Multivariate t Distributions and Their Applications

types of nonstationarity, global modeling and local stationary approaches in nonstationary covariance models. Chapter 9 concludes with space–time separable covariance functions and various approaches to developing space–time nonseparable covariance functions. There is also a brief discussion of spatialtemporal point processes. The book is intended as a text for a graduate-level course in spatial statistics. I believe that it would be a suitable text for a variety of reasons. First of all, the book provides comprehensive coverage of statistical methods for geostatistical data, lattice data, and point patterns. Not many books on spatial statistics have this feature. A book similar in scope is Cressie (1993), which is a well-regarded text on spatial statistics. Further, the book has a nice balance of statistical theory, methodology, and applications, with an emphasis on statistical methods. It contains many concrete examples that illustrate both theory and methods. In illustrating the methods, real and interesting data examples are drawn from many disciplines such as agriculture, ecology, geology, epidemiology, and meteorology. To illustrate the more abstract concepts and theory, the authors often give intuitive explanations and easy-to-understand examples. Finally, at the end of each of the first seven chapters, there are assignment problems for students. The problems are mostly related to technical derivations or proofs that supplement readings from the corresponding chapter. I found the exercises fitting and quite interesting. From my experience teaching spatial statistics, I think the book could be used for courses at different levels. Specifically, it could be used as the main text for a spatial statistics course at the master’s level. In this case, the audience would be master’s or beginning Ph.D. students in statistics, as well as nonstatistics graduate students with strong quantitative skills. Possible prerequisites are introductory probability theory, mathematical statistics, and linear models theory. For a more advanced Ph.D. level course, the book could be used as an introductory text for a Ph.D. student who is not familiar with spatial statistics to get acquainted with the main areas in spatial statistics. Depending on interests, the course might then delve into more advanced or more topic-specific texts such as Cressie (1993), Stein (1999), and Møller and Waagepetersen (2004). On the other hand, for a course aimed at introducing spatial statistics to nonstatistics graduate students who are not as quantitatively skilled, this book could be used as an advanced text in addition to some other more applied texts such as Goovaerts (1997), Schabenberger and Pierce (2002), and Waller and Gotway (2004). In the Preface, the authors fully acknowledge the limitations in the scope of the book. For example, their approach is “mostly model-based and frequentist in nature, with an emphasis on models in the spatial, and not the spectral domain” (Schabenberger and Gotway 2005). Regarding Bayesian hierarchical models for spatial data, Section 6.5 of the book gives a very nice overview, but there is certainly more in the literature. Interested readers can find more complex models and computational techniques in Banerjee, Carlin, and Gelfand (2003). Similarly, even though most of the basic elements in spatial point processes are covered in Chapter 3, there is more to spatial point processes such as statistical inference and simulation using Markov chain Monte Carlo methods. These and other more advanced topics in spatial point processes can be found in Diggle (2001) and Møller and Waagepetersen (2004). In terms of computing, the book is not intended to give hands-on guidance on how to use particular software packages. However, readers may find it helpful to consult the supplementary materials posted at the CRC Press website, which include software code for examples from the text. Overall, this is a wonderful book that systematically introduces readers to spatial statistics. With a writing style that is illustrative, clear, thoughtful, and cogent, teachers and students alike should find it a delightful text for this diverse and exciting field.