# Spatio Temporal Statistics with R

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.

Author: Christopher K. Wikle

Publisher: CRC Press

ISBN: 9780429649783

Category: Mathematics

Page: 380

View: 679

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.
Categories: Mathematics

# Spatial and Spatio temporal Bayesian Models with R INLA

However, classical simulation methods such as Markov Chain Monte Carlo can become computationally unfeasible; this book presents the Integrated Nested Laplace Approximations (INLA) approach as a computationally effective and extremely ...

Author: Marta Blangiardo

Publisher: John Wiley & Sons

ISBN: 9781118326558

Category: Mathematics

Page: 320

View: 554

Spatial and Spatio–Temporal Bayesian Models with R–INLA provides a much needed, practically oriented & innovative presentation of the combination of Bayesian methodology and spatial statistics. The authors combine an introduction to Bayesian theory and methodology with a focus on the spatial and spatio­–temporal models used within the Bayesian framework and a series of practical examples which allow the reader to link the statistical theory presented to real data problems. The numerous examples from the fields of epidemiology, biostatistics and social science all are coded in the R package R–INLA, which has proven to be a valid alternative to the commonly used Markov Chain Monte Carlo simulations
Categories: Mathematics

# Statistical Analysis of Spatial and Spatio Temporal Point Patterns Third Edition

Practical examples illustrate how the methods are applied to analyze spatial data in the life sciences. This edition also incorporates the use of R through several packages dedicated to the analysis of spatial point process data.

Author: Peter J. Diggle

Publisher: CRC Press

ISBN: 9781466560246

Category: Mathematics

Page: 268

View: 99

Written by a prominent statistician and author, the first edition of this bestseller broke new ground in the then emerging subject of spatial statistics with its coverage of spatial point patterns. Retaining all the material from the second edition and adding substantial new material, Statistical Analysis of Spatial and Spatio-Temporal Point Patterns, Third Edition presents models and statistical methods for analyzing spatially referenced point process data. Reflected in the title, this third edition now covers spatio-temporal point patterns. It explores the methodological developments from the last decade along with diverse applications that use spatio-temporally indexed data. Practical examples illustrate how the methods are applied to analyze spatial data in the life sciences. This edition also incorporates the use of R through several packages dedicated to the analysis of spatial point process data. Sample R code and data sets are available on the author’s website.
Categories: Mathematics

# Spatial and Spatio Temporal Geostatistical Modeling and Kriging

This text will also prove to be a valuable reference for researchers and practitioners in the fields of applied mathematics, engineering, and the environmental and health sciences.

Author: José-María Montero

Publisher: John Wiley & Sons

ISBN: 9781118762431

Category: Mathematics

Page: 400

View: 899

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
Categories: Mathematics

# Probability and Statistics with R

New to the Second Edition Improvements to existing examples, problems, concepts, data, and functions New examples and exercises that use the most modern functions Coverage probability of a confidence interval and model validation ...

Author: Maria Dolores Ugarte

Publisher: CRC Press

ISBN: 9781466504400

Category: Mathematics

Page: 983

View: 559

Cohesively Incorporates Statistical Theory with R Implementation Since the publication of the popular first edition of this comprehensive textbook, the contributed R packages on CRAN have increased from around 1,000 to over 6,000. Designed for an intermediate undergraduate course, Probability and Statistics with R, Second Edition explores how some of these new packages make analysis easier and more intuitive as well as create more visually pleasing graphs. New to the Second Edition Improvements to existing examples, problems, concepts, data, and functions New examples and exercises that use the most modern functions Coverage probability of a confidence interval and model validation Highlighted R code for calculations and graph creation Gets Students Up to Date on Practical Statistical Topics Keeping pace with today’s statistical landscape, this textbook expands your students’ knowledge of the practice of statistics. It effectively links statistical concepts with R procedures, empowering students to solve a vast array of real statistical problems with R. Web Resources A supplementary website offers solutions to odd exercises and templates for homework assignments while the data sets and R functions are available on CRAN.
Categories: Mathematics

# Geospatial Health Data

Geospatial Health Data: Modeling and Visualization with R-INLA and Shiny describes spatial and spatio-temporal statistical methods and visualization techniques to analyze georeferenced health data in R. The book covers the following topics: ...

Author: Paula Moraga

Publisher: CRC Press

ISBN: 9781000732030

Category: Medical

Page: 274

View: 473

Geospatial health data are essential to inform public health and policy. These data can be used to quantify disease burden, understand geographic and temporal patterns, identify risk factors, and measure inequalities. Geospatial Health Data: Modeling and Visualization with R-INLA and Shiny describes spatial and spatio-temporal statistical methods and visualization techniques to analyze georeferenced health data in R. The book covers the following topics: Manipulating and transforming point, areal, and raster data, Bayesian hierarchical models for disease mapping using areal and geostatistical data, Fitting and interpreting spatial and spatio-temporal models with the integrated nested Laplace approximation (INLA) and the stochastic partial differential equation (SPDE) approaches, Creating interactive and static visualizations such as disease maps and time plots, Reproducible R Markdown reports, interactive dashboards, and Shiny web applications that facilitate the communication of insights to collaborators and policymakers. The book features fully reproducible examples of several disease and environmental applications using real-world data such as malaria in The Gambia, cancer in Scotland and USA, and air pollution in Spain. Examples in the book focus on health applications, but the approaches covered are also applicable to other fields that use georeferenced data including epidemiology, ecology, demography or criminology. The book provides clear descriptions of the R code for data importing, manipulation, modelling, and visualization, as well as the interpretation of the results. This ensures contents are fully reproducible and accessible for students, researchers and practitioners.
Categories: Medical

# Statistics for Spatio Temporal Data

Let {Y(s;t): s ∈ Ds ,t ∈ Dt} denote a spatio-temporal random process that is a
statistical model for a phenomenon ... at time t and at geographical coordinates s
= (latitude, longitude, height); conceptually, Ds = sphere × R and Dt = R. Or, Y(s;t)
...

Author: Noel Cressie

Publisher: John Wiley & Sons

ISBN: 9780471692744

Category: Mathematics

Page: 588

View: 238

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.
Categories: Mathematics

# Advanced Spatial Modeling with Stochastic Partial Differential Equations Using R and INLA

This book has been authored by leading experts in spatial statistics, including the main developers of the INLA and SPDE methodologies and the R-INLA package.

Author: Elias T. Krainski

Publisher: CRC Press

ISBN: 9780429629853

Category: Mathematics

Page: 284

View: 326

Modeling spatial and spatio-temporal continuous processes is an important and challenging problem in spatial statistics. Advanced Spatial Modeling with Stochastic Partial Differential Equations Using R and INLA describes in detail the stochastic partial differential equations (SPDE) approach for modeling continuous spatial processes with a Matérn covariance, which has been implemented using the integrated nested Laplace approximation (INLA) in the R-INLA package. Key concepts about modeling spatial processes and the SPDE approach are explained with examples using simulated data and real applications. This book has been authored by leading experts in spatial statistics, including the main developers of the INLA and SPDE methodologies and the R-INLA package. It also includes a wide range of applications: * Spatial and spatio-temporal models for continuous outcomes * Analysis of spatial and spatio-temporal point patterns * Coregionalization spatial and spatio-temporal models * Measurement error spatial models * Modeling preferential sampling * Spatial and spatio-temporal models with physical barriers * Survival analysis with spatial effects * Dynamic space-time regression * Spatial and spatio-temporal models for extremes * Hurdle models with spatial effects * Penalized Complexity priors for spatial models All the examples in the book are fully reproducible. Further information about this book, as well as the R code and datasets used, is available from the book website at http://www.r-inla.org/spde-book. The tools described in this book will be useful to researchers in many fields such as biostatistics, spatial statistics, environmental sciences, epidemiology, ecology and others. Graduate and Ph.D. students will also find this book and associated files a valuable resource to learn INLA and the SPDE approach for spatial modeling.
Categories: Mathematics

# Displaying Time Series Spatial and Space Time Data with R

(Cressie and Wikle 2011) is a systematic approach to key quantitative techniques
on statistics for spatiotemporal data. ... of temporal data and spatial data, and
later combines these concepts to discuss spatiotemporal statistical methods.

Author: Oscar Perpinan Lamigueiro

Publisher: CRC Press

ISBN: 9781466565203

Category: Mathematics

Page: 208

View: 191

Code and Methods for Creating High-Quality Data Graphics A data graphic is not only a static image, but it also tells a story about the data. It activates cognitive processes that are able to detect patterns and discover information not readily available with the raw data. This is particularly true for time series, spatial, and space-time datasets. Focusing on the exploration of data with visual methods, Displaying Time Series, Spatial, and Space-Time Data with R presents methods and R code for producing high-quality graphics of time series, spatial, and space-time data. Practical examples using real-world datasets help you understand how to apply the methods and code. The book illustrates how to display a dataset starting with an easy and direct approach and progressively adding improvements that involve more complexity. Each of the book’s three parts is devoted to different types of data. In each part, the chapters are grouped according to the various visualization methods or data characteristics. Web Resource Along with the main graphics from the text, the author’s website offers access to the datasets used in the examples as well as the full R code. This combination of freely available code and data enables you to practice with the methods and modify the code to suit your own needs.
Categories: Mathematics

# Spatial Statistics and Spatio Temporal Data

The correlation .k/ appearing in the test statistic is estimated by the empirical
average over estimates of ij .k/, where ij .k/, at lag k D .h ... Consider a multivariate
spatio-temporal random field, Z.s;t/, under a LMC of order r defined by Equation
9.9.

Author: Michael Sherman

Publisher: John Wiley & Sons

ISBN: 0470974923

Category: Mathematics

Page: 240

View: 240

In the spatial or spatio-temporal context, specifying the correct covariance function is fundamental to obtain efficient predictions, and to understand the underlying physical process of interest. This book focuses on covariance and variogram functions, their role in prediction, and appropriate choice of these functions in applications. Both recent and more established methods are illustrated to assess many common assumptions on these functions, such as, isotropy, separability, symmetry, and intrinsic correlation. After an extensive introduction to spatial methodology, the book details the effects of common covariance assumptions and addresses methods to assess the appropriateness of such assumptions for various data structures. Key features: An extensive introduction to spatial methodology including a survey of spatial covariance functions and their use in spatial prediction (kriging) is given. Explores methodology for assessing the appropriateness of assumptions on covariance functions in the spatial, spatio-temporal, multivariate spatial, and point pattern settings. Provides illustrations of all methods based on data and simulation experiments to demonstrate all methodology and guide to proper usage of all methods. Presents a brief survey of spatial and spatio-temporal models, highlighting the Gaussian case and the binary data setting, along with the different methodologies for estimation and model fitting for these two data structures. Discusses models that allow for anisotropic and nonseparable behaviour in covariance functions in the spatial, spatio-temporal and multivariate settings. Gives an introduction to point pattern models, including testing for randomness, and fitting regular and clustered point patterns. The importance and assessment of isotropy of point patterns is detailed. Statisticians, researchers, and data analysts working with spatial and space-time data will benefit from this book as well as will graduate students with a background in basic statistics following courses in engineering, quantitative ecology or atmospheric science.
Categories: Mathematics

# Animal Movement

The book serves as a comprehensive reference for the types of statistical models used to study individual-based animal movement.

Author: Mevin B. Hooten

Publisher: CRC Press

ISBN: 9781466582156

Category: Mathematics

Page: 306

View: 315

The study of animal movement has always been a key element in ecological science, because it is inherently linked to critical processes that scale from individuals to populations and communities to ecosystems. Rapid improvements in biotelemetry data collection and processing technology have given rise to a variety of statistical methods for characterizing animal movement. The book serves as a comprehensive reference for the types of statistical models used to study individual-based animal movement. Animal Movement is an essential reference for wildlife biologists, quantitative ecologists, and statisticians who seek a deeper understanding of modern animal movement models. A wide variety of modeling approaches are reconciled in the book using a consistent notation. Models are organized into groups based on how they treat the underlying spatio-temporal process of movement. Connections among approaches are highlighted to allow the reader to form a broader view of animal movement analysis and its associations with traditional spatial and temporal statistical modeling. After an initial overview examining the role that animal movement plays in ecology, a primer on spatial and temporal statistics provides a solid foundation for the remainder of the book. Each subsequent chapter outlines a fundamental type of statistical model utilized in the contemporary analysis of telemetry data for animal movement inference. Descriptions begin with basic traditional forms and sequentially build up to general classes of models in each category. Important background and technical details for each class of model are provided, including spatial point process models, discrete-time dynamic models, and continuous-time stochastic process models. The book also covers the essential elements for how to accommodate multiple sources of uncertainty, such as location error and latent behavior states. In addition to thorough descriptions of animal movement models, differences and connections are also emphasized to provide a broader perspective of approaches.
Categories: Mathematics

# Spatio Temporal Heterogeneity

2. r ... In this chapter, purely spatial and purely temporal stochastic processes are
discussed as particular cases of spatio-temporal stochastic processes. ...
Recommended readings in spatial and temporal statistics are given in Section
2.6.

Author: Pierre Dutilleul

Publisher: Cambridge University Press

ISBN: 9780521791274

Category: Nature

Page: 393

View: 622

Our living environment continuously changes in space and time. This book explains how to capture and assess these changes through the relevant statistical framework. It is a useful guide to students, teachers and researchers in the fields of biology, ecology and environmental science. Codes on the accompanying CD-ROM aid analyses.
Categories: Nature

# Modern Spatiotemporal Geostatistics

An isotropic covariance model c 3(r, T) was chosen, where r = |s — s' | is the
spatial lag and 7' = It — t'| is the time lag. The estimated values of the covariance
are shown in Figure 8.7 as functions of the spatial and temporal lags.

Author: George Christakos

Publisher: Courier Corporation

ISBN: 9780486310930

Category: Science

Page: 304

View: 577

This scholarly introductory treatment explores the fundamentals of modern geostatistics, viewing them as the product of the advancement of the epistemic status of stochastic data analysis. The book's main focus is the Bayesian maximum entropy approach for studying spatiotemporal distributions of natural variables, an approach that offers readers a deeper understanding of the role of geostatistics in improved mathematical models of scientific mapping. Starting with a overview of the uses of spatiotemporal mapping in the natural sciences, the text explores spatiotemporal geometry, the epistemic paradigm, the mathematical formulation of the Bayesian maximum entropy method, and analytical expressions of the posterior operator. Additional topics include uncertainty assessment, single- and multi-point analytical formulations, and popular methods. An innovative contribution to the field of space and time analysis, this volume offers many potential applications in epidemiology, geography, biology, and other fields.
Categories: Science

# Spatiotemporal Data Analysis

How do we study the storm's mutation into a deadly twister? Avian flu cases are reported in China.

Author: Gidon Eshel

Publisher: Princeton University Press

ISBN: 9780691128917

Category: Mathematics

Page: 317

View: 284

A severe thunderstorm morphs into a tornado that cuts a swath of destruction through Oklahoma. How do we study the storm's mutation into a deadly twister? Avian flu cases are reported in China. How do we characterize the spread of the flu, potentially preventing an epidemic? The way to answer important questions like these is to analyze the spatial and temporal characteristics--origin, rates, and frequencies--of these phenomena. This comprehensive text introduces advanced undergraduate students, graduate students, and researchers to the statistical and algebraic methods used to analyze spatiotemporal data in a range of fields, including climate science, geophysics, ecology, astrophysics, and medicine. Gidon Eshel begins with a concise yet detailed primer on linear algebra, providing readers with the mathematical foundations needed for data analysis. He then fully explains the theory and methods for analyzing spatiotemporal data, guiding readers from the basics to the most advanced applications. This self-contained, practical guide to the analysis of multidimensional data sets features a wealth of real-world examples as well as sample homework exercises and suggested exams.
Categories: Mathematics

# Spatial and temporal statistics

sampling field soils and their vegetation Donald R. Nielsen, Ole Wendroth ... than
that of temporal variance (Heuvelink and Webster, 2001), only a few attempts
have been made regarding spatio-temporal description of soil and crop
processes.

Author: Donald R. Nielsen

Publisher: Catena-Geoscience-Publications

ISBN: UOM:39015060076646

Category: Mathematics

Page: 398

View: 226

Categories: Mathematics

# Spatio temporal Design

1Department of Applied Statistics, Johannes Kepler University Linz, Austria
2Faculty of Science, University of ... Efficient data acquisition as introduced in
Chapter 1 requires some prior understanding of the process to be observed,
ideally in the form of a spatio-temporal model or at ... The data are analyzed
using the statistical software R which provides a wide range of packages and
functions to work on ...

Author: Jorge Mateu

Publisher: John Wiley & Sons

ISBN: 9781118441886

Category: Mathematics

Page: 382

View: 622

A state-of-the-art presentation of optimum spatio-temporalsampling design - bridging classic ideas with modern statisticalmodeling concepts and the latest computational methods. Spatio-temporal Design presents a comprehensivestate-of-the-art presentation combining both classical and moderntreatments of network design and planning for spatial andspatio-temporal data acquisition. A common problem set isinterwoven throughout the chapters, providing various perspectivesto illustrate a complete insight to the problem at hand. Motivated by the high demand for statistical analysis of datathat takes spatial and spatio-temporal information into account,this book incorporates ideas from the areas of time series, spatialstatistics and stochastic processes, and combines them to discussoptimum spatio-temporal sampling design. Spatio-temporal Design: Advances in Efficient DataAcquisition: Provides an up-to-date account of how to collect space-timedata for monitoring, with a focus on statistical aspects and thelatest computational methods Discusses basic methods and distinguishes between design andmodel-based approaches to collecting space-time data. Features model-based frequentist design for univariate andmultivariate geostatistics, and second-phase spatial sampling. Integrates common data examples and case studies throughout thebook in order to demonstrate the different approaches and theirintegration. Includes real data sets, data generating mechanisms andsimulation scenarios. Accompanied by a supporting website featuring R code. Spatio-temporal Design presents an excellent book forgraduate level students as well as a valuable reference forresearchers and practitioners in the fields of applied mathematics,engineering, and the environmental and health sciences.
Categories: Mathematics

# Journal f r die reine und angewandte Mathematik

Author:

Publisher:

ISBN: BSB:BSB10525480

Category:

Page:

View: 915

Categories:

# Modeling Techniques in Predictive Analytics with Python and R

Statistics for Spatial Data (revised ed.). New York: Wiley. 299 Cressie, N. and
C. K. Wikle 2011. Statistics for Spatio-Temporal Data. New York: Wiley. Cristianini
, N. and J. Shawe-Taylor 2000. An Introduction to Support Vector Machines and ...

Author: Thomas W. Miller

Publisher: FT Press

ISBN: 9780133892147

Category: Computers

Page: 448

View: 194

Categories: Computers

# Bringing Bayesian Models to Life

Our code shows how to create every result and figure in the book so that readers can use and modify it for their own analyses. We provide all code and data in an organized set of directories available at the authors' websites.

Author: Mevin B. Hooten

Publisher: CRC Press

ISBN: 9780429516801

Category: Mathematics

Page: 574

View: 475

Bringing Bayesian Models to Life empowers the reader to extend, enhance, and implement statistical models for ecological and environmental data analysis. We open the black box and show the reader how to connect modern statistical models to computer algorithms. These algorithms allow the user to fit models that answer their scientific questions without needing to rely on automated Bayesian software. We show how to handcraft statistical models that are useful in ecological and environmental science including: linear and generalized linear models, spatial and time series models, occupancy and capture-recapture models, animal movement models, spatio-temporal models, and integrated population-models. Features: R code implementing algorithms to fit Bayesian models using real and simulated data examples. A comprehensive review of statistical models commonly used in ecological and environmental science. Overview of Bayesian computational methods such as importance sampling, MCMC, and HMC. Derivations of the necessary components to construct statistical algorithms from scratch. Bringing Bayesian Models to Life contains a comprehensive treatment of models and associated algorithms for fitting the models to data. We provide detailed and annotated R code in each chapter and apply it to fit each model we present to either real or simulated data for instructional purposes. Our code shows how to create every result and figure in the book so that readers can use and modify it for their own analyses. We provide all code and data in an organized set of directories available at the authors' websites.
Categories: Mathematics

# Handbook of Spatial Statistics

Time can be considered an additional coordinate and, thus, from a probabilistic
point of view, any spatio-temporal process can be considered a process on Rd+1
= Rd×R. In particular, all technical results on spatial covariance functions ...

Author: Alan E. Gelfand

Publisher: CRC Press

ISBN: 1420072889

Category: Mathematics

Page: 619

View: 948

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 introduction detailing the evolution of the field. It then focuses on the three main branches of spatial statistics: continuous spatial variation (point referenced data); discrete spatial variation, including lattice and areal unit data; and spatial point patterns. The book also contains a section on space–time work as well as a section on important topics that build upon earlier chapters. By collecting the major work in the field in one source, along with including an extensive bibliography, this handbook will assist future research efforts. It deftly balances theory and application, strongly emphasizes modeling, and introduces many real data analysis examples.
Categories: Mathematics