Gaussian Markov Random Fields

Gaussian Markov Random Fields

Author: Havard Rue

Publisher: CRC Press

Published: 2005-02-18

Total Pages: 280

ISBN-13: 0203492021

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Gaussian Markov Random Field (GMRF) models are most widely used in spatial statistics - a very active area of research in which few up-to-date reference works are available. This is the first book on the subject that provides a unified framework of GMRFs with particular emphasis on the computational aspects. This book includes extensive case-studie


Spatio-Temporal Models for Ecologists

Spatio-Temporal Models for Ecologists

Author: James Thorson

Publisher: CRC Press

Published: 2024-02-27

Total Pages: 294

ISBN-13: 1003851835

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Ecological dynamics are tremendously complicated and are studied at a variety of spatial and temporal scales. Ecologists often simplify analysis by describing changes in density of individuals across a landscape, and statistical methods are advancing rapidly for studying spatio-temporal dynamics. However, spatio-temporal statistics is often presented using a set of principles that may seem very distant from ecological theory or practice. This book seeks to introduce a minimal set of principles and numerical techniques for spatio-temporal statistics that can be used to implement a wide range of real-world ecological analyses regarding animal movement, population dynamics, community composition, causal attribution, and spatial dynamics. We provide a step-by-step illustration of techniques that combine core spatial-analysis packages in R with low-level computation using Template Model Builder. Techniques are showcased using real-world data from varied ecological systems, providing a toolset for hierarchical modelling of spatio-temporal processes. Spatio-Temporal Models for Ecologists is meant for graduate level students, alongside applied and academic ecologists. Key Features: Foundational ecological principles and analyses Thoughtful and thorough ecological examples Analyses conducted using a minimal toolbox and fast computation Code using R and TMB included in the book and available online


Spatio-temporal Design

Spatio-temporal Design

Author: Jorge Mateu

Publisher: John Wiley & Sons

Published: 2012-11-05

Total Pages: 320

ISBN-13: 1118441885

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A 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.


Statistics for Spatio-Temporal Data

Statistics for Spatio-Temporal Data

Author: Noel Cressie

Publisher: John Wiley & Sons

Published: 2011-04-12

Total Pages: 611

ISBN-13: 0471692743

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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.


Spectral-Spatial Classification of Hyperspectral Remote Sensing Images

Spectral-Spatial Classification of Hyperspectral Remote Sensing Images

Author: Jon Atli Benediktsson

Publisher: Artech House

Published: 2015-09-01

Total Pages: 277

ISBN-13: 1608078132

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This comprehensive new resource brings you up to date on recent developments in the classification of hyperspectral images using both spectral and spatial information, including advanced statistical approaches and methods. The inclusion of spatial information to traditional approaches for hyperspectral classification has been one of the most active and relevant innovative lines of research in remote sensing during recent years. This book gives you insight into several important challenges when performing hyperspectral image classification related to the imbalance between high dimensionality and limited availability of training samples, or the presence of mixed pixels in the data. This book also shows you how to integrate spatial and spectral information in order to take advantage of the benefits that both sources of information provide.


Statistical Inference and Applications of a Spatial-temporal Markov Random Field

Statistical Inference and Applications of a Spatial-temporal Markov Random Field

Author: Zack Nadrich

Publisher:

Published: 2020

Total Pages: 51

ISBN-13:

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Markov random fields (MRF) form a broad class of stochastic models frequently applied to spatial data. A generalization of Markov chains, the MRF models capture spatial correlation by introducing dependence among data on the surface through a chosen neighborhood structure. We introduce a three-dimensional MRF with such neighborhoods that incorporate spatial patterns as well as the time dimension to create a spatio-temporal model. The proposed clique configuration forces spatial dependencies to evolve through time, reflecting dynamics of an observed process.Our statistical inference approach to the Markov Random field is likelihood based. The complex form of the joint distribution of observed spatially and longitudinally dependent data does not allow a closed form of the likelihood function. We show that the pseudolikelihood of this MRF model, as applied to Bernoulli data, can be conveniently expressed as logistic regression. The theory of maximum pseudolikelihood estimation shows that our resulting parameter estimates are consistent and asymptotically normal. As a case study, we use our Markov random field specification to model the dynamics and spread of wildfires. We show that the model can be used to detect wildfire spread and explain the direction and speed at which a wildfire is moving, as well as changes in their behavior in time and in space. We also apply the Markov random field as a generative model in simulations to develop accurate, timely, and probabilistic wildfire spread forecasts, to complement state-of-the-art physical models.


Handbook of Spatial Statistics

Handbook of Spatial Statistics

Author: Alan E. Gelfand

Publisher: CRC Press

Published: 2010-03-19

Total Pages: 622

ISBN-13: 1420072889

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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


Modeling Spatio-Temporal Data

Modeling Spatio-Temporal Data

Author: Marco A. R. Ferreira

Publisher:

Published: 2024-11-29

Total Pages: 0

ISBN-13: 9781032622095

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Several important topics in spatial and spatio-temporal statistics developed in the last 15 years have not received enough attention in textbooks. Aims to fill some of this gap by providing an overview of a variety of recently proposed approaches for the analysis of spatial and spatio-temporal datasets.