Bayesian Modeling of Spatio-Temporal Data with R
Applied sciences, both physical and social, such as atmospheric, biological, climate, demographic, economic, ecological, environmental, oceanic and political, routinely gather large volumes of spatial and spatio-temporal data in order to make wide ranging inference and prediction. Ideally such inferential tasks should be approached through modelling, which aids in estimation of uncertainties in all conclusions drawn from such data. Unified Bayesian modelling, implemented through user friendly software packages, provides a crucial key to unlocking the full power of these methods for solving challenging practical problems.
Key features of the book:
• Accessible detailed discussion of a majority of all aspects of Bayesian methods and computations with worked examples, numerical illustrations and exercises
• A spatial statistics jargon buster chapter that enables the reader to build up a vocabulary without getting clouded in modeling and technicalities
• Computation and modeling illustrations are provided with the help of the dedicated R package bmstdr, allowing the reader to use well-known packages and platforms, such as rstan, INLA, spBayes, spTimer, spTDyn, CARBayes, CARBayesST, etc
• Included are R code notes detailing the algorithms used to produce all the tables and figures, with data and code available via an online supplement
• Two dedicated chapters discuss practical examples of spatio-temporal modeling of point referenced and areal unit data
• Throughout, the emphasis has been on validating models by splitting data into test and training sets following on the philosophy of machine learning and data science
This book is designed to make spatio-temporal modeling and analysis accessible and understandable to a wide audience of students and researchers, from mathematicians and statisticians to practitioners in the applied sciences. It presents most of the modeling with the help of R commands written in a purposefully developed R package to facilitate spatio-temporal modeling. It does not compromise on rigour, as it presents the underlying theories of Bayesian inference and computation in standalone chapters, which would be appeal those interested in the theoretical details. By avoiding hard core mathematics and calculus, this book aims to be a bridge that removes the statistical knowledge gap from among the applied scientists.
2. Jargon of spatial and spatio-temporal modeling
3. Exploratory data analysis methods
4. Bayesian inference methods
5. Bayesian computation methods
6. Bayesian modeling for point referenced spatial data
7. Bayesian modeling for point referenced spatio-temporal data
8. Practical examples of point referenced data modeling
9. Bayesian forecasting for point referenced data
10. Bayesian modeling for areal unit data
11. Further examples of areal data modeling
12. Gaussian processes for data science and other applications
Appendix A. Statistical densities used in the book
Appendix B. Answers to selected exercises
"This book is a fine addition to the literature on linear modelling of spatio-temporal data, both geostatistical and areal unit; the linkage to the author’s R package bmstdr is particularly useful."
– Peter Diggle (Lancaster University, UK)
"This book provides a heroic solo effort by an author who is at the top of the game in Bayesian spatio-temporal analysis. The author is a leader in this community with regard to computation for fitting these demanding hierarchical models. This volume enables applied researchers to implement sound Bayesian modeling, rather than "procedure-based" analysis, to address challenging spatio-temporal issues. The fact that it emphasizes modeling in building bridges to the practitioner’s application is one of its strongest virtues. The book is well illustrated with lots of graphics and boxes of code, doing this primarily within bmstdr and ggplot, two well-developed R-packages. Attractively, the book emphasizes model assessment and comparison in predictive space, a necessity with spatio-temporal data. The book’s accessibility is much appreciated, exemplified by a useful "jargon" chapter for basic ideas, complemented with suitable figures. In summary, there are several competitors out there now but this book finds its own place in terms of bringing state-of the-art modeling approachably to exigent application."
– Alan Gelfand, Duke University, USA
"This book fills an essential gap in the literature about spatial-temporal data modelling. It provides a valuable gentle introduction to the theory and current practice of Bayesian modelling without the need for the reader to fully master the deep statistical theories underpinned by rigorous calculus-based mathematics. Every topic in the book is linked to elaborations in R that takes the reader to the practical level quickly. The book provides valuable insights on all the steps of spatial-temporal data analysis, from the initial exploration to the more refined models. The language is not too technical, and the students will really appreciate chapter 2, ‘Jargon of Spatial and Spatio-Temporal Modelling’ summarising all relevant definitions in the field. I teach a class on spatial statistics, and I will be happy to use this book as a suggested textbook."
– Giovanna Jona-Lasinio, Sapienza University of Rome, Italy
"Bayesian spatio-temporal modelling is a complex research field with a daunting array of potential models to choose between and software packages to use. This book is an invaluable guide to statisticians and non-statisticians alike who are new to spatio-temporal modelling, by providing them with an accessible introduction to both Bayesian modelling ideas and the array of different types of spatio-temporal data structures and models that are available. Key to this is the array of practical examples that are illustrated throughout the book, which along with the discussion of the software options for fitting these models will enable others new to the field to easily apply the methods to their own data. The author is an expert in spatio-temporal modelling with long experience in this area with a diverse range of application specialities, and he provides clear and concise descriptions of all the key ideas and concepts."
– Duncan Lee, University of Glasgow, Scotland
"The quality of the paper and the printing is excellent. Many of the figures are in colors. Some are quite small, but with the scripts on the website you can recreate them yourself if needed. In summary, a good book with an emphasis on careful statistical modelling. On the publisher’s website (https://www.routledge.com/Bayesian-Modeling-of-Spatio-Temporal-Data-with-R/Sahu/p/book/9780367277987) the table of contents and more information are available."
– Paul Eilers, ISCB Book Reviews
"There are twelve chapters, two appendices, an excellent bibliography, and an extensive glossary
in this book. The topics covered in this book are examples of spatio-temporal data, needed
jargons for stochastic processes, exploratory data analytic methods, Bayesian inferential techniques,
Bayesian computations, point referenced spatial-temporal data with modeling, area unit
data modeling, Gaussian processes, statistical densities, and chapter exercises with solutions in the
appendices. The bibliography contains an extensive and up to date. The readers ought to read
first and recognize the terminologies before start reading this book. Some special features of
thiswell written book are about ocean chlorophyll data analyses, COVID-19 data analytic results,
isotropy,Matern covariance function,Monte Carlo integration,Hubbard Brook precipitation data
analytic results, childhood vaccination data in Kenya, method of batching, and autoregressive
processes among others."
– Ramalingam Shanmugam, Texas State University
"Sujit Sahu has been prolific at writing papers and creating R packages for spatio-temporal modelling. . . The book fulfils three roles: an introduction to spatio-temporal data analysis; a detailed reference text on Bayesian computation for spatio-temporal models; and a comprehensive vignette for the accompanying R package bmstdr. An elegant web site contains a full set of code for reproducing the analyses in the book. This book is a useful ‘‘beyond the basics’’ resource for anyone wanting to use random-effects models for solving scientific problems involving spatio-temporal data. The book has 12 chapters plus appendices and feels like longer text than the 400 pages it actually has. It is very well structured as a reference text and a reasonably knowledgeable statistician could absorb most sections without having read the previous material. Specifically, theory and computational methods are covered thoroughly but it is possible to read the more applied sections treating the inferential algorithm as a black box. There are extensive examples which consider both spatial prediction and using inference on model parameters to understand the underlying physical process."
– Patrick E. Brown, University of Toronto, Canada