Statistics for Spatio-Temporal Data (CourseSmart)

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Product Description

A state-of-the-art presentation of spatio-temporal processes, bridging classic ideas with modern hierarchical statistical modeling concepts and the latest computational methods

Noel Cressie and Christopher K. Wikle, are winners of the 2011 PROSE Award in the Mathematics category, for the book � Statistics for Spatio-Temporal Data� (2011), published by John Wiley and Sons. (The PROSE awards, for Professional and Scholarly Excellence, are given by the Association of American Publishers, the national trade association of the US book publishing industry.)

From understanding environmental processes and climate trends to developing new technologies for mapping public-health data and the spread of invasive-species, there is a high demand for statistical analyses of data that take spatial, temporal, and spatio-temporal information into account. Statistics for Spatio-Temporal Data presents a systematic approach to key quantitative techniques that incorporate the latest advances in statistical computing as well as hierarchical, particularly Bayesian, statistical modeling, with an emphasis on dynamical spatio-temporal models.

Cressie and Wikle �supply a unique presentation that incorporates ideas from the areas of time series and spatial statistics as well as stochastic processes. Beginning with separate treatments of temporal data and spatial data, the book combines these concepts to discuss spatio-temporal statistical methods for understanding complex processes.

Topics of coverage include:

• Exploratory methods for spatio-temporal data, including visualization, spectral analysis, empirical orthogonal function analysis, and LISAs
• Spatio-temporal covariance functions, spatio-temporal kriging, and time series of spatial processes
• Development of hierarchical dynamical spatio-temporal models (DSTMs), with discussion of linear and nonlinear DSTMs and computational algorithms for their implementation
• Quantifying and exploring spatio-temporal variability in scientific applications, including case studies based on real-world environmental data

Throughout the book, interesting applications demonstrate the relevance of the presented concepts. Vivid, full-color graphics emphasize the visual nature of the topic, and a related FTP site contains supplementary material. Statistics for Spatio-Temporal Data is an excellent book for a graduate-level course on spatio-temporal statistics. It is also a valuable reference for researchers and practitioners in the fields of applied mathematics, engineering, and the environmental and health sciences.

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Statistics for Spatio-Temporal Data (CourseSmart) Review

Cressie and Wikle's book is one of the first to address space time models from a statistical point a view and using many of the latest statistical models (the soon to be updated 2003 book Hierarchical Modeling and Analysis for Spatial Data also covered the topic). Hierarchical space time models, Dynamical linear models, incorporating scientific knowledge into your statistical model, and handling massive data by using Fixed Rank Kriging are some of the topics covered. However, there are many intricacies that need to be addressed when modelling spatial data or temporal data. So writing a book covering data using both indices is no easy task. The task to write a book on spatio-temporal models only becomes harder when the goal is to cover the topic from a Bayesian point of view (a field of analysis with its own intricacies that need to be addressed). I believe the authors did a good job in presenting some of the latest space-time models proposed in research. However, there are big issues that are not covered in the book.
- The importance of convergence diagnostics for Bayesian models must be emphasized one way or another when discussing these types of methods. The book pretty much does not touch on convergence at all.
- Research has shown that Matern covariance parameters such as the smoothing parameter and the range, cannot be consistently estimated. This may lead to convergence problems when using MCMC techniques to extract characteristics from the posteriors of these parameters of interest (I found out about this the hard way as a grad student). As a result, at best, only partially reliable inference from your Bayesian analysis may be obtained, a disappointing fact given how computationally intensive Bayesian methods are for space-time models. Considering the major issue, space-time Bayesian models can hardly be called state of the art (as tagged several times in the book). Sadly, this convergence issue is not mentioned at all in the book which would lead to frustration for those constructing these models to try to understand a process of interest.
- Kriging is referred to as the Best Linear Unbiased Predictor. In theory this is true, but this is assuming the spatial covariance parameters are known, which is not really the case in practice. Although this often does not affect much the results if the Gaussian distribution assumption holds, it may drastically affect prediction variances for non-Normal distributions. Cressie has done work on the subject. It appears this issue is not discussed in the book though and if so, it should be clearly emphasized.
- Fixed Rank Kriging (FRK) is referred to as a best linear unbiased predictor. Is it not! In fact, since in practice kriging is often implemented by plugging in estimated parameters into the equations (making the the resulting estimated best linear unbiased predictor an approximation), FRK is truly an approximation of an approximation of the best linear unbiased predictor.
The book proposes its methods as a way to conduct science the way it ought to be: in a critical way, transparent, reproducible and in an objective manner. But the points brought up above makes the book a bit disappointing since it is not critical about the methods that are proposed, which although useful, are certainly not perfect. If there is a new edition in the future, I suggest the authors cover some important material left out and also address some challenges faced when implementing these methods.

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