Spatial Analysis (eBook)

John T. Kent, Kanti V. Mardia (Autoren)

eBook Download: EPUB

2022
John Wiley & Sons (Verlag)
978-1-118-76357-5 (ISBN)

Infos

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.

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.

Rezensionen

The modern world of big data is often accompanied by little understanding. Often this data comes in a spatial form, and critically our understanding emerges from spatial analysis. It's not possible to imagine two better guides to this domain than John Kent and Kanti Mardia. In Spatial Analysis Kent and Mardia provide a comprehensive guide to modern thinking that is classically grounded. This book is a must-read for those who are taking understanding seriously as part of handling modern spatial data sets across the domains of machine learning, statistics and data science.

-- Neil Lawrence, DeepMind Professor of Machine Learning, University of Cambridge

[Spatial Analysis] is a delightful and authoritative book on the subject of spatial statistical analysis by two of the world's most eminent researchers in the field of spatial statistics and shape analysis. The book eloquently discusses most of the topics in spatial analysis in a wonderfully organised manner. For example, there are two chapters on random fields, two chapters on estimation methods, one on modelling and another large chapter on kriging. With another chapter on additional topics such as Co-kriging, Bayesian hierarchical modeling, spatio-temporal modeling, and thin plate splines this book covers most of the concepts researchers need to know in this area. The main emphasis of the book is on theoretical aspects but it does not lose sight of applications. The chapter one itself motivates the theory with several example data sets which include fingerprint of the famous statistician Sir R A Fisher. The book does justice to the theory by presenting and explaining it in an accessible format for all - graduate students and researchers. The book also provides enjoyable to read personal historical notes and anecdotes regarding the course of development of the theory of spatial analysis.

-- Sujit Sahu, Professor of Mathematical Sciences, University of Southampton

[Spatial Analysis] is a splendid text on spatial statistics written by two eminent scholars in the field who have beautifully presented a wide range of topics. The text begins with some very interesting examples of spatially oriented data and their features and is followed by some superbly compiled expository chapters. What is especially appealing, in my opinion, is the attention paid by the authors to the theoretical developments and exposition of seemingly abstruse topics. The book is compactly written while retaining mathematical rigor. Specifically, the chapters on different flavours of spatial random fields and that on conditional autoregression models stand out in terms of their clarity of presentation. Inference primarily focuses on likelihood based methods and kriging, while appearing somewhat late in the book (Chapter 7 out of eight chapters), receives a very detailed treatment that includes Bayesian prediction methods as well. In summary, this elegant text will serve students, researchers and scholars invested in spatial statistics very well as a source of reference as well as a text to build courses from. I congratulate the authors' on this wonderful accomplishment.

-- Sudipto Banerjee, PhD, Professor and Chair, Dept. of Biostatistics, UCLA Fielding School of Public Health

Textauszug

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.

1. 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).
2. 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 (1963) developed a comprehensive theory for stationary and intrinsic random fields; see Appendix B.
3. Social and medical science. Spatial continuity is an important property when describing characteristics that vary across a region of space. One application is in geography and environmetrics and key names include Cliff and Ord (1981), Anselin (1988), Upton and Fingleton (1985, 1989), Wilson (2000), Lawson and Denison (2002), Kanevski and Maignan (2004), and Schabenberger and Gotway (2005). Another application is in public health and epidemiology, see, e.g., Diggle and Giorgi (2019).
4. Splines. A very different approach to spatial continuity has been pursued in the field of nonparametric statistics. Spatial continuity of an underlying smooth function is ensured by imposing a roughness penalty when fitting the function to data by least squares. It turns out that fitted spline is identical to the kriging predictor under suitable assumptions on the underlying covariance function. Key names here include Wahba (1990) and Watson (1984). A modern treatment is given in Berlinet and Thomas‐Agnan (2004).
5. Mainstream statistics. From at least the 1950s, mainstream statisticians have been closely involved in the development of suitable spatial models and suitable fitting procedures. Highlights include the work by Whittle (1954), Matérn (1960, 1986), Besag (1974), Cressie (1993), and Diggle and Ribeiro (2007).
6. Probability theory and fractals. For the most part, statisticians interested in asymptotics have focused on “outfill” asymptotics – the data sites cover an increasing domain as the sample size increases. The other extreme is “infill asymptotics” in which the interest is on the local smoothness of realizations from the spatial process. This infill topic has long been of interest to probabilists (e.g. Adler, 1981). The smoothness properties of spatial processes underlie much of the theory of fractals (Mandelbrot, 1982).
7. Machine learning. Gaussian processes and splines have become a fundamental tool in machine learning. Key texts include Rasmussen and Williams (2006) and Hastie et al. (2009).
8. Morphometrics. Starting with Bookstein (1989), a pair of thin‐plate splines have been used for the construction of deformations of two‐dimensional images. The thin‐plate spline is just a special case of kriging.
9. Image analysis. Stationary random fields form a fundamental model for randomness in images, though typically the interest is in more substantive structures. Some books include Grenander and Miller (2007), Sonka et al. (2013), and Dryden and Mardia (2016). The two edited volumes Mardia and Kanji (1993) and Mardia (1994) are still relevant for the underlying statistical theory in image analysis; in particular, Mardia and Kanji (1993) contains a reproduction of some seminal papers in the area.

The book is designed to be used in teaching. The statistical models and methods are carefully explained, and there is an extensive set of exercises. At the same time the book is a research monograph, pulling together and unifying a wide variety of different ideas.

A key strength of the book is a careful description of the foundations of the subject for stationary and related random fields. Our view is that a clear understanding of the basics of the subject is needed before the methods can be used in more complicated situations. Subtleties are sometimes skimmed over in more applied texts (e.g. how to interpret the “covariance function” for an intrinsic process, especially of higher order, or a generalized process, and how to specify their spectral representations). The unity of the subject, ranging from continuously indexed to lattice processes, has been emphasized. The important special case of self‐similar intrinsic covariance functions is carefully explained. There are now a wide variety of estimation methods, mainly variants and approximations to maximum likelihood, and these are explored in detail.

There is a careful treatment of kriging, especially for intrinsic covariance functions where the importance of drift terms is emphasized. The link to splines is explained in detail. Examples based on real data, especially from geostatistics, are used to illustrate the key ideas.

The book aims at a balance between theory and illustrative applications, while remaining accessible to a wide audience. Although there is now a wide variety of books available on the subject of spatial analysis, none of them has quite the same perspective. There have been many books published on spatial analysis, and here we just highlight a few. Ripley (1988) was one of the first monographs in the mainstream Statistics literature. Some key books that complement the material in this book, especially for applications, include Cressie (1993), Diggle and Ribeiro (2007), Diggle and Giorgi (2019), Gelfand et al. (2010), Chilés and Delfiner (2012), Banerjee et al. (2015), van Lieshout (2019), and Rasmussen and Williams (2006).

What background does a reader need? The book assumes a knowledge of the ideas covered by intermediate courses in mathematical statistics and linear algebra. In addition, some familiarity with multivariate statistics will be helpful. Otherwise, the book is largely self‐contained. In particular, no prior knowledge of stochastic processes is assumed. All the necessary matrix algebra is included in Appendix A. Some knowledge of time series is not necessary, but will help to set some of the ideas into context.

There is now a wide selection of software packages to carry out spatial analysis, especially in R, and it is not the purpose in this book to compare them. We have largely used the package geoR (Ribeiro Jr and Diggle, 2001) and the program of Pardo‐Igúzquiza et al. (2008), with additional routines written where necessary. The data sets are available from a public repository at https://github.com/jtkent1/spatial-analysis-datasets.

Several themes receive little or no coverage in the book. These include point processes, discretely valued processes (e.g. binary processes), and spatial–temporal...

Produkt-Details

• Erscheint lt. Verlag: 28.4.2022
• Reihe/Serie: Wiley Series in Probability and Statistics
• Reihe/Serie: Wiley Series in Probability and Statistics
• Reihe/Serie: Wiley Series in Probability and Statistics
• Sprache: englisch
• Themenwelt: Mathematik / Informatik ► Mathematik ► Statistik
• Themenwelt: Mathematik / Informatik ► Mathematik ► Wahrscheinlichkeit / Kombinatorik
• Schlagworte: Angewandte Wahrscheinlichkeitsrechnung u. Statistik • Applied Probability & Statistics • Computer Science • Data Analysis • Datenanalyse • Gaussian process • Geostatistics • Image Analysis • machine learning • Multivariate Analyse • multivariate analysis • spatial analysis guide • spatial analysis handbook • spatial analysis textbook • Spatial Data • spatial data analysis • Spatial statistical analysis • spatial statistics • spatial-temporal modeling • Statistical Analysis • Statistics • Statistik
• ISBN-10: 1-118-76357-2 / 1118763572
• ISBN-13: 978-1-118-76357-5 / 9781118763575