Statistical Methods For Spatio Temporal Systems

Statistical Methods for Spatio-Temporal Systems presents current statistical research issues on spatio-temporal data modeling and will promote advances in research and a greater understanding between the mechanistic and the statistical modeling communities. Contributed by leading researchers in the field, each self-contained chapter starts w

Winner of the 2013 DeGroot Prize. 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 also 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.) Statistics for Spatio-Temporal Data has now been reprinted with small corrections to the text and the bibliography. The overall content and pagination of the new printing remains the same; the difference comes in the form of corrections to typographical errors, editing of incomplete and missing references, and some updated spatio-temporal interpretations. 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.

The world is becoming increasingly complex, with larger quantities of data available to be analyzed. It so happens that much of these "big data" that are available are spatio-temporal in nature, meaning that they can be indexed by their spatial locations and time stamps. Spatio-Temporal Statistics with R provides an accessible introduction to statistical analysis of spatio-temporal data, with hands-on applications of the statistical methods using R Labs found at the end of each chapter. The book: Gives a step-by-step approach to analyzing spatio-temporal data, starting with visualization, then statistical modelling, with an emphasis on hierarchical statistical models and basis function expansions, and finishing with model evaluation Provides a gradual entry to the methodological aspects of spatio-temporal statistics Provides broad coverage of using R as well as "R Tips" throughout. Features detailed examples and applications in end-of-chapter Labs Features "Technical Notes" throughout to provide additional technical detail where relevant Supplemented by a website featuring the associated R package, data, reviews, errata, a discussion forum, and more The book fills a void in the literature and available software, providing a bridge for students and researchers alike who wish to learn the basics of spatio-temporal statistics. It is written in an informal style and functions as a down-to-earth introduction to the subject. Any reader familiar with calculus-based probability and statistics, and who is comfortable with basic matrix-algebra representations of statistical models, would find this book easy to follow. The goal is to give as many people as possible the tools and confidence to analyze spatio-temporal data.

The book aims to investigate methods and techniques for spatial statistical analysis suitable to model spatial information in support of decision systems. Over the last few years there has been a considerable interest in these tools and in the role they can play in spatial planning and environmental modelling. One of the earliest and most famous definition of spatial planning was “a geographical expression to the economic, social, cultural and ecological policies of society”: borrowing from this point of view, this text shows how an interdisciplinary approach is an effective way to an harmonious integration of national policies with regional and local analysis. A wide range of spatial models and techniques is, also, covered: spatial data mining, point processes analysis, nearest neighbor statistics and cluster detection, Fuzzy Regression model and local indicators of spatial association; all of these tools provide the policy-maker with a valuable support to policy development.

Spatio-temporal Analysis of Extreme Hydrological Events offers an extensive view of the experiences and applications of the latest developments and methodologies for analyzing and understanding extreme environmental and hydrological events. The book addresses the topic using spatio-temporal methods, such as space-time geostatistics, machine learning, statistical theory, hydrological modelling, neural network and evolutionary algorithms. This important resource for both hydrologists and statisticians interested in the framework of spatial and temporal analysis of hydrological events will provide users with an enhanced understanding of the relationship between magnitude, dynamics and the probability of extreme hydrological events. Presents spatio-temporal processes, including multivariate dynamic modelling Provides varying methodological approaches, giving the readers multiple hydrological modelling information to use in their work Includes a variety of case studies making the context of the book relatable to everyday working situations

As climate change continues to dominate the international environmental agenda, phenology – the study of the timing of recurring biological events – has received increasing research attention, leading to an emerging consensus that phenology can be viewed as an ‘early warning system’ for climate change impact. A multidisciplinary science involving many branches of ecology, geography and remote sensing, phenology to date has lacked a coherent methodological text. This new synthesis, including contributions from many of the world’s leading phenologists, therefore fills a critical gap in the current biological literature. Providing critiques of current methods, as well as detailing novel and emerging methodologies, the book, with its extensive suite of references, provides readers with an understanding of both the theoretical basis and the potential applications required to adopt and adapt new analytical and design methods. An invaluable source book for researchers and students in ecology and climate change science, the book also provides a useful reference for practitioners in a range of sectors, including human health, fisheries, forestry, agriculture and natural resource management.

Assembling a collection of very prominent researchers in the field, the Handbook of Spatial Statistics presents a comprehensive treatment of both classical and state-of-the-art aspects of this maturing area. It takes a unified, integrated approach to the material, providing cross-references among chapters.The handbook begins with a historical intro

Theory of Spatial Statistics: A Concise Introduction presents the most important models used in spatial statistics, including random fields and point processes, from a rigorous mathematical point of view and shows how to carry out statistical inference. It contains full proofs, real-life examples and theoretical exercises. Solutions to the latter are available in an appendix. Assuming maturity in probability and statistics, these concise lecture notes are self-contained and cover enough material for a semester course. They may also serve as a reference book for researchers. Features * Presents the mathematical foundations of spatial statistics. * Contains worked examples from mining, disease mapping, forestry, soil and environmental science, and criminology. * Gives pointers to the literature to facilitate further study. * Provides example code in R to encourage the student to experiment. * Offers exercises and their solutions to test and deepen understanding. The book is suitable for postgraduate and advanced undergraduate students in mathematics and statistics.

Across scientific disciplines, an ever-growing proportion of data can be effectively described in spatial terms. As researchers have become comfortable with techniques for dealing with spatial data, the next progression is to not only model the data itself, but also the complexities of the dynamic environment it represents. This has led to the rise of spatio-temporal modeling and the development of robust statistical methods for effectively modeling and understanding interactions between complex and dynamic systems. Unfortunately, many of these techniques are an extension to existing spatial analysis methods and struggle to account for the data complexity introduced by the added temporal dimension; this has limited many researchers to developing statistical and visual models that assume either a static state of the world, or one modeled by a set of specific temporal snapshots. This challenge is especially acute in the world of public health where researchers attempting to visualize historical, spatial data, often find themselves forced to ignore shifting geographic features because both the tooling and the existing data sources are insufficient. Consider, as an example, a model of vaccine coverage for the administrative regions of Sudan over the past 30 years. In wake of civil war, Sudan was partitioned into two countries, with South Sudan emerging as an independent nation in 2011. This has an immediate impact on both the visual accuracy as well as the quantitative usefulness of any data generated from aggregate spatial statistics. Or, consider epidemiological case reports that are issued from local medical facilities, how does one account for the fact that their locations may change, or that new facilities may spring up or close down as time progresses. These are real-world problems that existing GIS platforms struggle to account for. While there have been prior attempts to develop data models and applications for managing spatio-temporal data, the growing depth and complexity of scientific research has left room for improved systems which can take advantage of the highly interconnected datasets and spatial objects, which are common in this type of research. To that end, we have developed the Trestle data model and application, which leverage graph-based techniques for efficiently storing and querying complex spatio-temporal data. This system simple interface to allow users to perform query operations over time-varying spatial data and return logically valid information based on specific spatial and temporal constraints. This system is applicable to a number of GIS related projects, specifically those attempting to visualize historical public health indicators such as vaccination rates, or develop complex spatio-temporal models, such as malaria risk maps.

Statistical Methods for Spatial and Spatio-Temporal Data Analysis provides a complete range of spatio-temporal covariance functions and discusses ways of constructing them. This book is a unified approach to modeling spatial and spatio-temporal data together with significant developments in statistical methodology with applications in R. This book includes: Methods for selecting valid covariance functions from the empirical counterparts that overcome the existing limitations of the traditional methods. The most innovative developments in the different steps of the kriging process. An up-to-date account of strategies for dealing with data evolving in space and time. An accompanying website featuring R code and examples