Covariance Modeling and Parameter Estimation for Stationary Spatio-temporal Gaussian Random Fields
Author: Benjamin Adam Shaby
Publisher:
Published: 2007
Total Pages: 204
ISBN-13:
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Spatial Statistics and Spatio-Temporal Data
Author: Michael Sherman
Publisher: John Wiley & Sons
Published: 2011-01-06
Total Pages: 190
ISBN-13: 0470974923
DOWNLOAD EBOOKIn 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.
Spatio-temporal Design
Author: Jorge Mateu
Publisher: John Wiley & Sons
Published: 2012-11-05
Total Pages: 320
ISBN-13: 1118441885
DOWNLOAD EBOOKA state-of-the-art presentation of optimum spatio-temporal sampling design - bridging classic ideas with modern statistical modeling concepts and the latest computational methods. Spatio-temporal Design presents a comprehensive state-of-the-art presentation combining both classical and modern treatments of network design and planning for spatial and spatio-temporal data acquisition. A common problem set is interwoven throughout the chapters, providing various perspectives to illustrate a complete insight to the problem at hand. Motivated by the high demand for statistical analysis of data that takes spatial and spatio-temporal information into account, this book incorporates ideas from the areas of time series, spatial statistics and stochastic processes, and combines them to discuss optimum spatio-temporal sampling design. Spatio-temporal Design: Advances in Efficient Data Acquisition: Provides an up-to-date account of how to collect space-time data for monitoring, with a focus on statistical aspects and the latest computational methods Discusses basic methods and distinguishes between design and model-based approaches to collecting space-time data. Features model-based frequentist design for univariate and multivariate geostatistics, and second-phase spatial sampling. Integrates common data examples and case studies throughout the book in order to demonstrate the different approaches and their integration. Includes real data sets, data generating mechanisms and simulation scenarios. Accompanied by a supporting website featuring R code. Spatio-temporal Design presents an excellent book for graduate level students as well as a valuable reference for researchers and practitioners in the fields of applied mathematics, engineering, and the environmental and health sciences.
Statistical Methods for Spatial Data Analysis
Author: Oliver Schabenberger
Publisher: CRC Press
Published: 2017-01-27
Total Pages: 444
ISBN-13: 1351991477
DOWNLOAD EBOOKUnderstanding spatial statistics requires tools from applied and mathematical statistics, linear model theory, regression, time series, and stochastic processes. It also requires a mindset that focuses on the unique characteristics of spatial data and the development of specialized analytical tools designed explicitly for spatial data analysis. Statistical Methods for Spatial Data Analysis answers the demand for a text that incorporates all of these factors by presenting a balanced exposition that explores both the theoretical foundations of the field of spatial statistics as well as practical methods for the analysis of spatial data. This book is a comprehensive and illustrative treatment of basic statistical theory and methods for spatial data analysis, employing a model-based and frequentist approach that emphasizes the spatial domain. It introduces essential tools and approaches including: measures of autocorrelation and their role in data analysis; the background and theoretical framework supporting random fields; the analysis of mapped spatial point patterns; estimation and modeling of the covariance function and semivariogram; a comprehensive treatment of spatial analysis in the spectral domain; and spatial prediction and kriging. The volume also delivers a thorough analysis of spatial regression, providing a detailed development of linear models with uncorrelated errors, linear models with spatially-correlated errors and generalized linear mixed models for spatial data. It succinctly discusses Bayesian hierarchical models and concludes with reviews on simulating random fields, non-stationary covariance, and spatio-temporal processes. Additional material on the CRC Press website supplements the content of this book. The site provides data sets used as examples in the text, software code that can be used to implement many of the principal methods described and illustrated, and updates to the text itself.
Random Fields on a Network
Author: Xavier Guyon
Publisher: Springer Science & Business Media
Published: 1995-06-23
Total Pages: 294
ISBN-13: 9780387944289
DOWNLOAD EBOOKThe theory of spatial models over lattices, or random fields as they are known, has developed significantly over recent years. This book provides a graduate-level introduction to the subject which assumes only a basic knowledge of probability and statistics, finite Markov chains, and the spectral theory of second-order processes. A particular strength of this book is its emphasis on examples - both to motivate the theory which is being developed, and to demonstrate the applications which range from statistical mechanics to image analysis and from statistics to stochastic algorithms.
Advanced Spatial Modeling with Stochastic Partial Differential Equations Using R and INLA
Author: Elias T. Krainski
Publisher: CRC Press
Published: 2018-12-07
Total Pages: 284
ISBN-13: 0429629850
DOWNLOAD EBOOKModeling 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.
A New Covariance Function and Spatio-Temporal Prediction (Kriging) for a Stationary Spatio-Temporal Random Process
Author: T. Subba Rao
Publisher:
Published: 2017
Total Pages: 0
ISBN-13:
DOWNLOAD EBOOKConsider a stationary spatio-temporal random process and let be a sample from the process. Our object here is to predict, given the sample, for all at the locations. To obtain the predictors, we define a sequence of discrete Fourier transforms using the observed time series. We consider these discrete Fourier transforms as a sample from the complex valued random variable. Assuming that the discrete Fourier transforms satisfy a complex stochastic partial differential equation of the Laplacian type with a scaling function that is a polynomial in the temporal spectral frequency, we obtain, in a closed form, expressions for the second-order spatio-temporal spectrum and the covariance function. The spectral density function obtained corresponds to a non-separable random process. The optimal predictor of the discrete Fourier transform is in terms of the covariance functions. The estimation of the parameters of the spatio-temporal covariance function is considered and is based on the recently introduced frequency variogram method. The methods given here can be extended to situations where the observations are corrupted by independent white noise. The methods are illustrated with a real data set.
Spatiotemporal Random Fields
Author: George Christakos
Publisher: Elsevier
Published: 2017-07-26
Total Pages: 698
ISBN-13: 0128030321
DOWNLOAD EBOOKSpatiotemporal Random Fields: Theory and Applications, Second Edition, provides readers with a new and updated edition of the text that explores the application of spatiotemporal random field models to problems in ocean, earth, and atmospheric sciences, spatiotemporal statistics, and geostatistics, among others. The new edition features considerable detail of spatiotemporal random field theory, including ordinary and generalized models, as well as space-time homostationary, isostationary and hetrogeneous approaches. Presenting new theoretical and applied results, with particular emphasis on space-time determination and interpretation, spatiotemporal analysis and modeling, random field geometry, random functionals, probability law, and covariance construction techniques, this book highlights the key role of space-time metrics, the physical interpretation of stochastic differential equations, higher-order space-time variability functions, the validity of major theoretical assumptions in real-world practice (covariance positive-definiteness, metric-adequacy etc.), and the emergence of interdisciplinary phenomena in conditions of multi-sourced real-world uncertainty. - Contains applications in the form of examples and case studies, providing readers with first-hand experiences - Presents an easy to follow narrative which progresses from simple concepts to more challenging ideas - Includes significant updates from the previous edition, including a focus on new theoretical and applied results
Modelling Longitudinal and Spatially Correlated Data
Author: Timothy G. Gregoire
Publisher: Springer Science & Business Media
Published: 2012-12-06
Total Pages: 404
ISBN-13: 1461206995
DOWNLOAD EBOOKCorrelated data arise in numerous contexts across a wide spectrum of subject-matter disciplines. Modeling such data present special challenges and opportunities that have received increasing scrutiny by the statistical community in recent years. In October 1996 a group of 210 statisticians and other scientists assembled on the small island of Nantucket, U. S. A. , to present and discuss new developments relating to Modelling Longitudinal and Spatially Correlated Data: Methods, Applications, and Future Direc tions. Its purpose was to provide a cross-disciplinary forum to explore the commonalities and meaningful differences in the source and treatment of such data. This volume is a compilation of some of the important invited and volunteered presentations made during that conference. The three days and evenings of oral and displayed presentations were arranged into six broad thematic areas. The session themes, the invited speakers and the topics they addressed were as follows: • Generalized Linear Models: Peter McCullagh-"Residual Likelihood in Linear and Generalized Linear Models" • Longitudinal Data Analysis: Nan Laird-"Using the General Linear Mixed Model to Analyze Unbalanced Repeated Measures and Longi tudinal Data" • Spatio---Temporal Processes: David R. Brillinger-"Statistical Analy sis of the Tracks of Moving Particles" • Spatial Data Analysis: Noel A. Cressie-"Statistical Models for Lat tice Data" • Modelling Messy Data: Raymond J. Carroll-"Some Results on Gen eralized Linear Mixed Models with Measurement Error in Covariates" • Future Directions: Peter J.
Spatio–Temporal Methods in Environmental Epidemiology with R
Author: Gavin Shaddick
Publisher: CRC Press
Published: 2023-12-12
Total Pages: 458
ISBN-13: 1003808026
DOWNLOAD EBOOKSpatio-Temporal Methods in Environmental Epidemiology with R, like its First Edition, explores the interface between environmental epidemiology and spatio-temporal modeling. It links recent developments in spatio-temporal theory with epidemiological applications. Drawing on real-life problems, it shows how recent advances in methodology can assess the health risks associated with environmental hazards. The book's clear guidelines enable the implementation of the methodology and estimation of risks in practice. New additions to the Second Edition include: a thorough exploration of the underlying concepts behind knowledge discovery through data; a new chapter on extracting information from data using R and the tidyverse; additional material on methods for Bayesian computation, including the use of NIMBLE and Stan; new methods for performing spatio-temporal analysis and an updated chapter containing further topics. Throughout the book there are new examples, and the presentation of R code for examples has been extended. Along with these additions, the book now has a GitHub site (https://spacetime-environ.github.io/stepi2) that contains data, code and further worked examples. Features: • Explores the interface between environmental epidemiology and spatio-temporal modeling • Incorporates examples that show how spatio-temporal methodology can inform societal concerns about the effects of environmental hazards on health • Uses a Bayesian foundation on which to build an integrated approach to spatio-temporal modeling and environmental epidemiology • Discusses data analysis and topics such as data visualization, mapping, wrangling and analysis • Shows how to design networks for monitoring hazardous environmental processes and the ill effects of preferential sampling • Through the listing and application of code, shows the power of R, tidyverse, NIMBLE and Stan and other modern tools in performing complex data analysis and modeling Representing a continuing important direction in environmental epidemiology, this book – in full color throughout – underscores the increasing need to consider dependencies in both space and time when modeling epidemiological data. Readers will learn how to identify and model patterns in spatio-temporal data and how to exploit dependencies over space and time to reduce bias and inefficiency when estimating risks to health.
