A Gentle Introduction to Spatio-Temporal Statistics The dynamic nature of our world is being increasingly captured by sensors as big data. Much of this big data can be indexed by its spatial location and time stamp. Spatio-Temporal Statistics with R, by Christopher K. Wikle, Andrew Zammit-Mangion, and Noel Cressie, provides an accessible introduction to analyzing spatio-temporal data using the programming language R.
The format for each of its stand-alone chapters is an explanation of methodology followed by hands-on application of relatively mature models and methodologies. R was chosen because it is open source, has strong community support, and has many packages that can be used for spatio-temporal modeling.
This book assumes that readers have a background in calculus-based probability and inference and are comfortable with basic matrix algebra representations of statistical models. However, to support those with a less robust background in these subjects, technical notes throughout the book provide short reviews of these methods and ideas, and the appendix contains a brief refresher on matrix algebra. The exercises in this book assume prior knowledge of R and familiarity with Tidyverse, a collection of R packages designed for data science. To further aid with the exercises, helpful R tips have been included.
Spatio-Temporal Statistics with R is a down-to-earth and engaging introduction to the topic, rather than a comprehensive book on the subject. More advanced and technically trained readers may wish to look at a previous book on the same subject by authors Wikle and Cressie, Statistics for Spatio-Temporal Data; however, this book does not include software or coding examples.
Since increasing the number of people who are analyzing spatio-temporal data was a fundamental goal of the authors, a PDF of the entire book is available, with support of the book’s print edition publishers. The hardcover edition of this book was published by Chapman and Hall/CRC as part of The R Series in 2019, ISBN 9781138711136.
– ArcUser (Spring 2019, GIS Bookshelf), a publication of Esri, Redlands, California
Readers interested in finding a broad introduction to statistical methods with spatiotemporal structure will find ample resources in the titular work. The contents are laid out in six chapters, with the first providing motivation for the book and the rest following the workflow of a typical analysis. Thus, Chapter 2 details common data structures, visualization, and exploratory tools typical to the area. The authors then build up from general (Chapter 3) spatiotemporal models to what they define as descriptive (Chapter 4) and dynamic (Chapter 5) spatiotemporal models. They make this distinction as a way to differentiate both how models can be viewed and used. The latter point focusing more specifically on the difference between prediction and inference—a point that’s well made at a time when the rise of “Big Data” has made the line separating the two increasingly blurry. True to any analysis workflow, the book finishes with an overview of techniques and tools for evaluating and comparing the models developed in the previous chapters. The authors cover a number of approaches ranging from Frequentist generalized additive models to Bayesian process models. Throughout all of these topics, the authors work to build the reader’s intuition for the nuances in working with these models. This can be seen in their discussion of the integro-difference equation’s complexities, illustrated in Chapter 5 through helpful graphics or their warning of the potential for confounding fixed and random effects in basis expansions in Chapter 4. No matter the subject, the authors take care to ensure the reader’s understanding is more than just skin-deep. Along side the book’s theoretical development, the authors provide numerous R code examples and package recommendations applied to topical datasets in “Labs” at the end of each chapter. This gives readers interested in a “hands-on” approach an easy way to jump in and start looking at and working with the data. For those interested in reading further, in either theory or specialized analysis, the authors provide a number of worthwhile references to their own and other works throughout the book. Whether needing a refresher on common spatiotemporal model specifications or a good reference for code examples and exploratory data tools, any analyst who finds themselves interested or working in spatiotemporal data will find this book a helpful resource.
– Adam Peterson (December 2019, Biometrics), Department of Biostatistics, University of Michigan, Ann Arbor, Michigan
To help statisticians understand and apply appropriate statistical methods, the authors provide this highly interesting book, intended as an introduction to spatio-temporal statistics with R. The book is divided into six chapters, each of them standing alone and in a form such that they can be read separately. The first chapter is an introduction to spatio-temporal analysis. It is useful because it introduces the reader to the definitions of the various concepts used in this branch of statistical analysis and explains the fields of application of spatio-temporal analyses. One of the main qualities of this chapter is to give a clear explanation of the differences between spatial analyses, temporal analyses, and spatio-temporal analyses… the authors explain and develop several methods used to explore spatio-temporal data, such as Hovmöller plots and the Trelliscope method. Moreover, the authors provide readers with a solid basis for one of the major challenges with such data: data exploration… To conclude, this is a very clear introduction to spatio-temporal analysis using R, it is thorough and is suitable for readers of different levels. The possibility to experiment with the topics introduced in each chapter with a dedicated R ‘Lab’ is a good way of learning to apply these models. Moreover, appendices are provided to further extend the development of the topics covered in the different chapters.
– Sébastien Bailly (December 2019, ISCB News), French Institute of Health and Medical Research, Grenoble, France
Spatio-Temporal Statistics With R is an excellent book both for those seeking a broad overview of the current spatio-temporal practices and for those wanting practical spatio-temporal examples or applications. This book is quite accessible, with only a basic understanding of spatial statistics needed. Previous exposure to Bayesian statistics is also helpful, particularly in later chapters. Even without those backgrounds, the authors provide overviews that allow readers to focus on the main concepts. By the authors’ own admission, there are some sections that are less in depth than other texts (e.g., Cressie and Wikle 2011 [Statistics for Spatio-Temporal Data. Wiley, Hoboken, NJ]), but the authors provide plentiful references throughout the book. This makes the book easier to read while still providing sufficient direction to anyone needing more information.
One of the best aspects of the book is the applications with R. After each chapter, the authors provide R Labs that walk through examples and connect code with the theory. In a classroom setting, these R Labs could be used as demonstrations or, with simple modifications, assessments. The authors also provide extended case study examples, which help tie together multiple concepts.
The first three chapters introduce readers to spatio-temporal data and several techniques for investigating that data. Chapter 2, which discusses tools for exploratory analysis, is a particularly useful chapter even to those without much experience in spatial or spatio-temporal statistics. Even if someone only read Chapter 2, they would still walk away both with a good understanding of how to approach spatio-temporal data and with an appreciation for the complexities of the data. Chapter 3 develops these ideas further by considering models that do not explicitly account for spatio-temporal dependence. The authors show how these simple models can help users understand the data despite the importance of spatio-temporal dependence.
Chapters 4 and 5 are the book’s core sections: models that account for spatio-temporal dependencies. Chapter 4 details more traditional approaches to spatio-temporal statistics (described as “descriptive” models by the authors), such as estimating covariograms and making predictions using kriging. In Chapter 5, the authors discuss “dynamic” models, which investigate spatio-temporal data as a spatial process that evolves through time. This chapter focuses on linear dynamic spatiotemporal models in a setting where time is discretized. The authors provide references to other variations (e.g., when time is continuous), noting these are beyond the scope of the book. Finally, Chapter 6 discusses how to evaluate spatio-temporal models. Each section (model checking, model validation, and model selection) is not particularly in-depth and provides only an overview of the topic; however, the authors provide direction to more detailed discussions. Additionally, the R Lab at the end of the chapter effectively wraps the process of evaluation into a cohesive example.
Overall, this book provides a great overview of current spatio-temporal methodology and practices. It could easily be used in a graduate course, by someone interested in learning the fundamentals of spatio-temporal statistics, or as a resource for practitioners of spatio-temporal statistics. The text reads smoothly, and concepts are introduced at a level that should be understandable even to those who are relatively new to the field. Each chapter builds on the previous chapters, which produces a practical framework for how to do spatio-temporal statistics. In the sections lacking in-depth discussion, the authors supply enough references to guide readers seeking more information. The R Labs are an excellent component that allow readers not only to make the connection between theory and application, but also to try new techniques with guided examples.
– Nicholas W. Bussberg (January 2021, The American Statistician), Department of Mathematics and Statistics, Elon University, North Carolina
Two-page book review:
Christopher K. Wikle, Andrew Zammit-Mangion and Noel Cressie (2019): Spatio-temporal Statistics with R. Chapman and Hall/CRC, 396 pp.
“This extremely useful book contains extensive R code and hands-on “Lab” sections at the end of each chapter that walk you through data processing and implementation. This is exactly what an applied statistics book needs to be relevant, allowing the reader to immediately start analyzing data and interrogating output. The book focuses on the Bayesian hierarchical perspective and applications in the geophysical sciences. The authors do a great service emphasizing the inferential point of view (e.g., characterizing uncertainty for model parameters and forecasting) providing a distinct contrast with other current paradigms such as Deep Learning. The structure is concise and logical with a nice progression from exploration and visualization, space-time regression, descriptive models (e.g., kriging) and then dynamic space-time models, with an emphasis throughout on dimension reduction and basis function perspectives which is timely and increasing in importance.”
– J. Andrew Royle, Senior Scientist, USGS Patuxent Wildlife Research Center
“This book is a comprehensive and very readable tutorial on modelling and visualizing spatio-temporal (ST) processes. It emphasises the need to understand an ST process before attempting to model it. Along the way, the reader learns the descriptive phase of exploratory analysis and moves on to the dynamic modelling of ST processes. Only then does the reader move onto the rich libraries of R tools available for the model construction. In the final phase the reader learns how to assess the models he or she has created with the goal of improving them and ultimately choosing the best one. All this is accomplished using a hands-on approach through lab work that involves complex datasets and the very large library of R packages now available. Thus, the reader will learn amongst many other things, how to animate their spatial plots of data and the use of Trelliscope for visualizing large ST datasets. For data wrangling, the reader learns about the dyplr and tidyr R packages. And the reader will master a lot of the skills needed for spatial regression with generalized linear models, Bayesian hierarchical modelling, using the integrated nested Laplace (INLA) approximation, spatial prediction and future forecasting. Of particular note is the connections the book develops with stochastic partial differential equations and uncertainty quantification, that are developed through discussion of dynamic modelling. This book will have a prominent place in my reference library.”
– James V. Zidek, Professor Emeritus, University of British Columbia, Canada
“This book provides the ideal modern approach to the analysis of spatial-temporal data and implementation of associated models. The theory is laid out clearly by masters of the field and the accompanying R code, packages, and data laboratories both in the text and available online bring the subject to life. This is not a book to sit on your shelf – it should be on your desk for ready access and continual use.”
– Marc Mangel, University of California, Santa Cruz (USA) and University of Bergen (Norway)
“Spatio-Temporal Statistics with R is the perfect companion to the earlier title by the authors on Statistics for Spatio-Temporal Data. This newest book augments the reader’s skillset by showing how to implement a variety of methods to create spatio-temporal graphics and perform data analysis. By making a massive set of data and code available, this book encourages the reader to follow along on the computer while working through the chapters. In fact, a unique element of the authors’ approach is that they provide a solid review of existing software and complement that with a new software package so that no techniques fall through the cracks. I also particularly like the series of text boxes throughout the book that detail expert tips for computing and include technical comments for more advanced readers. It is this masterful blend of information that beginners and power users alike will find critical for enhancing their understanding of spatio-temporal statistics in practice. This book will be recommended reading for all of my future graduate students!”
– Mevin B. Hooten, Professor, Colorado State University and U.S. Geological Survey, USA
“This book is an excellent offering from some of the leading researchers and authors in the field of spatio-temporal statistics. The book will be especially useful for scientists and researchers seeking a hands-on approach to statistical modeling and analysis for spatio-temporal data. The text is organized beautifully and offers a pleasing blend of technical material and computer programs for implementing a variety of spatio-temporal models. What is especially attractive is the detail with which the computer programs have been explained and exemplified. The theoretical and more technical material are supplied as “Technical Tips” in conspicuous boxes that accompany the modeling and computing details. The book will be useful to methodologists and practitioners working on spatio-temporal analysis and will especially appeal to the broader scientific community who will enjoy the very accessible treatment of spatial-temporal modeling and computing in an open-source and highly accessible software environment.”
– Sudipto Banerjee, Professor and Chair, Department of Biostatistics, University of California Los Angeles, USA