, robustness, shape analysis, image analysis, spatial statistics, and spatial-temporal modelling.

Kanti V. Mardia is a Senior Research Professor and Leverhulme Emeritus Fellow in the Department of Statistics at the University of Leeds, and a Visiting Professor at the University of Oxford. During his career he has received many prestigious honours, including in 2003 the Guy Medal in Silver from the Royal Statistical Society, and in 2013 the Wilks memorial medal from the American Statistical Society. His research interests include bioinformatics, directional statistics, geosciences, image analysis, multivariate analysis, shape analysis, spatial statistics, and ??spatial-temporal modelling.

Kent and Mardia are also joint authors of a well-established monograph on Multivariate Analysis.

SPATIAL ANALYSIS

Explore the foundations and latest developments in spatial statistical analysis

In Spatial Analysis, two distinguished authors deliver a practical and insightful exploration of the statistical investigation of the interdependence of random variables as a function of their spatial proximity. The book expertly blends theory and application, offering numerous worked examples and exercises at the end of each chapter.

Thorough introduction to stationary random fields, intrinsic and generalized random fields, and stochastic models
Comprehensive exploration of the estimation of spatial structure
Practical discussion of kriging and the spatial linear model

Spatial Analysis is an invaluable resource for advanced undergraduate and postgraduate students in statistics, data science, digital imaging, geostatistics, and agriculture. It's also an accessible reference for professionals who are required to use spatial models in their work.

Autorentext

John T. Kent is a Professor in the Department of Statistics at the University of Leeds, UK. He began his career as a research fellow at Sidney Sussex College, Cambridge before moving to the University of Leeds. He has published extensively on various aspects of statistics, including infinite divisibility, directional data analysis, multivariate analysis, inference, robustness, shape analysis, image analysis, spatial statistics, and spatial-temporal modelling.

Kanti V. Mardia is a Senior Research Professor and Leverhulme Emeritus Fellow in the Department of Statistics at the University of Leeds, and a Visiting Professor at the University of Oxford. During his career he has received many prestigious honours, including in 2003 the Guy Medal in Silver from the Royal Statistical Society, and in 2013 the Wilks memorial medal from the American Statistical Society. His research interests include bioinformatics, directional statistics, geosciences, image analysis, multivariate analysis, shape analysis, spatial statistics, and spatial-temporal modelling.
Kent and Mardia are also joint authors of a well-established monograph on Multivariate Analysis.

Leseprobe
Preface

Spatial statistics is concerned with data collected at various spatial locations or sites, typically in a Euclidean space . The important cases in practice are , corresponding to the data on the line, in the plane, or in 3-space, respectively. A common property of spatial data is "spatial continuity," which means that measurements at nearby locations will tend to be more similar than measurements at distant locations. Spatial continuity can be modeled statistically using a covariance function of a stochastic process for which observations at nearby sites are more highly correlated than at distant sites. A stochastic process in space is also known as a random field.

One distinctive feature of spatial statistics, and related areas such as time series, is that there is typically just one realization of the stochastic process to analyze. Other branches of statistics often involve the analysis of independent replications of data.

The purpose of this book is to develop the statistical tools to analyze spatial data. The main emphasis in the book is on Gaussian processes. Here is a brief summary of the contents. A list of Notation and Terminology is given at the start for ease of reference. An introduction to the overall objectives of spatial analysis, together with some exploratory methods, is given in Chapter 1. Next is the specification of possible covariance functions (Chapter 2 for the stationary case and Chapter 3 for the intrinsic case). It is helpful to distinguish discretely indexed, or lattice, processes from continuously indexed processes. In particular, for lattice processes, it is possible to specify a covariance function through an autoregressive model (the SAR and CAR models of Chapter 4), with specialized estimation procedures (Chapter 6). Model fitting through maximum likelihood and related ideas for continuously indexed processes is covered in Chapter 5. An important use of spatial models is kriging, i.e. the prediction of the process at a collection of new sites, given the values of the process at a collection of training sites (Chapter 7), and in particular the links to machine learning are explained. Some additional topics, for which there was not space for in the book, are summarized in Chapter 8. The technical mathematical tools have been collected in Appendix A for ease of reference. Appendix B contains a short historical review of the spatial linear model.

The development of statistical methodology for spatial data arose somewhat separately in several academic disciplines over the past century.

Agricultural field trials. An area of land is divided into long, thin plots, and different crop is grown on each plot. Spatial correlation in the soil fertility can cause spatial correlation in the crop yields (Webster and Oliver, 2001).
Geostatistics. In mining applications, the concentration of a mineral of interest will often show spatial continuity in a body of ore. Two giants in the field of spatial analysis came out of this field. Krige (1951) set out the methodology for spatial prediction (now known as kriging) and Matheron…